They Did It: Google Personalizes Search & It Is Not Evil - <AUTHOR> http://www.readwriteweb.com/archives/they_did_it_google_personalizes_search_it_is_not_e.php

<comment><USER2> _Just last week, I wrote that Google+ was going to mess up the Internet by turning Web search into a popularity contest._

Didn't google revolutionize search over a decade ago by doing exactly that?

<comment><AUTHOR> I see what you mean. But at that time, Google results weren't tied to personal identities, which had no clear definition yet, and that's what this whole Google+ project has been about.

</comment></comment><comment><USER3> This includes Google+ content but not GDocs/Gmail content? If Google wants to really personalize my search and discovery I want universal tags. Let me browse my content by tags across services. If I have 2 documents, 1 contact and 3 emails tagged (labeled) 'HN' I want to be able to go into gmail (or some other page) search label:HN and see all 6 'things'

<comment><USER4> Enable 'Apps Search' from here:

<https://mail.google.com/mail/u/0/?shva=1#settings/labs>

</comment></comment><comment><USER5> I thought that facebook would be the first to come out with personalized search. It is so interesting watching the Big Four poke and prod at each others moats. It will be watching to see how everything pans out in the next 10 years.

</comment><comment><USER6> He's basically saying he overstated his claims in the previous article by conflating current implementation with how things were going to be indefinitely.

As a writer and content-producer his whole notion of 'evil' seems to be tied to identity and attribution. Discussions on this page about privacy are independent of that. In fact there's two meanings of privacy even on this page: leaking your private data to your friends, and concerns about how much Google knows about you.

I wish we could talk about these three issues separately, skipping increasingly-content-free words like 'evil' and 'privacy'.

</comment><comment><USER7> Discussion on Google's announcement: <http://news.ycombinator.com/item?id=3447048>

</comment><comment><USER8> The technical definition of "do no evil" was that google search would not promote any single entity based on who they are, rather they would let algorithms and data govern the core ranking. This seems to be the first VIOLATION of this principle. A HACK has been inserted into the core search ranking where if the content belongs to google, it is being given a preferential treatment and higher score. Why should a photo on picasa be more highly ranked than one on flickr? Seems the ranking team is just taking a short-cut by only using the data on google's internal properties in the ranking.. Come on, crawl the rest of the web !! There is interesting content out there..

</comment><comment><USER9> "It is not evil".

Keep telling yourself that.

Google is selling you to the world, and this is just one more way to get you on their site and making money for them.

<comment><USER10> And? What's evil about advertising?

Seriously, I'm surprised to see this kind of comment ranked so highly on HN. Google makes products. Most of them are good, some of them are excellent. In exchange, they show you ads. The alternative is making the user pay. There's nothing wrong with this arrangement; it's the default monetization strategy for a huge number of companies.

The core of the argument seems to be that Google knows too much about you, and is selling your personal data to advertisers. That's not really the case, though. Google isn't going to ESPN and saying, "Here's John Smith from Deerborn, Michigan. He's 38, has a wife and a 4 year old daughter, and cheats on his taxes. Give me $50." They're simply allowing advertisers to target users fitting a certain profile. Now, you may not be comfortable with how much Google knows about you, and that's fine, but targeted advertising is hardly _evil_.

<comment><USER11> Totally agree. "You are the product" is such a reductive, partisan talking point that at this point it's actually a pretty good filter for intellectual honesty and critical thinking.

I wrote a whole blog post about it here: [http://blog.byjoemoon.com/post/9910020865/you-are-the- produc...](http://blog.byjoemoon.com/post/9910020865/you-are-the-product)

</comment></comment></comment><comment><USER12> Might this be a trojan horse? This feels like what Facebook does... they announce a feature which raises public concerns about privacy, then they play it down a bit on the first release and then proceed to push it as originally planned on a subsequent iteration.

<comment><AUTHOR> Well, if you read my post last week, you know I'd be the last person to let them off easily, but now that they've put this opt-out control in, they can't well take it way. That would be suicide.

<comment><USER12> It would be suicide to do it _now_. What about in some months, when everybody has forgot about the debate and most of the users are constantly logged on google+ and use the feature as their standard search? Again, Facebook does it all the time and manages to pull it off on a regular basis.

<comment><AUTHOR> I can't think of an example of Facebook taking away a _preference_ setting that users have adopted. Even Facebook doesn't take away controls it has freely given. It would be one thing to take away the toggle button. That might happen, and it would suck if it did. But to go in and pull out a user setting that people are using, that would be astonishing.

<comment><USER13> How about the ability to hide your friends list from people you aren't friends with?

<comment><AUTHOR> Oh, yeah, that's a good one. That was a long time ago.

</comment></comment></comment></comment></comment></comment><comment><USER14> Google search is great.

Everything else is done better by someone else.

<comment><USER15> OK, can you tell me better alternatives to gmail, youtube, gdocs?

<comment><USER16> ...and to Google Maps, Google News, Google Voice, Google Chrome...

</comment></comment></comment><comment><USER17> I reject your premise.

Further segregating the echo chamber of the internet is not a good thing.

<comment><AUTHOR> But here's the thing: this actually _lifts_ the lid on the echo chamber to be more open than it was yesterday. Google recognizes that global search is a necessary option. Before this update, it looked like G+ was just going to be rammed down every Google user's throat. Now we can opt out without having to log out!

<comment><USER18> I agree with you. Prior to this, the only way to get global search was to add &pws=0 to the URL. Now, it's a button. It's a big step forward, and not that I don't like the "bubble", it has its advantages (increased relevance). It's fantastic to be able to switch between the two modes at the click of a button, and it's something we didn't have before.

<comment><AUTHOR> It's not just a button, either. You can opt out entirely from preferences.</comment></comment></comment></comment>


Monads explained in Clojure by Brian Marick - <AUTHOR> https://vimeo.com/album/2206951/

<comment><AUTHOR> Note, this is a repost of <http://news.ycombinator.com/item?id=4992062> which went overlooked, but I added a vimeo album to link to all 4 videos.

</comment><comment><USER2> Great, glad you reposted this, I loved his introduction to the tutorial: "there is an ancient mayan profecy that someone every person on earth will do a turorial on Monads" :)</comment>


Beacon (YC W14) Offers A New Approach To Crowdfunding Journalism - <AUTHOR> http://techcrunch.com/2014/02/12/beacon-y-combinator-launch/

<comment><USER2> Obviously you're focusing on journalists now, but there are other groups of content creators who might be into your product; I see cartoonists and photographers are mentioned in the article. I wonder whether this model would be useful to young academics, too - especially those who are moving to careers outside of academia but might still like to conduct and share research. Publishing in academic journals is (supposed to be) a way to get your research out there, and peer review does matter. But academic journals don't pay their authors, and often have very limited audiences. It seems like Beacon could help solve those problems. Maybe another interested population for you in the future!

<comment><USER3> Yeah, I'd second your thoughts about academic contributors.

I know a few HCI grad students who are interested in sharing their work in more informal kinds of venues (I'm one of them). Sure, conference papers are nice, but almost no one reads them. A lot of research in our field would appeal to a more general audience.

<comment><USER4> Yes! I think it could work awesome for academia - particularly in a format where the value transaction is really transparent and well documented.

You could even imagine a time where citing sources actually trickles money back to them to reflect their value to a new study.

If you know grad students, I'd love to chat with them: firstname.lastname@example.com

</comment></comment></comment><comment><USER5> I've given a lot of though about current state of journalism and my conclusion was that the current model is wrong for two reasons 1\. conflict of interests 2\. lack of transparency

@1 There are two main sources of capital for journalists - government or companies that buy ads. The problem is when they can put pressure to not write of unjust acts that may conflict with their interests. The solution is to provide founding from large enough group of people when there is no dominant subgroup. Models has to be highly distributed to avoid bribing users[1]. There needs to be upper limit of funding e.g. 99$ or 10%[2] to dilute influence of a single user. Even better for a 5$ a month I can get credit which I can allocate.

@2 Log everything. Brutal transparency. That's the only way I can think of.

So you're going to make something people want, right? :) I want to be able to vote what is important for me. I want to post an issue and let other judge if it's worth investigating.

[1] I'm amazed how often pattern of distributed models occurs and works very well (Bitcoin, Git etc.). [2] That may have a similar effect as Twitter's 140 chars limit

<comment><USER4> Yep, you've kinda nailed it. We're moving towards that on Beacon. But right now our primary focus is on helping writers convert their existing readership into paying subscribers.

As the content offering as a whole becomes more robust, you'll start seeing more of the effects you're looking for.

It's really simple and old fashioned: You think certain information or perspectives are valuable, you pay for them.

We're just updating the underlying tech and user experience to modern times ;)

</comment></comment><comment><USER4> cofounder of Beacon here - would love to get grilled by the HN denizens and get feedback about what we're doing!

<comment><USER6> Do you plan on helping journalists distribute their content outside of the main Beacon site? I imagine some have their own following but others want to use the site to help gain readership on/off your platform.

