Ask HN: Where did you top out in math classes? - <AUTHOR>

Pretty much everyone (except perhaps tenured professors of mathematics) hits that point in their math training when they realize "I'm just not smart enough to get this."  What point in your math career did you hit a brick wall? <comment><USER3> Recent evidence tends to indicate that 'not smart enough' is probably a myth. Almost everything can be attributed to exposure and effort at some point rather than some innate smartness.

A lot of advanced math takes some serious concentration to understand. For some non-practical aspects, I found that I lacked the motivation rather than ability to understand it . One particular class where I seemed to hit my tolerance was a theoretical linear algebra class. I could understand the practical applications of most of the topics but some of the theory seemed just out of reach. The book was extremely dry and I think the professor may have been taking lessons from Ben Stein.

Give me a private tutor, a theoretical linear algebra for dummies book, and a pending disaster for which this is the solution, and I bet the outcome would be a little different.

<comment><USER4> Would you happen to have any links or book references to this "recent evidence"? While most of success comes from effort and discipline, I've always been under the impression that only the naturally gifted (who also have discipline and drive) can/have achieve/achieved certain things. The dwarf down the street from me will never be a professional football player, and someone with a 100 IQ will never be an astronaut. I've always felt the you-can-always- achieve-whatever-you-want-no-matter-what-if-you-want-it-bad-enough approach to be more than a little cliched and misguided. If recent scientific evidence has disproved this stance of mine, I'm open to changing it.

<comment><USER5> To be honest, I believe that all intelligence comes from innate motivations and practice. You suddenly become 10x more "intelligent" when you actually give a shit or get some innate joy or obsession relieved when you do it. If that is something that is constant within you, you become more and more practiced and a virtuious cycle results. Nothing is too hard to explain, it's just mathematicians are really horrible at communicating.

<comment><USER6> For whom, though? Brains are complicated, but if yours is severely damaged (through a stroke or head injury) motivation is not necessarily going to fix that. And as far as I know, there aren't any permanent ways to raise IQ. Some environmental factors lead to higher childhood IQ, but these vanish by adulthood. And there are tricks people can use to bump up their scores on IQ tests, but I haven't seen a situation in which practicing for test A raises your score, years later, on test B. This stuff is just more static than that.

The danger with what you're saying now is that someone with an IQ of 90 -- someone who could be a fine contributor to society in lots of practical, necessary fields that don't require lots of abstract thinking -- could be inspired to throw away lots of time and risk lots of frustration trying to be a mathematician. We should deal with the fact that wasting education on someone who can't use it is as much a tragedy as failing to educate someone who can use it. By pretending that 'smart' just means 'trying hard', you're doing more harm than good.

<comment><USER7> The problem may be that our predictors are terrible. There are a lot of Nobel prize winners who later discover their 'dismal' performance on IQ tests. I know grad students at Princeton who've confided sub-100 IQ scores, bad SAT's, horrible performance on one math test or another -- it's like this big, shameful secret for otherwise brilliant people.

Everyone carries around the absurd burdens of judgments and measurements, but they don't always mean what people think they mean.

<comment><USER6> Are there any other quantifiable variables with such high predictive power? I'd be really interested if there were some other test that could better estimate the odds that someone would get a degree, earn lots of money, stay out of jail, vote often, delay having kids, etc.

It would be interesting to know more details, which I'm sure you can't divulge without violating someone's privacy. But it would be neat to find out if those people had other skills that correlate strongly with IQ, like the various digit-memorization/recitation tests, or reaction time. Were these people autistic? Were they taking a test in a language they didn't know too well?

<comment><USER7> They weren't autistic, and there didn't seem to be any strange behaviors socially, and they were quite inquisitive and swift on the uptake.

I once heard IQ defined as "ability to navigate bureaucracy, getting the answers others think correct in a manner testwriters imagined, and color in the lines" (paraphrased). This may have something to do with the phenomenon here.

The odds that someone would 'get a degree, earn lots of money, stay out of jail, vote often, delay having kids, etc.' seem to have more to do with successfully conforming to certain values of society's upper-middle class.

I think I'm capable of inventive thought, but I don't particularly want to get another degree, or earn much money, or delay having kids, or vote often, and the sort of things that one has to do to stay out of jail, are, honestly, quite often absurd, and I often rail against them.

And if you start to observe, closely, just how these things are tested, you'll start to get the impression that maybe bright people will find their ways through the cracks more than anticipated. There's an enormous weight given to quick answers -- time directly influences scoring. Linear answers are expected, and alternative interpretations are docked. There's often insufficient information in the questions, or it's based on a model of the world that's wrong. Domain knowledge like mathematics or vocabulary is brought into it. Analogies are made to hone in on _one_ relationship from the many that could exist. Scorers of essays give insufficent weight to substance and too much to form -- despite their lipservice, they are indeed swayed by big words.