<comment><USER4> Maybe in the future but the reality is that the last 10 years have been focused on distribution of content as the primary goal. We're focused on monetization, and helping creators make more money and delivering more value for readers who support them.</comment></comment></comment>


Omega: flexible, scalable schedulers for large compute clusters [pdf] - <AUTHOR> http://static.googleusercontent.com/media/research.google.com/en//pubs/archive/41684.pdf <comment><USER2> Is there a reason why they don't use AI?</comment>


Happy birthday Pi - <AUTHOR> http://www.abc.net.au/unleashed/44652.html

<comment><USER2> From the article: 'Oxford mathematician E.C. Titchmarsh wrote that: "It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know."'

I'm not much of a mathematician but I can at least relate.

<comment><USER3> I don't think Titchmarsh had fully thought that statement through. Would the concept "irrational" be interesting if it didn't have a practical use?

To illustrate: Pi, 6, and 86 are three elements of the dwwoelfel set. I think that even the most curious mathematician could tolerate not knowing that fact.

</comment></comment><comment><USER4> In addition, it's PI day in 10 days (3/14).

<comment><USER4> Today!</comment></comment>


Paul Graham: Why Y Combinator Replaces The Traditional Corporation - <AUTHOR> http://www.fastcompany.com/1818523/paul-graham-why-y-combinator-replaces-the-traditional-corporation <comment><USER2> Didn't Ronald Coase's theory of the firm predict this, right after the first world war?

(As transaction costs (search costs, costs to contract, costs to outsource, etc.) go down, optimal firm size goes down. In an efficient market for contracting, like IT, tiny startups turn into long-term profitable small- headcount companies (dropbox has, what, 70 people?). In inefficient markets, you end up with huge or state-owned companies, like in natural resource exploitation or the third world.)

<comment><USER3> I've been told Coase not only foresaw the present trend towards more, smaller companies but also figured out the underlying dynamics. But I admit I haven't actually gotten around to reading "The Nature of the Firm."

<comment><USER4> He also predicted the first Gulf War, the election of Obama and the Great Fire of London. Wait, wrong guy...

In all seriousness though, while the technology factors certainly enable some 'shrinkage' of the firm, human factors change less, which to me indicates that YC like agglomerations will not replace the corporation in many circumstances. In other words, it's easier to find people these days, but as contractors, are they really still going to slog it out for a company day in and day out for years? Most people out there are not like YC founders, would be my bet, and are reasonably happy with their 9/5 jobs, and with not having to hustle to find the next gig. On the positive side, these people will also retain the tacit knowledge inherent in many human activities, and provide a sense of continuity that a shifting network might have trouble fostering outside a small core. Apple, for instance, has 60,000+ employees, according to the web page - that's not what I'd consider a small core + network, even though they certainly outsource a lot. So... trend, yes, but fairly slow once the low- hanging fruit that tech can provide has been integrated.

The other big question I have in this vein is whether it will remain so cheap to create a company, or if it's an anomaly, and in the future more capital will be required for anything serious. My guess is that the long term _is_ towards cheaper, but who knows what may happen.

BTW, Wikipedia says it's just an article, and here's the summary for those interested:

<http://en.wikipedia.org/wiki/The_Nature_of_the_Firm>

<comment><USER2> There are definitely arguments against "everyone an independent contractor", but ending up with a bunch of 1-50 person sized companies instead of a much smaller number of 50k person companies seems very likely. This is a net win for everyone in that failure happens faster, thus allowing resources to be allocated more efficiently -- it also allows high performing individuals and teams to be accurately compensated for their success, vs. the strict seniority or internal-politics systems in larger organizations.

There's an argument for internal communications costs vs. external communications costs (Coase's thing) -- if it's more efficient to communicate within a trusted firm vs. between firms, you end up with huge firms. Things like tight-knit social networks outside of the firm (college alumni, things like YC, sites like hn, various ethnic diaspora in history, ...) would create some kind of hybrid, too, where a lot of interconnected small firms would work, so each firm could be smaller than otherwise. This would actually be interesting research for someone in economics or sociology -- I'd look at formal networks like YC and informal networks like casual coworking and web forums.)

<comment><USER4> Yes, I think it's an absolutely fascinating subject, and while I have some instincts, who knows which way it could go.

To have some predictive value, what other industries besides web companies that are super cheap and easy to start, might morph towards this kind of structure? Or, here's another one: this industry has long been dominated by giants: IBM, Microsoft, Google, and so on. Will we see the end of that?

(And just to be clear, I think what pg has done is fantastic, and he/them are quite praiseworthy, etc... I'm just pushing back a bit on the idea. I can't foresee doing business with PG or YC, so I have no interest in not calling it like I see it)

<comment><USER5> Not just our industry. You know that cornucopia of different brand names you see at the supermarket? They're all owned by like 5 giant corps.

I agree with Coase's reasoning and I'd like to agree with his prediction, but there are some empirical problems with it as of now.

</comment></comment></comment></comment></comment></comment><comment><USER6> This was an interesting point in the context of comparing YC to a large company:

 _Comparing himself to an air-traffic controller, Graham says much of his time is spend making introductions and helping the YC community solve problems within the network_

Most of the large companies I've worked with are missing somebody in the "air- traffic controller" role. It can be very difficult for individual employees to understand all the resources that are available within the company, or who they should contact with a particular question. YC might actually have an advantage in this area.

<comment><USER7> > _Most of the large companies I've worked with are missing somebody in the > "air-traffic controller" role._

I've worked for 3 large companies, and have had the opposite experience. The problem is that everyone is trying to be an air-traffic controller. So much so, that honest work is being avoided.

<comment><USER8> Deep corporate hierarchies encourage politics and associated power struggles. Part of moving up in that environment is to have others perceive you as an "air-traffic controller" of a segment of the company, a master of your domain. This sometimes results in people in "manager" roles with 1 or 2 direct reports, where the "manager" does no actual work, but spends inordinate amounts of time coordinating with other teams or politicking. Honest work avoided.

I'm not excusing that behaviour but if you've spent enough time at a big company, you'll see motivations for it.

Contrast that to pg's air-traffic controller role in the YC network, providing value to all the startup people he connects.

It will be interesting to see how well pg's positive influence scales as YC continues to grow.

</comment></comment></comment><comment><USER9> YC has nothing to do with replacing the traditional corporation. To do that YC companies would have to have sustainable business models and actually make a profit.

How many YC companies have ever made a real profit before being bought? How is the YC model sustainable without existing large corporations like Google or Yahoo or Linkedin waiting to buy out the startups?

YC is about grooming startups ready to be bought out in talent acquisitions after a period of rapid growth, not about creating sustainable businesses with viable products.

<comment><USER3> I remember people saying things like this in the first few years but it's surprising to encounter it now.

If people who think we're in the business of grooming startups for HR acquisitions stopped to do the math, they'd realize we'd be acting against our own interests if we focused on that. Essentially all the returns in startup investing (for us as for any investor) come from the big successes. Whereas we often make zero from early acquisitions.

<comment><USER10> Ok, I'll bite Mr. Corporation Replacer. Where does the long-term R&D investment come from?

Microsoft Research alone outspends Y Combinator by a factor of 50,000,000. And they're thinking 10+ years out. Money aside, their internal expertise and contact network far exceeds "the guy who made Django."

Kudos for what you've done, but when you start talking this way I feel obligated to point out that you're a grain of sand on the beach compared to the Fortune 50--or even CMU/Berkeley/MIT.

You're doing something totally different. Own it. Say what you're for, not what you're against. Say what you're building, not what you're killing.

The fact that people who interview you keep painting you into these corners means that the general public still doesn't understand what's going on with YC. Less hyperbole, more concise vision. Your essays often achieve this, your PR should too.

<comment><USER3> _Where does the long-term R &D investment come from?_

Mostly from the same place Microsoft's R&D budget comes from: the companies' own revenues.

<comment><USER4> But if they're small, lean companies, is there room for people to just go off and do random things with little eye to profits?

An example would be someone like Simon Peyton-Jones at Microsoft:

<http://research.microsoft.com/en-us/people/simonpj/>

Much of what he does may eventually filter down to the rest of the company, but there's a real risk that some of it won't, or that it'll be picked up by someone outside of Microsoft, etc...

How does that sort of thing work out with a number of small companies networked together?

<comment><USER3> I've seen some very small companies do things that would count as research projects in some places. E.g. Etherpad.

<comment><USER11> While Etherpad is somewhat research-y, it is a product. The difference between Etherpad and what SPJ does is about as big as between a mathematician working on car collision simulation and one working on abstract algebra.

</comment></comment></comment></comment></comment></comment></comment><comment><USER12> I'd like to add that I think and hope that the trend is for traditional corporations to keep getting replaced by a larger number of lean companies (where's it's possible). The larger the corporation (by total employee count) the less nimble they become. I think companies consisting of a small number of highly skilled individuals can focus on what they do best and work with other small companies on the work they need.

For example, traditional corporations I've worked for have had large HR departments. Now where I work (with 40 employees) we use another company to handle most of the HR functions. This allows us to focus on our core business model.

<comment><USER13> "The larger the corporation (by total employee count) the less nimble they become."

That's because of antiquated management structures. Look at Gore and Associates (makers of Goretex) for a modern corporate structure. Elements of a corporation should be almost completely independent and the only reason they are part of one entity is because of synergies and cooperation.

To give a toy example, McDonalds might grow and slaughter their own cows because they can better place them near their distribution facilities. Buying from a third party might create unnecessary overhead.