Even tests like GRE physics are bad. They claim to be testing rapid physical intuition, but in practice what divides good from poor scores is prior experience with 100 simple systems and the ability to get the factors of 2 and pi right with three minutes per question.

<comment><USER6> I think your quote comes from Cosma Shalizi. Thomas Sowell addressed that complaint years before by noting that most of the countries where you find that modern complexity are pretty nice places to live, whereas other places are hellholes. The correlation between IQ and income holds true for places outside of the US, too, so one might be tempted to think that a bureaucratic, find-objective-answers, fill-out-these-forms-in-triplicate society is better than most of the brutal alternatives.

"...seem to have more to do with successfully conforming to certain values of society's upper-middle class. I don't particularly want to get another degree, or earn much money, or delay having kids, or vote often, and the sort of things that one has to do to stay out of jail, are, honestly, quite often absurd, and I often rail against them."

My point is that, all else being equal, you _could_ get a great job if you chose to, and that if you do illegal things, you apparently do them in such a way that you won't get caught. IQ seems to correlate with the ability to delay gratification, which itself seems to be a better predictor of success than IQ (sadly, it hasn't been tested in a rigorous, long-term way -- so it can't match the hundred or so years worth of data people have compiled on IQs).

One of the reasons that these tests emphasize time is that 'quickness' is a component of IQ. Francis Galton, the first guy to really study the subject, liked to think of things in that way -- and given that physical reaction time correlates so well with IQ, he had a point.

I agree that the essay part of standardized tests is messed up. Lots of the recent changes to tests seem to arise from political correctness. Test-makers found out that you can't design a test that has predictive value without getting politically incorrect results, like lots of men on the extremes, or lots of high-IQ Jews and Asians and low-IQ Mexicans and blacks. So they periodically adjust the scoring mechanism or the test to get bell curves closer to the same median and standard deviation (more focus on the median than the SD, since most of the people who complain about such things don't know what 'standard deviation' means). So keep that in mind when complaining about the essay, or the rebalanced scores, or the analogies (which were dropped from the SAT -- analogies happen to be more IQ-weighted than other categories of questions).

<comment><USER7> For the most part, life in latin america seems a lot happier than in more bureaucratically encumbered states. So I don't really buy that argument.

My main point is that truly excellent thought doesn't depend on the same skills that would allow scoring highly in an IQ test. In many cases such skills would inhibit it. In an IQ test it helps to rapidly adapt to the assumed constraints of the problem and come quickly to the closest, most linear answer. If you have a mind compelled to bring questions back to reality, to challenge assumptions or think of things from many different angles, you'll do, on the whole, more poorly than if you had not. But these behaviors are sometimes precisely what you'd want!

<comment><USER6> _For the most part, life in latin america seems a lot happier than in more bureaucratically encumbered states. So I don't really buy that argument._

The millions of immigrants from there to here don't seem to buy your argument. Which Latin American countries do you mean?

"... truly excellent thought doesn't depend on the same skills that would allow scoring highly in an IQ test."

I happen to agree with you! One thing that's bugged me for years is that you can't design a test that distinguishes, in advance, between cleverness and original stupidity. So that means that whole lot of time-consuming activities can only be measured after the fact if at all. The difference in our views, I think, is that I would argue that IQ tests measure the kind of raw data- processing skills that are useful in any situation (the military tests people heavily, and for all tasks they've found that IQ correlates positively with results -- I think for some technician jobs, it explains about 60% of the variance in individual performance). There just aren't any studies I know of showing that people with low scores on IQ tests go on to succeed in any measurable way. It would be convenient, to say the least, if you argued that the success-deficit among low IQ people is more than compensated for by a success-surplus that happens to be impossible to measure. So I'd like to know if you can find some way to quantify your argument. It would change my thinking on a lot of subjects if I found that doing poorly on an IQ test predicted doing well at some other task.

<comment><USER7> In happiness surveys, Latin America does pretty well -- I think as a region it comes out on top.

This is contentious, but for most of the immigrants, they didn't move because the culture was more enjoyable here. Most of the Latin American immigrants had ther livelihood strip from them in two stages: one, from general industrialization pressures that have affected practically every country, forcing specialization into cash crops to compete, two, increasing competition from the USA and other countries, coupled with crop failures endemic to semi- arid areas.

The few areas in which modestly educated Latin Americans could reliably compete were in _illegal_ cash crops (for which they had less competition in the USA), which continues to cause economic distruption and criminal activity, and manual labor. Those forced into either business might have better chances in the USA, but on the whole they're happy countries. When you're there, you can feel it.

As for success and low IQs, if I recall correctly, someone got the bright idea of testing Caltech professors while Feynman was there -- this may have been prompted after he won the nobel prize, and found out his score from highschool was 125. When they tested the professors, the scores were surprisingly low. I forget who it was, but someone got to make a big deal of his 105 score, since it was three points higher than Feynman's.