I'm sorta oversimplifying things, but I'd recommend reading

"Re-Creating the Corporation" by the late Russell Ackoff to appreciate why corporations exist (and why sometimes they shouldn't)

[http://www.amazon.com/Re-Creating-Corporation-Design- Organiz...](http://www.amazon.com/Re-Creating-Corporation-Design- Organizations-Century/dp/0195123875/ref=sr_1_1?ie=UTF8&qid=1329944656&sr=8-1)

<comment><USER14> In-n-Out Burgers does run their own butcher department. The company structure worked pretty well too, since the company did not stumble when a big chunk of the executive team and the CEO died in a plane crash. see [http://fora.tv/2009/07/14/In-N- Out_Burger_Stacy_Perman#Histo...](http://fora.tv/2009/07/14/In-N- Out_Burger_Stacy_Perman#History_of_Tragedy_Behind_Iconic_In-N- Out_Burger_Chain)

</comment></comment></comment><comment><USER15> "Graham is the cofounder of Y Combinator, the investment firm that plugs seed money ($18,000 on average) into early stage startups in exchange for mentorship and access to its ever-growing network of alumni."

Maybe I'm not understanding this right, but the phrase "in exchange for", seems like it should have read "in addition to". Can someone please clarify?

<comment><USER16> Maybe not the most clear sentence since it leaves out the equity part; it's conveying that it provides seed money plus mentorship/networking in exchange for a modest equity from the startup.

Could be better organized as: "... Y Combinator, the investment firm that plugs seed money (~$18,800) into early stage startups and offers mentorship and access to its ever-growing network of alumni, _in exchange_ for a modest equity (~7%) of the startup."

<comment><USER15> Aha! Thanks for the explanation. Now I get it.

</comment></comment></comment><comment><USER17> Being part of community of talented people is a great thing. In addition to having a large pool of people to ask for help though, I think a great benefit is that YC companies help each other out without being directly asked. For example, other YC companies might try to make a conscious effort to use Hipmunk to buy flights, or Airbnb.

In addition to trying to use each others' services, YC companies will probably often give each other feedback about what could be improved about each other's services.

Compare this to the alternative of trying to launch a new service, gain customers, and get feedback on your own.

</comment><comment><USER18> I wouldn't bet against the underlying trend (keiretsu collectives of innovative, smaller companies outcompeting traditional corporations), but Y Combinator is the wrong posterchild for this movement, for a couple of reasons:

1\. Y Combinator's success criteria for its startups involves a liquidity event - there's no mention of a company staying privately owned and profitable as being a successful outcome (<http://ycombinator.com/about.html>). This is unsurpising given that pg himself exited to Yahoo

2\. To date, YC liquidity events have all been sales to medium-to-large companies (<http://yclist.com/>). There may be a couple of big IPOs on the horizon, which is great, but the general trend is for Y Combinator-funded startups to be acquired by big corporations, which boosts those large companies' competitiveness and innovation capability

So I would certainly say that Y Combinator's structure is unusual and admirable - but de facto it acts much more like a pilot fish for traditional corporations (creating some kind of new, syncretic innovation model for them), rather than as a replacement for them.

Do I think a r/evolution of the Y Combinator model could replace the traditional corporation? Certainly, but this will be done by "slowcubators" rather than by traditional incubators. A slowcubator looks like this:

1\. No expectation of a liquidity event in the child companies. It's expected instead for the child companies to become self-sustaining, profitable businesses a la GitHub or Plenty of Fish

2\. Significant shared tech IP - this is something a Y Combinator can't do, because shared tech IP makes it impossible to acquire a startup. But it makes huge sense for a slowcubator, because a) acquisitions are the exception, not the norm, and b) there are huge cost savings to be made by sharing tech IP across properties (think private PAAS, Chef recipes, AdWords automation tools etc). Joltid is the posterchild of shared tech IP driving multiple successful startups

3\. Staff incentives which are not structured around focusing 100% on one product until it exits or dies, but instead encourage staff to rotate within the slowcubator's companies to where they are currently needed most. It's great that the Django creator can answer a YCfounder's questions over some beer and pizza, but in a slowcubator he would be hands-on helping multiple products to be as good as they can be (as DHH does at 37signals)

In the same way that the startup acquisitions of the past decade shaped the incubator model that we see today (and is exemplified by YC), I fully expect the bootstrapped successes that we are seeing today to give rise to a wave of slowcubators - the best of which will indeed rival (if not replace) the big corporation.

<comment><USER3> _the general trend is for Y Combinator-funded startups to be acquired by big corporations_

This is the mistake. It's the general trend only by number of companies, not by valuation or number of people. Measured by valuation, the majority of our portfolio is not interested in being acquired.

<comment><USER18> So does that mean that you've done a survey of all the companies in your portfolio, and classified them by whether they are interested in IPO or acquisition (or no liquidity event at all)? And then have you attached a current valuation to each of these companies - what's that valuation based on in the absence of a liquidity event?

Can you share the % splits? Would be a really interesting (and yet still anonymous) snapshot of the portfolio companies' intents in the aggregate...

<comment><USER3> Dropbox and Airbnb alone account for more than half the value of companies we've funded, based on the valuations of their last rounds.

</comment></comment></comment></comment><comment><USER19> The description given reminds me somewhat of Keiretsu, the successors of the old Zaibatsu. The Keiretsu are families of companies interlocked through personal relationships between executives, mutual interlocking share holdings and secondment of workers -- tied together around a bank or finance company.

I believe KPCB were referred to as a Keiretsu for encouraging their portfolio to buy from each other -- eg, getting Netscape to buy servers from Sun etc.

<comment><USER7> > _I believe KPCB were referred to as a Keiretsu_

There was a time when it was fashionable to imitate Japanese business, so VCs actively pursued this type of PR. So it's more likely that KPCB issued PR about itself calling itself a Keiretsu, having the added benefit of seeming much larger than they are. (The Keiretsu were large conglomerations.)

Now, not so much of that PR is being created.

EDIT: I thought I remembered them self-referencing keiretsu. This is from 2001, look at the bottom:

<http://web.archive.org/web/200012122131/http://www.kpcb.com/>?

Arrogance was a strong suit. Last I knew, IRRs from funds in that timeframe were negative _and that included Google!_.

<comment><USER19> Interesting point. I was a kid in the 80s, but I certainly remember the mild hysteria about needing to be More Like The Japanese.

</comment></comment></comment><comment><USER20> Maybe I don't know what it's like to be a YC founder, but couldn't you say the exact same thing about just being in San Francisco?

What's more, the SF network extends to people who are not just in startups, but also established companies, universities, and even unrelated things (like the Because We Can people, who are making a business out of custom CNC products.)

Or do YC people collaborate more closely than that? Give up their time more freely to a fellow YC'er?

<comment><USER21> I feel a personal obligation to meet with any YC company that wants to meet with me, the same way I would if a good friend asked me to meet with someone. I've taken enough from that network that I want to give back.

If someone cold-emails me, or has a mutual acquantance do an introduction, I usually don't feel as obliged.

<comment><USER20> But I'm not talking about cold-emailing -- I'm talking about personal relationships. They just aren't defined by having the same seed funder.

When I walk down the street in SOMA or the Mission, I too am likely to run into a developer that I know. And I'm not even a very social person. But I've been around the Valley & SF for almost six years now.

Maybe YC gets you off the ground faster, maybe you get that in year one. Still, I hope you are also reaching out to make connections with non-YCers.

</comment></comment></comment><comment><USER22> Coworking communities around the world are having a very similar effect.

</comment><comment><USER23> I like the idea of replacing traditional corporations, and YC is certainly good at what they do, but how much of this success is just a result of internet startups having no physical products?

I'd like to see more places like Incubation Station come about - <http://www.theincubationstation.com> \- or hear about similar incubators for consumer products if anyone knows any.</comment>


Technical Counsel for CEOs and CTOs - <AUTHOR> https://www.boltsource.io <comment><AUTHOR> We help your engineering org work smarter and sleep better.</comment>


The New Yorker Reveals Five Uncomfortable Truths About U.S. And Russia - <AUTHOR> https://theintercept.com/2017/02/28/the-new-yorkers-big-cover-story-reveals-five-uncomfortable-truths-about-u-s-and-russia/ <comment><USER2> This isn't very compelling or even really coherent:

1\. Obama and Clinton disagreed on Russia, with Clinton being the more hawkish of the two, but maybe they don't anymore.

2\. It would be bad if there was another Cold War.

3\. It's likely we interfere in their politics too.

4\. The authors are unsatisfied with the evidence behind the DNC hack Russia attribution.

5\. Russia is a distraction from other problems.

Even if you accept all the authors premises, what does this add up to?

<comment><USER3> > _Even if you accept all the authors premises, what does this add up to?_

That both sides engage in jingoism?

(The article in New Yorker is a tiring and annoying read. I may not always like Greenwald's rhetoric but in this case, he correctly highlights the lack of evidence. In an age of rumours and unfounded - but indeed plausible - accusations, the referenced piece seemingly lacks sense of irony.)