My point is that these measures can be stunningly irrelevant, and, if so, while they might have some utility for, say, selecting an undergraduate class, they are often best ignored by an _individual_ when it comes time to decide what one is capable of.

</comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment><comment><USER8> I don't know, how about every subject?

Multiplication. Long division. Algebra. Geometry. Trig. Calc.

I was never very motivated to study math. The problem was, my older brother was very into it(and now is a math grad student, ever-so-slowly getting his thesis together). This set a model that I could not hope to emulate, but it only meant my mom pushed me more, talked to the school to get me into the advanced/accelerated classes I didn't really want to take. She probably would have done some of that without my brother around, but not as much.

This led me down the "please the parents" line of study, which naturally meant some surreptitious, embarrassed attempts at cheating. This only made me feel worse, of course.

In college I started into computer science, thinking that I at least liked the programming. But integral calc sunk me for good, and in a particularly bad quarter that was my low point, I tried taking linear algebra as well as a repeat of calculus, thinking that perhaps the extra pressure would do something good.

Of course not. I dropped linear algebra and failed calc again. After that, I decided to declare in economics, restarted calculus with the "ez-for-econ- majors" series and sailed through those courses with a solid B average. I struggled through, but passed on the first try, the two intermediate econ courses which started introducing serious mathematical modelling. The remainder of the major was electives, and not difficult ones.

I never knew, until after that whole period of my life was over with, exactly what was holding me back. Now I'm pretty sure that it's about motivation and dedication. My brother is fairly normal but can get interested enough in math problems to sacrifice his well-being. The genius researchers of the field sacrifice well-being regularly, without really knowing it, and are typically slightly unhinged socially.

As for myself, I tend to run away from a challenging math problem. So, even if I'm forced to tackle it, it will probably take me 10 times as long to solve as it would my brother(not even factoring in his years of experience now). Once I overcome those hurdles particular to a new category of problem I am fine, but I have to take considerable effort to do so.

Summing that difference up over a long-term period like that of a college course, the best students can zoom far ahead because of this motivation factor, even if they aren't necessarily the _smartest_. Indeed, many math students reach the upper-division levels on memorization alone and get stuck from there, as proofs take on more and more importance. That's a major failing of current math education in the United States - overdependence on rote techniques. (The former Soviet educational system, OTOH, had probably some of the strongest math education, and much of it has been translated to English - pick up a book from that period and you will probably see a small and dense text that introduces high-level concepts in great, if unforgiving, detail. Very different from the thick drill+practice textbooks I'm used to.)

My conclusion: many academic fields can accommodate a half-hearted practice. Math is not one of them. And our society doesn't respect that difference, shoving it under the rug as "I'm just not good at math."

<comment><USER9> "The former Soviet educational system, OTOH, had probably some of the strongest math education, and much of it has been translated to English - <USER2> up a book from that period and you will probably see a small and dense text that introduces high-level concepts in great, if unforgiving, detail. Very different from the thick drill+practice textbooks I'm used to."

Could you provide a url for some of these? Should I look up any specific publishers? Thanks in advance!

<comment><USER10> I second that.

This is one of the best ones:

[http://books.google.com/books?id=ikMAzFXpFOsC&printsec=f...](http://books.google.com/books?id=ikMAzFXpFOsC&printsec=frontcover)

btw if anyone wants to do a collaborative chapter by chapter self-study, just send me a private message. I have had it on my shelf for a while but haven't taken the time to do a few pages a day as intended.

</comment></comment></comment><comment><USER7> I'm not sure I ever had that reaction. I explored a few topics in different lectures in grad school which were pretty obtuse: ergodic theory, for example. I didn't get it, but I assumed it was because the topic wasn't suited to lectures, and after learning of the basic direction they were headed in and setting out myself, I found I could get pretty far.

I've seen others give up on some topic rather than the method they used to try to understand it. It's the equivalent of someone saying "I can't get math" because they're spending all of their time remembering formulae, or someone saying "I'm no good at programming" while spending their time reciting bubble sort line by line in preparation for the exam. Giving up on higher mathematics is like that. Almost always, there's some path to real understanding -- you just have to find it.

</comment><comment><USER11> In retrospect, I topped out in my upper division coursework for the math major. I still got B's and even some A's in those courses (Real Analysis, Abstract Algebra), but I was reduced to studying solution sets rather than mastering the material creatively. This was when I got more interested in applications (optimization, scientific programming, etc).

I figured I'd pick a grad program in Industrial Engineering so that I could get away from math and more into applications. Unfortunately, I picked Berkeley. A graduate intro to optimization was pretty much a series of proofs about convex sets. Same deal for stochastic processes (it might be different with different professors, though). BTW, this isn't meant as a knock on Berkeley - this theory focus is a big part of why it's such a powerhouse program. But it probably wasn't the right choice for me. I've heard Stanford is more flexible (I've also heard the grass is greener, so who really knows).