<comment><USER4> It's interesting how the same article can support different opinions just because of context. The points which Greenwald - a serious professional, to say the least - makes may look just strange enough to suspect that each one of them is left unfinished, and questions regarding them unanswered - and so the whole impression is - not there. For example, lack of evidence - as soon as you think you have one, you're left to wonder what to do with that piece of evidence, if the proposition of the article relies on the absence of something in which you aren't sure.

</comment></comment></comment><comment><USER5> DiabloD3: What's the typical reaction when you share Intercept posts with people?

Most of Greenwald's stuff has the ring of truth to it, but you'd never guess that from the way people react. Not agreement, not disagreement, but more like when someone just politely keeps talking after you've farted audibly.

Do you get the same reaction?

<comment><AUTHOR> I don't really read Greenwald. I just share articles on here that I think the SV community on here would find interesting, and certainly do affect them and their ability to do business.

Disclaimer: I do not support any political candidate that is too far off the edges of the map, ie, both Clinton and Trump were bad picks if you're pro- SV... and Trump has already proved that in the scant time he's been in the White House.

</comment></comment><comment><USER6> > _its lead cartoon dystopically depicting a UFO-like Red Square hovering over > and phallically invading the White House_

I'm sorry, what? Am I the only one who thought it was a clear nod to _Independence Day_?

</comment><comment><USER7> Wow. Journalism.

</comment><comment><USER7> "This article challenges my beliefs, so I guess I'll flag it."

Pathetic.

<comment><USER8> I do a search almost every day for "US", "Trump", "Obama", etc. because I am curious about what Hacker News thinks about the US political situation, yet I know that these discussions will be flagged instantly before I see them on the front page. It's really unfortunate because Hacker News is probably the most intelligent moderately-large online community I've ever found, and I'd like to both learn from others and share my own knowledge on these topics. I appreciate the mods, but I don't like the throw-their-hands-up response that these threads always become uncivil. Some topics are so important that they need to be discussed regardless, and the denizens of Hacker News are not just bystanders to these issues but instead are the highly intelligent and influential builders of these apparatuses that underlie modern society and facilitate the abuses of governments.

</comment></comment><comment><USER9> pls stop posting political propaganda #fakenews to a hacker site</comment>


Show HN: Emburse – Employee Debit Cards with Oversight - <AUTHOR> https://www.emburse.com/ <comment><AUTHOR> Founder here - looking for feedback on the product. You can think of Emburse as being like AmEx with Expensify-like features built-in. If you're in the process of transitioning from having all spend on a shared corporate card to having cards for each department or employee, definitely take a look.

<comment><USER2> Best of luck.

Minor item: FAQ says that pricing will be available by end of 2015, which has just passed.

As for product feedback, I've literally never understood the appeal of debit cards over credit cards. I get cash back, delayed payments/free float, better anti-fraud, and better purchase protections with a credit card. So, I wish you the best of luck, but I don't "get it" unless there's a largish market that can't get (or can't handle) credit cards.

<comment><AUTHOR> For now, we're starting with a debit card product because they're easier to launch. Eventually, as the product gains more traction, it will be easier to launch a credit product with the advantages you're looking for.

Which that said, there's plenty of opportunity as a debit card product. We believe that no financial product right now really prioritizes spend control and bookkeeping accuracy in the way we do within our product.

</comment></comment></comment><comment><USER3> The concept piqued my interest but after reviewing the FAQ, I am a bit underwhelmed. The upside is that I get better oversight, the downside is that all expenses are on a prepaid cash only basis (since it's a prepaid card, I have to front the money well before the purchase is made). Purchasing card programs are not just about oversight, they are also about cash flow and trade credit optimization. It seems that the app only addresses oversight.

<comment><AUTHOR> For some companies such as those in manufacturing, enhanced oversight and better spend control are necessary card program requirements. I agree that business credit would add significant value. Thanks for the suggestion.

</comment></comment><comment><USER4> Love what Emburse is doing with company expenses.</comment>


WAT the WTF do programmers use as debug strings? - <AUTHOR> http://zachholman.com/posts/debug-strings/

<comment><USER2>
        "\x1B[1;36;40m" "\n" "\x1B[0;37;40m"

I keep a file sitting around with versions for different colors/languages.

<comment><USER3> Thank you for this idea! My worst days will now be in color from now on. :)

</comment></comment><comment><USER4> Really? I give location and context and the Why of the message. I make sure that every message is unique (unlike the code I changed in a certain once- prominent US firm's three-letter operating system) as well. I clearly know nothing and shouldn't be in the profession.

<comment><USER5> really? i think you might be mistaking exception logging for quick debug lines, like when a certain line isn't being hit for some reason and you just want to quickly know if it does hit. you would clearly delete these quick messages before checking in. No need to get so dramatic ...

<comment><USER4> Really. Identical error and debugging messages that might as well have all said "Foo!" across a 300,000+ LOC subsystem.

</comment></comment></comment><comment><USER6> In PHP I tend to do something like:

        dd(__DIR__.'/'.__FILE__.':'.__LINE__);

Which prints out the current script and line, and then stops execution (where dd is var_dump+exit).

</comment><comment><USER7> "this should never happen" and/or "how did you get here?"

</comment><comment><USER8> I use the ever eloquent, "yolo".

</comment><comment><USER9> herp, derp, flurp, and slurp are immensely useful words for one-off variables in an interactive interpreter.</comment>


Mathematics for the Adventurous Self-Learner - <AUTHOR> https://www.neilwithdata.com/mathematics-self-learner <comment><USER2> I know this is going to be the case for likely nobody, but I have browsed most of the self-study math threads that pop up here as a forever-on-my-todo-list thing and I have a remark to make:

 _I have yet to find a guide that does not start with the assumption that you graduated highschool._

That is a very reasonable assumption to make. We are in a community of technology and engineering, it would be a bit ridiculous to assume the people you are surrounded by did not have a fundamental base of mathematics.

But the times I have tried to go through these _teach-yourself_ materials, it went from zero to draw-the-rest-of-the-fucking-owl real quick. [0]

I have been programming for 14 years, but stopped doing schoolwork around age 12, and never did any math beyond pre-algebra.

Does anyone know of materials for adults that cover pre-algebra -> algebra -> geometry -> trigonometry -> linear algebra -> statistics -> calculus? At a reasonably quick pace that someone with a family + overtime startup hours could still benefit from?

[0] [https://i.imgur.com/RadSf.jpg](https://i.imgur.com/RadSf.jpg)

(Also, curse the Greeks for not using more idiomatic variables. ∑ would never pass code review, what an entirely unreadable identifier)

<comment><USER3> I hope I'm not too late here, but if you are in the US I would _highly, highly_ recommend signing up for developmental classes at your local community college. _You are exactly whom those classes are for._ If you've tried on your own before and struggled to stay motivated, doing it in a structured way, in 15 week "sprints", may be just the kickstart to your self-study program you need.

Disclaimer: I was a full-time community college professor for a decade. I had no idea what a resource they were. It's small money compared to either the alternative of a university or not succeeding. If you use them you _will_ succeed. It's what they do, and they've been doing it for a very long time.

<comment><USER4> Seconding this. After high school, I worked in industry until I got bored, and went back to school starting with community college. I'd never thought I was good at math, and I placed into pre-college algebra. Programming had taught me to think methodically, so I crushed those early classes. Fast-forward a decade; I've got a PhD in math (nothing like what I set out to do; I just followed my passion).

<comment><USER5> That is extremely inspiring. Can you speak more to how you went from industry to a community college to getting into and completing a PhD program? Did you quit your job to return back to school? What area did you end up specializing in and what do you do now?

<comment><USER4> Long and short, I got sick of the tedium in web development, quit my job and went back to school. The dot-com bubble had just burst, and I had been taking occasional classes including a very inspirational data structures course which planted the seed with formal proofs.

After I went back to school, I tutored in the math study center to pay the bills, which really helped cement not just the learning but also the notion that I could survive academia. I'd gone in with a plan to study engineering, but after I transferred to university, I kept dawdling on the math prerequisites and not taking the engineering courses that needed them. So it kinda gradually dawned on me that math was what I loved, and away I went.

I never strayed too far from computers. I'm a graph theorist, specializing in computation; had I known better I'd have gone into computer science because that's where I see the most progress being made.

<comment><USER6> > had I known better I'd have gone into computer science because that's where > I see the most progress being made.

Interestingly this is similar to what my two advisors (one from the math department and one from CS) suggested to me. It would be easier to do the math I like in a CS department than it would be to do the CS I like in a math department. Do you feel like math departments are more conservative when it comes to working outside the discipline?

</comment></comment></comment></comment></comment></comment><comment><USER7> I pretty much followed the same route as OP re-studying mathematics seriously after 10 years in industry after initially doing a CS degree and doing mostly software engineering but transitioning into Data Science the last 3 years. When I saw Book of Proof then Spivak then Apostol on his list I chuckled because that's exactly the route I ended up following as well. Studying from 04:30 to 06:30 in the week and about 8 hours split up over the weekend, Spivak took 8 months to complete (excluding some of the appendix chapters) but if you can force yourself to truly master the exercises - and Spivak's value is the exercises - then you're close to having that weird state called "mathematical maturity" or at least an intuition as to what that means. You can forget about doing the starred exercises, unless you're gifted. Spend a lot of time on the first few chapters (again, the exercises), it will pay off later in the book. It was a very frustrating experience and I had so much self doubt working through it, it's an absolutely brutal book. Some exercises will take you literally hours to try and figure out.

If you do Book of Proof first you will find Spivak much easier, since Spivak is very light on using set theoretic definitions of things. Even the way he defines a function pretty much avoids using set terminology. Book of Proof on the other hand slowly builds up everything through set theory. It was like learning assembly language, then going to a high level language (Spivak) and I could reason about what's going on "under the hood". Book of Proof is such a beautiful book, I wish I had something like it in high school, mathematics would have just made sense if I had that one book.

I read a quote somewhere, think it was Von Neumann that said, you never really understand mathematics, you just get used to it. Keep that in mind.

<comment><USER8> So, you've made all that effort, how does it help you in your new role as a data scientist? Is there anything you do now that requires "mathematical maturity"? Or is it something that can be learned much quicker on as needed basis?

<comment><USER7> There are a lot of charlatans in the Data Science space who lack the necessary mathematical background for their roles. For me it was necessary to get a rigorous understanding of probability theory, and applied probability theory is basically what mathematical statistics is about. My background was CS and software so R, Python, data visualisation and ML operationalization is by and large the easy part of Data Science to me. If you pick up any book like Bishop's or ESL you will be extremely frustrated if your mathematical background is not there. I didn't feel comfortable creating predictive models for production use that I didn't completely understand what was going on "under the hood", the assumptions being made and how they could fail. It's the only ethical thing for any engineer to do.

<comment><USER8> I do deep learning research for a living. I've taken graduate classes in probability, stochastic processes, optimization algorithms, and signal analysis (ECE PhD). I almost never completely understand what's going on under the hood of my models as soon as they get larger than a single neuron XOR mapper. That does not prevent me from finding ways to improve the performance of very large models (millions of parameters and dozens of layers). I agree that there are some papers (or the two books you mentioned) that can be quite dense and heavy on math, but I can't say I've ever felt like I needed any math other than basic calculus, linear algebra, and prob/stats 101 to understand almost all ML methods that people actually use in real world. Obviously if you want to make breakthroughs in theoretical ML, then sure, you do need the mathematical maturity (mostly because you will need to be formally proving things), but if you're a regular data scientist? Can you give some example what kind of math is involved in your predictive models?

</comment></comment></comment></comment><comment><USER9> A couple prior HN discussions with great comments related to learning mathematics:

[https://news.ycombinator.com/item?id=19811715](https://news.ycombinator.com/item?id=19811715)

[https://news.ycombinator.com/item?id=20446796](https://news.ycombinator.com/item?id=20446796)

[https://news.ycombinator.com/item?id=11469494](https://news.ycombinator.com/item?id=11469494)

</comment><comment><USER10> Initially I heard about Euler's famous Basel problem. Years later I got to solving it for my self (for curiosity and fun). I guess what intrigued me was to think of trigonometric sine as an infinite polynomial...After I worked it out, I had indeed seen the fire in Euler's own eyes...I could see how excited he was at having discovered something amazing...But this got me into hooked into math history. What I really wanted was how people came about discovering the Taylor's series...the intuition behind it. So that is how I came across John Stillwell's book. I have to warn people it is rather academic. But if, you, as a self-learner, is excited about mathematics, I would suggest Norman J Wildberger's youtube lectures on mathematics history. I find the buildup to calculus quite fascinating. J. Stillwell's book was the recommended reference in those lectures...

</comment><comment><USER5> One thing I don't think is discussed enough is the process of how self- learners in math get critical feedback. Most advanced level math textbooks do not have solutions to check their work against nor do they have a way to get feedback by an expert and this is essential for learning. Least with programming, you can get immediate feedback and know whether what you did is correct or not.

<comment><USER11> Learn proofs well and you get pretty good and knowing when you're right. Enough for almost any problem you'll be likely to encounter in a math textbook anyway.

<comment><USER12> I strongly disagree.

It's a little like saying "learn programming well enough and you'll know if some piece of code works as expected without running it."

<comment><USER13> > "learn programming well enough and you'll know if some piece of code works > as expected without running it."

That is 100% true.

Obviously the code needs to be self-contained (not calling into other unknown code) but so do mathematical proofs.

</comment></comment></comment></comment><comment><USER14> This is so difficult. I've been doing it off and on for twenty years and not made much of a dent in things.

The hardest part I think is understanding and measuring your progress. In school you've got exams and classmates to compare against, profs to talk to. Alone it's much harder. "Do I understand this well enough?" "Did I do the problems right?" (Especially with proof problems, how do you _know_ you're right?). "I can work through some problems one by one, but it feels like something fundamental I'm missing. Am I, or is this chapter really just about some tools?"

Then it's way too easy to say well I'm never actually going to use any of this so why am I doing it ... and take a few months off and come back forgetting what you'd learned.

<comment><USER15> I've tried a few things recently that help with that:

1\. _Don 't do exercises_ unless you want to. Completionism is a trap.

2\. _Take notes_. Rewrite things in your own words. Imagine you're writing a guide for your past self.

3\. _Ask questions_. Anytime you write something down, pause and ask yourself. Why is this true? How can we be sure? What does it imply? How could this idea be useful?

4\. _Cross-reference_. Don't read linearly. Instead, have multiple textbooks, and "dig deep" into concepts. If you learn about something new (say, linear combinations) -- look them up in two textbooks. Watch a video about them. Read the Wikipedia page. _Then_ write down in your notes what a linear combination is.

Anyway, everyone's different of course, but these practices have been helping me get re-invigorated with self-learning math. Hope they help someone else out there. I welcome any feedback!

(edit: formatting)

<comment><USER16> this is excellent execellt advice. seriously anyone interested in learning math, chancing on this comment, should write it down. i wish i could upvote many more times. i have a bachelors in pure math and am 10 years out. i have time and again revisited things and didn't make good substantive progress until i came to these same exact conclusions.

especially the part about skipping the exercises. if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them. a lot of exercises are a hazing ritual or imagined by the author to be a dose of bitter medicine (i'm looking at you electrodynamics by jd jackson) since they mistakenly believe all readers are formal students.

the most important exercise is to mull over and consider what you're reading/learning. naturally dovetails in to asking question: what happens if i remove a hypothesis from a theorem, what happens if i add one, is there an analogy to another object/group/measure/etc, etc.

also read multiple books ([http://libgen.is/](http://libgen.is/) is your very very good friend and generous friend). a lot of math authors (no matter how esteemed they are) are terrible writers or make mistakes (look up errata for previous editions of your favorite book).

the only thing i'd add is to learn to use LaTeX to take notes - it is much easier and faster and neater.

<comment><USER17> > _this is excellent execellt advice ... especially the part about skipping > the exercises. if you 're not trying to write a dissertation or pass a qual > (and you're just interested in learning and being exposed) then you don't > need to do them_

I think this is deeply mistaken. In a well-chosen book, such as the ones in the submitted article, doing the exercises is not to test your memorisation, it's to develop your understanding.

Math is not a spectator sport. Reading _about_ math is fine, but it will not take root and develop unless you engage with it, and the exercises are the way to do that.

Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it.

<comment><USER16> >Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it.

Isn't that literally exactly what I said?

> if you're not trying to write a dissertation or pass a qual (and you're just > interested in learning and being exposed) then you don't need to do them

<comment><USER17> The submission and this entire thread is about learning math. That, to me, implies learning to do, not learning about. Yes, you said:

> _if you 're not trying to write a dissertation or pass a qual (and you're > just interested in learning and being exposed) then you don't need to do > them_

There's ground in the middle, and this thread is about that. This thread is not about learning for tests and qualifications, nor is it about "being exposed", it's learning _how to do the math._

And for that you need to do the exercises. You don't need to do all of them, you don't need to be completionist about it, but if you don't do the exercises, if you don't actually _do the math_ then you won't actually be able to do the math.

Specifically, you said (quoting again):

> _if you 're ... just interested in learning ..._

There's a difference between learning about and learning to do. If you meant just "learning about" then you are at odds with the entire thread. True, in that case you don't need to do the exercises, but I don't think that's what people are talking about here. I think people are talking about being able to do the math.

And if you meant "learning to do" then in my opinion you are wrong, and one needs to do a large slab of the exercises.

Otherwise it's fairy floss, and not steak.

My apologies if all this seems overkill, but there's a real danger of talking past each other and being in violent agreement, and I wanted to state explicitly and clearly what I mean, and why I thought you said something different.

<comment><USER16> > you won't actually be able to do the math

but i'm not a mathematician. i don't need to be able to __do math __anymore than i need to be able to __do history __(while reading serious history books).

>And if you meant "learning to do" then in my opinion you are wrong, and one needs to do a large slab of the exercises.

no i didn't. that's precisely why i used the word "exposed".

>violent agreement

we don't agree but i'm not being violent. but my responses are short and yours are long.

i do not see the exercises as essential for anyone other than practicing mathematicians. i have read a great many serious math books (i just recently finished Tu's Manifolds book and am now reading Oksendal's SDEs). i read them without doing absolutely any exercises but following the rest of the guidelines in the post i responded to. the experience is gratifying because i learn about new objects and new ways of thinking about objects i've already learned about. that's absolutely the only thing that matters __to me __.

but let me ask you something

>That, to me, implies learning to do, not learning about.

here's a fantastic explanation of the topological proof of Abel-Ruffini

[https://www.youtube.com/watch?v=zeRXVL6qPk4](https://www.youtube.com/watch?v=zeRXVL6qPk4)

would you say that I don't understand that proof if i haven't done any exercises related to it? and therefore would you say I didn't learn any math by having watched that video?