At this point, I topped out in grades as well as understanding, because I didn't have the motivation to continue. I tanked, and squeaked by with a MS. I actually missed problems that I would have gotten right as an undergraduate. I was thinking "I've had enough of proofs, I just don't want to do this anymore."

In a way, I got a lot out of the experience. My interest in academics waned, and I pretty much just started hacking with like-minded students. In other words, I finally, belatedly arrived at the process of becoming self-educated, which is really the only kind that sticks, right?

</comment><comment><USER12> Long division. 1st grade.

I never really topped out, because I always figure that when I don't understand something, I'm not smart enough to get it _yet_ , but that doesn't mean I'll never get it.

This pattern started, as I said, in 1st grade with long division. My dad had been trying to teach me math early, and I whizzed through addition, subtraction, and multiplication, but I just couldn't understand long division. My mom (who always took a dim view of acceleration) said "Just let him learn it in school with the other kids." So that's what we did, and when 3rd grade rolled around and we did long division in class, I got it right away.

I did similar things with algebra (dad first tried to teach me it in 2nd grade, didn't get it then, but I started rederiving it on my own in 6th grade and my teachers figured it was time to get me an algebra textbook) and logarithms (which I first tried in 8th grade, but didn't understand for 4 full years...that was my block through all of high school).

As for how far my formal mathematical training has gone - I aced up through vector calculus in college, and also took discrete math late in college and aced it. Also took Functions of a Complex Variable and Mathematical Logic, but got lost around halfway through each of them. Passed, but not really competent in them.

<comment><USER13> Most of us have forgotten how to do long division on paper - I guess. It is quite a nice exercised (if a bit geekish) to rediscover it on your own.

</comment></comment><comment><USER14> With one notable exception, math seems very easy to me. I open the book, write down verbatim anything labeled _Definition_ , _Theorem_ , or _Lemma_ , and trace through anything labeled _Proof_. There's nothing particularly hard about it -- you just have to make sure you actually _do_ every step listed inside your head.

It is a little slower than reading for pleasure, but with practice, I'd say only by about half.

I think the primary reason I do well, though, is that I take adderall for ADHD. Stimulants make it trivially easy to maintain the necessary level of focus, but whenever I forget to take them before a lecture or study session, I'm gnashing my teeth and tearing my hair out by the end.

<comment><USER15> As with most subjects there are levels of understanding.

One level is the ability to understand what other people are saying or doing. Another is the ability to do it yourself.

Once you get to higher level classes, at least where I went to school, the reading is relatively light but the work is relatively hard.

I don't think most people had trouble understanding the proofs -- they had trouble applying the lessons in a novel way to exercises and problems they'd never seen before.

</comment></comment><comment><USER16> I went to Cornell College, which schedules classes on a "block plan", one class at a time for a month each. My first semester, I took four consecutive courses in calculus. By the fourth one, I was extremely burned out on math and barely squeaked by.

I ended up taking a couple more math classes before graduating (discrete math and linear algebra), have continued to study math on my own, and have recently been contemplating a master's degree in math, just because I want to learn more.

All of that is to say, I'm not sure that the math brick wall is constant, but perhaps sometimes you need to take a break to allow your mind to digest what you've learned so far.

</comment><comment><USER17> When taking 2nd level honors linear algebra, we were given a takehome exam. I spent ~40 hrs on it and got just under the median grade. I was able to pull out a decent grade in that class, and I graduated with a degree in math, but now I know I'm not smart enough to hack it as a professor.

Not that I'd want to, anyway. Math is a great subject, but it's not what I'd want to do with my life.

</comment><comment><USER18> Algebraic number theory, when I was a graduate student in Oxford.

Well, sort of -- by that point I was pretty firmly on the CS side of the fence, and was just sitting in on the number theory classes out of interest. I probably could have grokked class field theory and L-functions if I had taken the time, but I was busy and it wasn't my research area...

</comment><comment><USER19> Didn't. Just lost interest.

<comment><USER20> Same. Realized I wasn't going to go through life as either a mathematician or a physicist, so didn't pursue beyond Calc 2.

</comment></comment><comment><USER21> there's learning on an academic track timeframe, and there's learning. there are lots of courses i took which i did not do well gradewise, but i learned a lot, enough to go back and re-learn the material at my own pace and better.

ultimately, all learning is self-taught.

</comment><comment><USER22> My undergraduate degree is in Computer Science, which at the time I attended the university was (if one was doing their degree in the College of Arts and Sciences vs. School of Engineering) in the math department. In the end I ended up going further than I would have naturally (just by the nature of department requirements).

First response to this question would be "what kind of math"? In terms of continuous math, I've topped out at Differential Equations (much like any other CS Major). In terms of discrete mathematics I topped out at abstract algebra (the first class that made me sigh with relief upon seeing actual numbers) and combinatorics. I felt that I could certainly go on further in the discrete field (I particularly regret not taking number theory - other than what I've learned in cryptography courses - and graph theory).