<comment><USER17> We agree that if you want actually to be able to do the math then you need to do the exercises.

Do we agree that if you don't do the exercises then you probably won't actually be able to do the math?

You are discussing learning _about_ the math, and not eventually being able to do it, because you say that you don't care about becoming a mathematician, therefore you don't need to do the math. Fair enough.

But my reading is that that's not what this thread is about. This thread, and the original submission, is about learning how to _do_ the math.

> _i do not see the exercises as essential for anyone other than practicing > mathematicians._

I think you're wrong. Knowing how to actually do the math has proven useful to many people for whom it is a tool in their craft/job/employment. Learning Linear Algebra properly, being able to actually do it rather than just talk about it, can be enormously useful in Machine Learning.

>> _That, to me, implies learning to do, not learning about._

> _here 's a fantastic explanation of the topological proof of Abel-Ruffini > ... would you say that I don't understand that proof if i haven't done any > exercises related to it? and therefore would you say I didn't learn any math > by having watched that video?_

Understanding a single proof implies very little about one's ability to actually do the math. I've met many people who are math enthusiasts and who have watched hundreds of math videos. They say they understand all of what they've seen, and yet they are unable to do the simplest proofs, or the most elementary calculations.

My experience of people's abilities is that if they haven't done the exercises, they usually can't actually do the math.

But you complain about the length of my replies, so I'll stop. I think I've made my position clear, and I think I understand what you're saying, even if I don't agree with it.

<comment><USER16> >You are discussing learning about the math

You keep repeating this but you're evading the question about abel-ruffini and the question about whether reading a history book is "learning about history" as opposed to learning history.

You're making a weird distinction. People learn in different ways. Some by doing exercises and some by just playing with the objects. I wonder how you think actual research mathematicians learn new math from papers that don't include exercises lol.

You edited your response.

>I've met many people who are math enthusiasts and who have watched hundreds of math videos

There's a difference between watching numberphile or whatever and essentially watching a lecture on a proof. Very few people are watching/consuming rigorous expositions. I think that's the difference not the lack of exercise.

<comment><USER17> Learning about history is not the same as then being able to do research in history, nor being able to apply the principles learned from it in context. So no, reading a history book is learning about history, not necessarily being able to "do history".

> _You 're making a weird distinction._

As someone who has done a PhD, done research in math, done research in computing, worked in research and development in industry, taught math, and headed a team doing research in technology, this is a distinction that I can clearly see. My inability to explain it to you is regrettable.

> _People learn in different ways._

Yes they do.

> _Some by doing exercises and some by just playing with the objects._

Doing the exercises _is_ playing with the objects to try to answer specific questions. Good exercises are carefully constructed to help the reader learn how those objects work in an efficient manner.

> _I wonder how you think actual research mathematicians learn new math from > papers that don 't include exercises lol._

In my experience research mathematicians learn now math from papers by, in essence, constructing their own exercises based on what they're reading. In general it takes significant experience and training to be able to do that.

Clearly you don't think one needs to do the exercises subsequently to be able to do the math. Good for you.

I disagree.

<comment><USER16> >As someone who has done a PhD, done research in math, done research in computing, worked in research and development in industry, taught math

Me too so now what? I don't think your credentials give you any real authority but just make you look like you're gatekeeping.

>Doing the exercises is playing with the objects to try to answer specific questions.

Great so then we're in agreement: playing with the object _is_ doing the exercise.

The funny thing is that at one time I actually did all of the exercises in volume 1 of apóstol's calculus. You know what effect on me it had? I was so bored I didn't read volume 2. And today I'd still need to look up the trig substitutions to do a vexing integral.

<comment><USER17> > _I don 't think your credentials give you any real authority ..._

It wasn't intended to, it was to provide a context for my opinion.

So let me state my opinion as clearly as I can, and then I'll leave it.

* Math is a "contact sport" ... you have to engage with it;

* Reading books is not, of itself, engaging with the math;

* Watching math videos is not, of itself, engaging with the math;

* Well designed exercises are a valuable resource;

* If you can easily do an exercise, skip ahead;

* If you can't do an exercise, persist (for a time);

* Ignoring the exercises is ignoring a resource;

* For the vast majority of people, doing the exercises is an efficient way to engage with the material;

* To say "ignore the exercises" is, for the vast majority of people, an invitation to not bother engaging with the subject;

* Doing _all_ the exercises is probably a waste. Doing _none_ of them is an invitation to end up with a superficial overview of the subject, and no real understanding.

<comment><USER14> See? It's pretty hard. This is what I've been dealing with for the last 20 years of on and off trying to get through the bigger Rudin book and a couple others.

 _Just_ reading doesn't get much at all. Not even a superficial overview. I tried it. It's essentially a meaningless combination of words after a certain point.

Reading extremely thoroughly is actually marginally useful. Stopping to think, do all these assumptions matter, why, what if one of them changes, etc, pencil in hand, making notes, testing things out. I've managed to "understand" the topics when doing this, and so far it's been the highest ROI method. But it does still leave one feeling like something is missing. Just because you can sight read music doesn't mean you're an expert on the piano.

Doing exercises is a huge jump on investment, and the return on that investment is a bit questionable from my experience. A couple reasons: first you don't know if you did them right. If you did them wrong then that's negative ROI. Second you don't know what a "reasonable" workload is. It varies by author. Is it three problems per chapter, is it all of them, are some orders of magnitude more difficult than others? Without some guidance it's hard to know if your difficulties are due to not understanding basic material, or due to that problem being a challenge geared toward Putnam medalists. So they may cause you to question your understanding and thus mentally roadblock you unnecessarily. And finally with proofs (and this may be a me thing), it's pretty easy to say "I guess this is okay(?)" and move on, even if you're not sure. Since nobody is ever going to review it, and it's _just_ a homework problem, it's very very hard to will oneself to make sure every assumption is correct and you're not missing anything, even if you feel like there's a good chance you are. Or perhaps I just don't have the constitution to do so.

So while I think doing exercises is necessary for a deeper understanding, I don't know whether the ROI is worth it outside of a classroom perspective. You need feedback for exercises to be beneficial. At least, I feel like I do.

Finally, is even taking a class that useful if the end state is that two years from then you'll have forgotten most of it and so what was the point. Can you claim knowledge of a subject that you've never actually used beyond some homework problems and exam questions, or is this _still_ a superficial understanding? Having an ends where that knowledge gets used seems critical.

I feel like I have some knowledge but I don't feel like I'm _there_ yet. But I don't know if I know where _there_ is. Maybe that's the biggest challenge. Does completing a Ph.D. even get you to _there_? No idea. But, I guess it's up to the individual to decide what they want out of it. Nobody can determine that for you.

</comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment><comment><USER18> For all the adventurous self-learners out here, we would like to invite you to our self-study group named Integer Club.

IRC: [https://webchat.freenode.net/#integerclub](https://webchat.freenode.net/#integerclub)

Slack: [https://bit.ly/integerclubslackinvite](https://bit.ly/integerclubslackinvite)

Mailing list: [https://groups.google.com/d/forum/integerclub](https://groups.google.com/d/forum/integerclub)

We pick up old concepts from popular textbooks and literature as well as new stuff from new literature in both mathematics and computer science. We plan to have online meetings periodically to share what we learn, work through popular literature, and have a few talks on interesting topics.

It is a tiny community right now that hangs out at Freenode IRC but the Slack channel is there too if you are more comfortable with that.

</comment><comment><USER19> I think it's great that people are posting book links like this, however, what I've found most helpful is actually having _someone_ to help guide you.

I realize how lucky I was that I found a Discord server ran by a math PhD graduate who is willing to help us guide our learning. From this, I've started learning Algebra and Analysis (just starting with the latter). It's nice to have someone to discuss problems with when you get stuck and to guide you. Likewise, he can suggest exactly which problems I should do for a give chapter, that way I don't spend my time doing ones that just repeat the same simple things over and over and can focus on nice, conceptual ones. So, if you can, please try to find someone to help guide you, or be that guide for someone else! Having it has made me seriously consider going back for a mathematics masters (and maybe PhD), switching from my physics background.

<comment><USER20> Could you share the discord server? Thank you.

<comment><USER19> I'm not the owner, and it's a small server, so I don't feel comfortable. Sorry. I think I found the owner through /r/math, so you might be able to find his old post there though.

</comment></comment></comment><comment><USER21> As someone who dropped out of highscool after 10th grade and never went to university/college one great way I've found for learning mathematics without any foundational basis is trying to learn CG/3D programming.

I always felt like maths was too abstract to keep me engaged, but when the output of your work is immediately observable visually it becomes a lot more engaging. There's just something so much more satisfying being able to "see" the results.