I could have received a Math major, but that would have required taking the analysis series (real and complex), which I felt would go beyond my level of abilities (particularly since I was aiming for an early graduation and wanted to take as much of classes that I felt would interest me more).

</comment><comment><USER23> I was required to take two semesters of Statistics as an undergrad. I didn't think it was especially difficult, but I didn't see applications for the things I was interested in (mainly Computational Linguistics at the time).

A few years later, pretty much all Computation Linguistics/Natural Language Processing research revolved around Machine Learning approaches, which is largely Probability and Statistics applied in various ways. I really kicked myself for not taking Statistics more seriously at the time, and not learning more.

I was away from this field for about a decade, but have been working with researchers in this field again in my current job and have been taking classes to catch up. In addition to Probability and Statistics, I've been learning Linear Algebra as fast as I can and want to take a course on Optimization.

So, I suppose the moral of the story is: you never know when that particular branch of Mathematics that doesn't seem at all relevant to you might suddenly turn out to be very relevant.

</comment><comment><USER15> I have yet to find it, but Algebraic Topology took me a long, long time to get.

<comment><USER14> My first thought on reading this was "dude, you stole my answer."

After thinking about it for a while, though, I think General Topology is worse. I still don't get it. Or, what's worse, maybe I do get it, and just don't care enough about the subject to register that fact.

<comment><USER24> I got it I think and still open up the books every now and then, but it was about topology and model theory that I started to question its applicability. I remember asking my lecturer this (I could have phrased it a little better in hindsight, I sort of burst out during a lecture 'whats the point of this' The lecturer got a little upset :-)).

Transfinite numbers are always my favorite example of something way out there, different sorts of infinities and which infinity is bigger than the other, the models are beautiful, but I couldn't spend my life arguing about them. I think for most people maths starts losing its relevance a lot earlier, it justs takes some longer to admit it, because it's prettiness is so seductive :-).

</comment></comment></comment><comment><USER25> Calculus III... I think I could have got it, but it's tough material and I had a terrible professor, so I didn't really learn any Calculus III. I passed and did much better in my final math course, a one semester differential equations/linear algebra hybrid course.

<comment><USER25> Also, my first semester I took one class of "Honors" calculus which was a proof based differential+integral Calc course. I dropped that really fast in favor of Calc II. So I also hit a wall at proof based calculus. Most of the people who actually took the class didn't get it either and resorted to memorizing all the proofs needed to derive calculus.

</comment></comment><comment><USER26> I never bothered to invest much to the math classes. The benefit didn't seem so large.

Of course, now I see how completely stupid that line of thought is. The time I saved by not attending classes or demonstrations was indeed not well spent.

</comment><comment> a-priori My most advanced math course is currently Calculus II (integral calculus and so on). However, I don't believe it's my "wall", and I'm planning on taking courses on differential equations and linear algebra whenever I have some time.

</comment><comment><USER27> Set theory & mathematical logic.

Learning math is all about spending time with the material. I find that upper- level math is easier than lower-level topics. Less grunt work, more pondering.

<comment><USER14> Foundations proofs are _the worst_. I can still remember proving something like "For every left-paren, there is a matching right-paren." Ugh.

</comment></comment><comment><USER28> I don't know if I topped-out, but I did lose interest. Calc III felt hard with not very much useful information (my comp sci advisers basically gave me grief for taking it). Linear Algebra sparked my interest again, but only because it started out wicked hard and then (just like with Calc years before), it just "clicked" and suddenly it was a lot easier/interesting. I didn't pursue further because after I graduated I preferred diving into new compsci (and engineering) concepts rather than focusing in math areas.

</comment><comment><USER29> Last class I attempted was trig, and failed completly. I enjoy math, but have given up untill after I finish collage.

</comment><comment><USER30> I'm still asymptotically approaching the "top out limit point".

</comment><comment><USER31> I very nearly hit that point taking Differential Equations my last semester, but thanks to persistence and a very helpful prof, I got over it. Not sure where I'd have ended up if I kept going, but I've always regretted not taking more abstract/"modern" algebra

</comment><comment><USER32> Seems to me all or most human understanding of maths is poor. Most things, even if we can prove them, we can not really understand them.

I wonder if there is a different way to understand maths out there.

<comment><USER33> you're probably a victim of rote learning math classes. learning math for real (getting it) is not a linear process. lots of aha moments where lots of concepts fall into place suddenly and then you move on to more advanced things.

that said, I would consider everything below calculus to be merely clever ways of tallying stones. algebra can be tricky at times (abstract algebra sucks) but it is really not that interesting in of itself (yes you can solve a lot of practical problems with it but the questions aren't generally interesting, so the answers aren't that interesting). you do need to have it down pat in order to "get" calculus however. And if you "get" at least the basic concept of calculus down a lot of things fall in to place.

OTOH I could be totally biased and/or wrong, but I personally didn't really see how math could describe complex systems in a way that let me _get_ those complex systems until calc. Some really mind blowing aha moments.

<comment><USER32> I did understand a lot of maths, I just mean that I think the way we do maths often is not really understanding. If we have proved something with a hundred step proof, I might be able to verify every single step of the proof and conclude that it is correct. But we might not really have a feel for why it is correct. Can't really think of a good example right now :-/ I mean usually we jump through quite a few hoops to prove something - maybe there are other ways of looking at it that would make more sense.

One example might be the autistic people who just know if a number is prime or not. Not sure if they are really doing anything special, or just calculating really fast, though.

<comment><USER13> If you search long enough you usually hit upon a prove that does looks more like a really explanation than like pulling a rabbit out of a hat.

</comment></comment></comment></comment><comment><USER34> Got my masters in math, then kinda lost interest, but I'm pretty sure that everything is understandable with a little effort. When I get genuinely interested, no effort is required at all.

</comment><comment><USER35> Vector Calc, because I stopped caring. Somehow Diff. Eq. held my interest but vector didn't. Calculating the area of partial 3D oval objects for the sake of doing it was painful.

<comment><USER13> Diff. Eq.: Difference Equation or Differential Equation?

</comment></comment><comment><USER13> Perhaps differential equations for me. But that's more a question of motivation. I like optimization more and look forwand to having more lectures.

</comment><comment><USER36> Multivariable Calc and Linear Algebra kicked my ass. I didn't really do much beyond that.

</comment><comment><USER37> Math is pointless if you are not planning to apply it at some point in your later career. Learning algebraic topology when you are studying digital circuits is like learning literary analysis - it may make you feel smart, but it's a damn waste of time.

</comment><comment><USER38> My first math class at MIT. :-\

</comment><comment><USER39> Geometry, Logic, Trigonometry

</comment><comment><USER40> For me the brick wall was social, not related to the math, and I hit it in geometry class in 10th grade. Our teacher was an idiot, and had trouble solving the more difficult proofs at the end of the homework. Day after day I would go up to the board and write down the solution to the problem he couldn't solve. Then, I would get an F for not turning in my homework, which I rightly considered to be a waste of my time, and the people who copied down my answers would get an A's. That was when I decided I had enough formal mathematical education. I taught myself the math to do AP chemistry in high school and tested out of pre calculus in 2000 in college. I am currently teaching myself calculus from Michael Spivak's Calculus. You couldn't get me back in a math class, but I love learning math.

</comment><comment><USER41> did he mean "tap out"? as in UFC "tap out"?

can't get enough of Math (although I barely passed Linear Algebra and Numerical Analysis). Maybe it's the challenge. I shall try more of it when I take up a Masters in CS. :P</comment>


Id Software parent stakes claim on Carmack's Oculus Rift technology - <AUTHOR> http://arstechnica.com/gaming/2014/05/id-software-parent-stakes-claim-on-carmacks-oculus-rift-technology/

<comment><USER2> Mind boggling, how is one supposed to change jobs? A company pays good money to attract top talent, but they must forget best practices and experience they developed at their previous job. Experience and knowledge should be allowed to follow the employee.

<comment><USER3> I had the good fortune of getting some advice from a couple of veterans of the Dallas gamedev community: they can't take what you have in your head, your knowledge and skills.

That said, the anticompetitive behavior of large tech companies and small game companies and startups is really saddening to watch.

They want us bound to desks with golden chains, doomed forever to toil on their pet products.

The key to growing as an engineer and the development of a new technology in general is being able to "play"\--being able to talk to other older, wiser, and/or crazier folks without fear of repercussion or reprisal, of being able to develop something which may or may not go anywhere.

You know, the sort of innovation that patents were _supposed_ to protect.

</comment></comment><comment><USER4> Carmack be quaking with rage at those heretics as they try to spell doom for Oculus.</comment>


Startup School is going global - <AUTHOR> http://blog.ycombinator.com/startup-school-is-going-global <comment><USER2> Yet another respectable move for YC. Hopefully this will spur more global interest in starting a startup. One thing I really appreciate YC in recent year is making the startup school videos online so those can't attend will not miss the talk. Of course those attend will meet tons of amazing people. Bringing in smart and talented people into one room just sparks insightful conversations. First in valley, and now globally.

Thanks, YC. That is so unselfish.

<comment><USER3> > One thing I really appreciate YC in recent year is making the startup school > videos online so those can't attend will not miss the talk. Of course those > attend will meet tons of amazing people.

Conferences in this day and age are strange beasts. The value of going to listen to someone is, IMO, lower relative to the past because of videos, and, even better, transcripts and notetakers who summarize and eliminate all the blah blah blah. The value of talking to people in person though, is still pretty high, as well as serendipitous meetings and discussions. I'd love to see people experiment with different formats that involve less of the former and maximize the latter.