Plus as a self-taught programmer, I find it much easier to learn front-to-back by deciding on a desired outcome and working towards it, rather than progressively building up abstract fundamental skills that can later be combined to achieve a desired outcome (which is essentially the traditional academia path for learning STEM fields)

<comment><USER22> This is why I love to do game development without using a game engine. It gives you a reason to learn math, optimize your code down to the metal, all while having fun playing your game.

<comment><USER21> Yeah I've been self-learning 3D "the hard way" and have been really enjoying it.

Keeping it as low-level as possible, I'm using CycleJS for dataflow management and Regl.js for drawing via a CycleJS-Regl.js driver.

All state is explicitly managed observables/streams in CycleJS, which maps out to Regl.js draw commands, which are basically raw frag/vert shaders with some bindings mapping my state from CycleJS to appropriate uniforms/attributes.

I probably would be able to produce some usable output much faster if I used an engine like Unity or a framework like Three.js, but I feel like I would have missed out on gaining so much knowledge by only working with high-level abstractions and never having to even touch GLSL code.

</comment></comment></comment><comment><USER23> I came to the IT industry after a bachelor degree in math, 5 years in and all the math I know is gone I still remember some Fourier, signal processing and probability statistics that I never used in my day job, or anywhere else.

Time is valuable, it's the most valuable thing a human being has, I understand it's the hobby of OP to learn all this math, but unless you are going to use it why wasting all the time?

</comment><comment><USER24> I've been pursuing mathematics as a hobby for the last 2 years or so. I got a mathematics major in undergrad so my motivating factor was mainly to explore some areas that I hadn't done coursework on, primarily algebra and number theory. (I focused more on logic in undergraduate/grad.)

I really enjoy how the subject is divorced from a lot of the modern attention demands and encourages more of a 'zen' thinking style.

As others have highlighted, it can be difficult. I work full-time as a software engineer and at the end of the day there's usually not much left in the tank in terms of "creative work". The morning is usually more productive for me - generally I'll spend 10-15 minutes on the commute in reading over the proof of some lemma or working through some computational exercise.

Things that have helped me:

\- Focusing on a particular problem area rather than just "mathematics". The classical problems of Gauss and Euler tend to be more my speed than the modern mathematical problems of Hilbert or beyond. What started my journey was looking into the insolubility of the general quintic polynomial equation, something you learn in high school as a random factoid but has a lot of depth.

\- Studying from small textbooks that I can fit in a backpack, so I can "make progress" during my commute. Dummit + Foote might be a great algebra reference but it's just too bulky to transport.

\- Limiting the scope of how I think about the activity - my goal isn't to master these concepts on the level of a mathematics graduate student, it's more on the order of Sudoku. If I don't get something, that's okay. People spend their whole lifetimes learning this material and I'm just trying to fit this into whatever creative time I have left after the full-time job is done.

</comment><comment><USER25> Do any of you all have some tips for understanding mathematical notation? I feel this is often poorly explained, and it feels like a language all its own that just does not speak to me. I did pretty well in calculus, but I still don't really understand what the dx was supposed to represent and in reality I was just really good at pattern matching when it wasn't supposed to be there anymore.

I try to read papers now and again with a math orientation, and I quickly get lost when trying to translate the concepts into cryptic formulas, and often when they make the "obvious" transition from step 3 to step 4 I just have no idea how they got there.

I feel this is by far my biggest barrier to understanding most mathematics, and I have thus far found no way to overcome it.

<comment><USER26> I think usually the problem is "almost getting it" and trying to move forward, which means small uncertainties add up and all the sudden one is totally lost without being sure exactly why. So it's important to go back and make sure each piece of notation is crystal clear before moving forward.

Any statement in math is meant to be directly translatable to human language. You should be able to read it out loud in English and know exactly what you mean when you say it.

Unfortunately, sometimes math uses awful notation. For example, df/dx. This is a case where df doesn't mean anything (or at least it's not normally well- defined), and dx doesn't mean anything either (same comment). But the notation as a whole means something. If we write g = df/dx, then we can understand that g is a function whose input is x and output is the slope of f at x.

</comment></comment><comment><USER27> The most key piece of advice is to take walks. Walking is essentials for mathematics. Many times when walking with my father he would turn for home and start walking faster, and by that sign I knew that he wanted to get home and write down a lemma.

<comment><USER28> I'm glad you posted this, because I use walks this way too. And because it reminds me of William Rowan Hamilton and the quaterions!

</comment></comment><comment><USER29> This is a solid read, with good book recommendations. After several years of tinkering with self-learning I bit the bullet and applied to a MSc in Applied Math program. (via ep.jhu.edu) I've had to take some pre-reqs to get started since it's been almost 20 years since I have been in a college math class, but it's been an enlightening journey re-learning calculus and now dipping my toes into differential equations. I don't think I could have gotten this far with self-learning, but I realize YMMV.

I will say I don't feel like single-variable real number calculus tells the whole story. I had taken that and linear algebra in undergrad but never any further, and now that I've taken single and multiple variable calculus, with real and complex numbers, plus integration of linear algebra ideas, the mathematical model feels a lot more like a cohesive whole to me, highlighting fundamental ideas that only barely peek through in a typical Calculus I class. I would encourage anyone talking to calculus to at least do the typical Calc II class, if not Calc III/multivariate. There is a beauty and structure to building up from calc I through III that I was missing before.

</comment><comment><USER30> I'm pretty skeptical about these "best of" lists of books for self-directed mathematics education.

I have my own "best of" list that is very different to this list, although there are a couple of crossovers.

If you are fortunate enough to have access to a university library (or libraries) I would _highly_ recommend inquiring about access to their general collection. I was also fortunate enough to study mathematics to a university- level three-year degree at a research university. So I had an excellent head start.

A HUGE part of my journey of collecting my "perfect library" of mathematics self-tuition and reference books (and course books) was to do my own research on collecting the perfect titles. I started when I was in the early days of my mathematics degree and I used resources like Amazon, Usenet, libraries (already mentioned), and ... that was about it.

Another important question to ask yourself is the following:

"Why am I doing this?"

Life is short and by the time you hit middle age, if you have a family or bills to looks after, are you REALLY going to want to lock yourself away in your study room to learn Lebesgue integration instead of focusing on the rest of your life?

Consider that people fail to emphasise is that mathematics is a social activity much more than many people realize.

Exercise: Find the topics of mathematics that are important to your goals and are missing from the list and find your favorite books or two that cover/s these topics.

Exercise: Consider whether your interest in (self-directed) mathematics is so sincere such that you have a serious application in mind, that you might be better off enroling in a course? Even if it's a night course that last a couple of years, you will meet a LOT of people who can help in ways that are immensely more productive than trying to do this all by yourself.

I recently purchased volume 1 of my favorite calculus and analysis book. It's an incredible masterpiece. The coverage of topics is much broader and more interesting than Aposotol or Spivak. The latter books are both very good but they also have myopic, one-track pedagogical approaches and limited themes in their coverage.

Exercise: Find your own favorite introductory calculus book that is suitable for the motivated student.

<comment><USER7> > I recently purchased volume 1 of my favorite calculus and analysis book.

Which book would that be if I might ask? I'm wagering... Courant? ;)

<comment><USER30> Indeed :-)

Courant & John, to be exact.

</comment></comment></comment><comment><USER31> I recently had the experience of taking my first graduate-level probability course. It assumed quite a strong familiarity with real/complex analysis, and I suffered quite heavily. Something of note was that once I finally managed to "peel back" the analysis, the underlying intuition made a lot of sense for the simplest cases in probability (e.g. hypothesis testing between two normal distributions is a matter of figuring out whose mean you are "closer" to).

I am of the opinion that notation is a very powerful tool for thought, but the terseness of mathematical notation often hides the intuition which is more effectively captured through good visualizations. I would really like to take self-driven "swing" at signal processing, this time approaching it through the lens of solving problem on time-series data, since as a programmer I believe that would be quite useful and relevant.

<comment><USER32> In my opinion, the issue here is notation and a bit more. I did about eight years of college in math, changed paths, changed careers, changed careers again to ML/DL research, and now will finish a CS undergrad degree this month.

I put it in context because it's not quite a direct comparison since I have been in greatly different situations and ages between studying math and CS, but putting that aside, I have to say I have greatly enjoyed the computer science means of teaching more than math, doubly when it comes to self- learning. Concepts in math are generally taught entwined with the means of proving those ideas. That's important if you're a grad student looking to be a math researcher, but (IMO) it is not so great if you're a newer student or learning on your own and trying to grasp the concept and big picture. A proof of a theorem can be (and too often is) a lot of detail that really doesn't help you grasp the concept the theorem provides or is used towards, often because it involves other ideas and techniques from higher levels or just different types of math, both of which are out of the scope of the student learning the topic. Worse yet, it is standard for a proof to be written almost backwards from how it would be thought out. Anyone from a math educational background has the experience in homework of solving a problem, then rewriting it almost in total reverse to be in the proper form to submit. This means not only is the proof of the theorem not useful towards conceptual understanding, reading the proof doesn't show you chronologically how you would discover it yourself. That is a lot of overhead cost to break through to get to real understanding, real learning. As you mention, notation as well is another thing you need to break through.