<comment><USER4> I go to conferences because the level of passion and excitement in the discussions (and friendly arguments) had there greatly surpasses anything I've come across at a meetup. It's a shame they usually cost almost $1000 or more apiece.

</comment></comment></comment><comment><USER5> > We're starting with New York and London, but in the coming years we hope to > head to Asia, South America and Africa.

I hope they have India on their radar! It would be awesome for the Indian Startup scene to hear all those great speakers live!

<comment><USER6> I doubt YC would want to enter India market. For all the talent and entrepreneurial spirit that Indians have our startup culture sucks. There are several reasons:

1\. The infrastructure: India doesn't have the tech infrastructure. Take the 3 major e-commerce requirements for example: internet access, online payment and delivery. Even the basic internet infrastructure in India sucks. Most people access the internet over their phones because getting home internet is still a pricey affair for most people. A pretty small number of people have access to credit cards and for those who do, processing payment online is a huge pain. The postal infrastructure is also pretty bad. India post is flaky and other courier companies are pretty bad or expensive or both.

2\. Government interference: Indian government is inconsistent, heavy-handed and has very little interest in improving the tech sector. Most state governments are downright hostile.

3\. Lack of exit opportunities: Indian tech sector lacks big players who can provide the entrepreneurs and investors meaningful exits. The culture of acquisitions as a meaningful way to get market advantage is not there. Your only hope is sell to a American or a European company looking to gain a foothold in the region (rare) or IPO (even rarer).

4\. Corruption and general apathy: To get anything meaningful done in India is a struggle. From getting setup as a company to getting a good internet connection. You have to fight corruption and apathy of the organizations (both public and private) you are dealing with.

5\. Labor laws: Labor laws in India are a joke. They are a relic of the socialist times and are heavily biased on the side of the employees. Setting up any type of manufacturing or operations in India is a legal nightmare. If that's not enough, the trade unions operate as a mafia and its downright dangerous to deal with them.

There is a lot of opportunity in India too but until we overcome the problems that entrepreneurs and investors face, Indian tech startup scene would never take off.

<comment><USER7> I thought the idea of Startup School was to "sell" YC to founders there, along with the implicit idea of moving to SV. Seems like a stronger case for India than a lot of other places (great founders, but fucked up environment, so they have the most relative advantage to moving, especially if they can keep enough connections to India to continue to recruit for remote or relo.)

<comment><USER6> I don't know what Sama's plan is but it doesn't scale very well. If you plan to fund thousands of promising startups, I don't know if you would want to bring them all to the US. The biggest reason for that for the first few years startups succeed more in one geographical region (as in one industry industry segment and one customer profile) and asking them to move might not be the best of idea. It will work for some but will destroy some other promising companies.

</comment></comment></comment></comment><comment><USER8> UK is too far for most of Europe. Berlin would've been a more optimal choice. UK has pretty poor/insane border policies, too, as we all know by now, and not too eager to visit it.

<comment><USER9> Yep. Germany is part of the Schengen accord, and most people from Europe can travel there without a visa (even if they are not part of the EU yet). While England requires visas for most countries.

Also, London is not really a tech center anyways. Poor choice.

<comment><USER10> > _" Also, London is not really a tech center anyways. Poor choice."_

A lot of tech companies have made London their base, including some prominent YC companies. London is so big that it's many things to many people so if you think it's 'not really a tech center', please elaborate why.

<comment><USER11> For what it's worth entrepreneur.com had London as #7 globally in the Top 20 Startup Ecosystems, the highest in Europe but well behind SV and Tel Aviv. [http://www.entrepreneur.com/dbimages/article/the- worlds-20-h...](http://www.entrepreneur.com/dbimages/article/the- worlds-20-hottest-startup-scenes.jpg)

</comment></comment></comment></comment><comment><USER12> I appreciate the idea of making startup school a more global event. Frankly speaking for a lot of entrepreneurs making a trip to the bay area can be a substantial dent on their pockets. I attended the previous year's startup school and the experience and outcomes was phenomenal. I hope the quality of speakers continues to maintain the current high standards and provide deep and much needed insight.

</comment><comment><USER7> This is a great idea!

I wonder how YC could do a "Startup School Asia" \-- in general, for a larger percentage of Asian founders, travel between countries in Asia is difficult, compared to European founders (where IMO you could have SS in virtually any major city and be no worse than 50% as good as any other in terms of access; London is great but expensive, Berlin would be my pick.)

Singapore is probably the easiest and best choice for Asia, but there are strong arguments for HK/SZ, Beijing, Shanghai, one of ~10 cities in India, etc.

<comment><AUTHOR> There was a lot of debate over whether we should do the first European SUS in London or Berlin. Both cities are great and each has its benefits.