I have found computer science and related classes to be taught more constructively. Concept is given first, and then your job as student learner is to construct it. Coming from the ML field, I love comparing math and CS proofs of topics here. Explanations from CS people of back propagation, for example, are always visual, and books/courses will have you construct a class and methods to do the calculations. Someone with a bit of programming knowledge can follow along in their language of choice. Math explanations get into a ton of notation from Calc 3+, and it's going to take a lot of playing around and frustration to get a working system out of the explanation. Even the derivation section on Wikipedia is not something most people will understand and be able to turn into useful output.

The more I see other ways concepts are taught, the more I wish math had been taught a different way. There is a lot to break through in order to get to real understanding, just by the way it's formed and taught.

</comment></comment><comment><USER33> I am always astonished to learn that there are such self-learners in the world. I wonder how it is even possible to have a family and spend whole day building a startup - I cannot imagine that startup work is less than 8 hours a day - and then at evening they learn math or other complicated branch of science. What time and more especially how much energy they have for the family? Are these guys superhumans? I never was able to achieve such level of daily energy spent without trapping in burn out. I am not critiquing or being jealous here, just having genuine interest. How is it possible to be sustainable across so many years?

<comment><USER34> I have my doubts that the people who write these kinds of posts truly did everything they say. As you say, it just does not seem possible to thoroughly work through all those math books + raising multiple kids + maintain friendships + working out daily (as he claimed he did) + work full time + things like cleaning and shopping and other chores.

</comment></comment><comment><USER35> Wow that's a brutal list of books... I'm impressed the author could work through all of that in just six years! I feel like math is a subject you need to get back again and again to refresh in order to retain. I got some pretty good grades in linear algebra back in the day... but I don't really remember much about it right now, sigh.

My strategy to get back to study math these days is getting to learn Wolfram Mathematica and Sage. Once I can move around those two, I feel like I will be able to create a tighter feedback loop on whatever Math subject I'm happen to be studying at the time.

</comment><comment><USER36> Does anybody have any experience with _How to Prove It?_ by Velleman? Recently I was thinking of starting on it, but I'm not sure about the level of commitment necessary.

<comment><USER37> I worked through this book to learn how to do proofs. It turned out way more fun than I expected. The book really did demystify proofs for me. It took several months of studying - there are many exercises. But completely worth it. I'm glad I have read this book before studying Group theory and Real analysis.

<comment><USER36> Thanks!

</comment></comment></comment><comment><USER38> I would recommend _Conceptual Mathematics: A First Introduction to Categories_ by Lawvere.

It is written by a true pioneer. And also, you will impress your friends by your hipster foray into category theory.

However, this book is far from being hipster. Also, I would not be surprised if a high school student would be able to follow this book over the course of a year or two.

If you titled the book: _Sarcastic introduction to how simple set theory is_ then I would actually be fooled that it were the correct title.

</comment><comment><USER39> There is 3 books listed that essentially cover the freshman (first year) courses in Calculus. And 4 for Linear Algebra. If you work your way through even 2 different books for one topic, you are going to have a broader foundation in the topic than a normal math student in a normal university after completing the corresponding course. And you will have spent much more time, too. University courses don't usually cover everything that is in a textbook. And students don't usually read books through. In fact, students usually try to skim the course notes just enough so that they can solve the weekly problem sets.

There is maybe nothing wrong with being thorough with the elementary topics if you're studying for fun. But if you're studying for applications, I think you should cover the basics only adequately, and then quickly move on to more advanced topics. Basic Calculus is only the foundation, stuff that is actually useful in applications comes later. Basic Linear Algebra can be useful in its own right, but the advanced stuff is even more useful.

I suggest building an adequate foundation, not a comprehensively thorough foundation, and then moving on to the more powerful stuff. Which varies depending on what you actually want to use math for.

<comment><AUTHOR> To be clear, I don't at all advocate that people work through all the Calculus books. Likewise for the Linear Algebra books. My aim was to provide alternative options (which are easier, cheaper, etc.)

</comment></comment><comment><USER40> Another book similar to Morris Kline's _Mathematics for the Nonmathematician_, which the OP mentioned, is Lancelot Hogben's _Mathematics for the Million_. Originally published in 1937, it has been in print ever since, through several revisions. This also takes a historical approach, beginning with numbers and counting, measure and Greek geometry; and eventually covering calculus, matrices, probability, and statistics.

You can take a look at it, at the Internet Archive,

[https://archive.org/details/HogbenMathematicsForTheMillion/m...](https://archive.org/details/HogbenMathematicsForTheMillion/mode/2up)

</comment><comment><USER41> I found the Real Analysis course to the really really hard back in university. I thought it was like the CS information analysis when looking at the course title. It was nothing like that at all. It didn't help that the professor teaching it was pretty bad. I remember he used to jog into the class carrying a tennis racket and in tennis sporty dress with headband, seemingly just coming back from a tennis practice and acting to be cool. People just rolled their eyes. The teaching was just reading off the book. Darn, it was one of the top schools. How did this clown get in?

</comment><comment><USER42> The perenial self-learning mathematics curriculum is hbpms.blogspot.com.

</comment><comment><USER43> This is fantastic. I recently been studying set theory and discrete mathematics as a self-directed learner and it is incredibly helpful to see others hewing the same path.

</comment><comment><USER44> I love stuff like this. I graduated with an MS and never understood Calc II+. It was always memorization and repeating various theorems etc on the test. But, I didn't truly grok the fundamentals. I was just a good test taker and it bothers me to this day. So, learning math has been a continuing project of mine and things like this are beautiful.

So grateful. The world is wide open to the self learner in this day and age.

We are very lucky.

</comment><comment><USER45> Completely unrelated question but: how do you go about finding out that there is an opportunity to build a small business selling Microsoft teams and slack integration apps? I'm stuck in the mindset that software companies make billions of dollars or no money at all. I've not seen the right kind of indie hacker post that talks about how exactly people size their ideas and how much money is possible to make.

</comment><comment><USER46> It was a great read. I bookmark this post hoping one day to buy a couple of the recommended books. It's just too hard for me right now to find the time. Life is too busy with a family, a full time job, and all the distractions around. Self learning is one of the most enjoyable things.

</comment><comment><USER47> Practice makes a master. More importantly, the _true_ understanding only comes through practice. Also, more often than not to "understand" something comes down to simply _getting used_ to it (which is how we learn things in the elementary school). Practice is the key.

</comment><comment><USER48> Fyi, for those who like working with lecture notes, much of the material for the math course at Oxford is online as well (no solutions, though):

[https://courses.maths.ox.ac.uk/](https://courses.maths.ox.ac.uk/)

</comment><comment><USER49> Not sure if mentioned, another good book: Analysis by its History

</comment><comment><USER50> [http://www.goodtheorist.science/](http://www.goodtheorist.science/) this is a step by step for theoretical physics.

</comment><comment><USER51> Does anyone know a good historical approach to maths? Like, start with Pythagoras?

Even something purely in the modern era, learning about Fourier and Weiner, harmonic analysis, etc.

<comment><USER51> The best historical treatment I've yet found is the Time-Life book on mathematics. [https://www.amazon.com/Mathematics-David- Bergamini/dp/B0007G...](https://www.amazon.com/Mathematics-David- Bergamini/dp/B0007G5WYG)

I know that Freeman Dyson attributes his proficiency in math to his love of math, which he claims was kindled as a teenager by reading Bell's "Men of Mathematics"

</comment></comment><comment><USER52> Buy a chalk board! There is no more enjoyable way to work through problems. This is especially true as the problems become more complex.

</comment><comment><USER53> Is there a list that inclines towards abstract math that can be helpful to solve programming problems?

</comment><comment><USER54> Thank you for such an inspiring piece

</comment><comment><USER55> Aren't applications like Brilliant actually really good to do this?

</comment><comment><USER56> Not quite sure why everyone needs to learn so much math.

</comment><comment><USER57> I am going to suggest something that might go against this idea of self- studying math.

Do not do it alone. I mean, it is okay to self-learn mathematics as much as possible but don't let that be the only way to learn. Find a self-study group where you can discuss what you are learning with others.

I think the social-effect can be profound in learning. I realized this when I used to learn calculus on my own. My progress was slow. But when I found a few other people who were also studying calculus, my knowledge and retention grew remarkably. I think the constant discussion and feedback-loop helps.

With round the clock internet connectivity, it is easier to find a self-study group now than ever.

<comment><USER58> It's not super clear to me how this actually works in practice. I've seen there is one public math meetup in SF, but the topic is usually different from the one I want to study.

I'm glad to see there are online options for groups like Stack Exchange or tighter group's like the one integerclub mentions, but I still seem to run into the same problem. For example, I'm not sure how to get a group of people that are interested in reading book X when I want to start it. If anyone has advice on that, please share.

<comment><AUTHOR> Yep, this has been the story of my learning experience. I've studied mathematics pretty much entirely on my own, but it's not because I wouldn't love to have company!

Having said that, I think it probably would be sufficient to find _just one_ other person who is at the same level of mathematical maturity and has the same degree of commitment to change the entire learning experience for the better. You don't need a big group.

</comment></comment></comment><comment><USER59> In mathematical history, there is a lot of discredit to Indian mathematics and their contributions.

Number System, Algebra, Geometry, Trigonometry, Calculus, ...

[https://en.wikipedia.org/wiki/Indian_mathematics](https://en.wikipedia.org/wiki/Indian_mathematics)</comment>