We have some awesome YC alum in London (and the YC community there is growing), and we're excited that they'll be joining us in July. We'd love to do something in Berlin as well.

<comment><USER7> IMO the best way for YC to do something to start with in Germany would be to get involved in CCC/31c3. (CCC is a weird combination of IEEE/ACM and hackerspaces, and huge in Germany)

A "how to turn your project into a company? should you, and why?" talk by YC (ideally, with European YC company founders, ideally in the product spaces most interesting to CCC hackers) would be awesome. The downside is it's 27-30 DEC in Hamburg.

<comment><USER10> In principle there isn't any reason a YC partner couldn't just give a talk if they wanted to. For example Harj did a session at HackerNews London just over two years ago [1]. I don't recall it being an official 'YC Event', just one of the partners who happened to be in the UK at the time and was willing to do it.

However, looking at the current list of YC partners [2], I don't see many that might have ties to Europe, such that they'd be visiting much (never mind the imposition of giving up family/holiday time to give a 'work' talk).

[1] [http://vimeo.com/30800728](http://vimeo.com/30800728)

[2] [http://ycombinator.com/people.html](http://ycombinator.com/people.html)

</comment></comment></comment></comment><comment><USER13> "Startup School is a free, one-day event where you'll hear stories and practical advice from founders and investors."

Not being a fan of rah rah one day type seminars [1] I'd like to know the percentage of people who attend these types of 1 day events and actually go away with something tangible that allows them to create something as opposed to just feeling good or pumped up for a short period.

Separately, the act of actually traveling somewhere to attend is a bit different [2] than not traveling or not being able to (for reasons other than money). I wonder how that will change the benefits of the material presented.

[1] Forgetting the quality level, which I'm sure is high, it reminds me of real estate or investment seminars that go from town to town. (Of course those also have another ulterior purpose (to sell books or dvd's)).

Edit [2] I mean the level of commitment would seem to be higher for someone who actually decides to make a journey and attend to better their future vs. someone who doesn't (not that people who attend locally wouldn't travel of course..)

<comment><USER14> I see the value as twofold:

a) being inspired [by the right kind of founders, not get-rich-quick schemes] and pumped up. It could mean the difference between launching your startup and staying in your comfy day job

b) random encounters of other people who are more like you than most people you meet everyday. That also has tremendous value. But you'll never know if you never show up.

</comment></comment><comment><USER15> I am looking to apply to the New York instance, as it is close to where I am located, however I am not exactly sure what someone would get out of going. From the outset it seems as though it would be very valuable to go, but I can't really tell what the tangible benefits are from going.

It is clear that I would be able to see world class speakers - but I can also do that online as I did last year when I watched a large portion of the talks posted. So is it also a networking event (obviously all these are that to some degree)?

I guess I am just trying to figure out if it is worth taking a day away from my startup, and spend money to get up to NYC to go (assuming I even got in). Can anyone with experience having gone to one of these give some insight? Thanks.

<comment><USER16> If you are in the "in" group, there's an invite-only event the night before. That is obviously valuable as you will have been vetted in some way thus draw more attention from vc's etc.

Otherwise, if you've seen the videos of previous years, you'll get exactly the same (which is quite good), however I am disappointed in the lack of slides to go with the presenter video recordings.

So if you don't have an in for the pre-event, there's not a whole lot to be gained by a physical presence.

<comment> bra-ket God, this is obnoxious, why do you need to desperately try to draw attention of the freaking VCs? They will come to you and beg on a doorstep for a precious minute of your time if you have a working business. Talk to users and iterate on your product, don't waste your time listening to god damn inspirational talks and schmoozing with investors.

<comment><USER16> not saying you desperately need to do anything, just stating the only real benefits of a physical presence I see....

</comment></comment></comment></comment><comment><USER13> Question for the OP, YC, PG, dang, or anyone else.

YC owns both startupschool.com and startupschool.org but you have the .com redirecting to the .org

While .org can be (and often is used) for anything it is typically associated with organizations and more specifically non-profits [1]. So I'm curious why you don't simply have this info under the .com since obviously the overwhelming majority of your involvement is on a for profit basis (the companies you fund are almost always for profit) and the school, while free, is really a marketing feeder for YC which is for profit.

[1] Source: Me, I've been doing this "domain thing" since the mid 90's.

</comment><comment><USER17> I wonder , is this a part of an effort to scale YC globally ?

<comment><USER18> Could be testing the waters for that. Could also be prep work for a contingency plan if US startup visas don't happen.

<comment><USER19> I'm under the impression that the UK will grant a Tier 1 (Entrepreneur) visa to founders that have access to £50,000 in VC funding[0]. It would make a lot of sense of YC to open up shop here in the UK.

[0] [https://www.gov.uk/tier-1-entrepreneur/access- to-50000-inves...](https://www.gov.uk/tier-1-entrepreneur/access- to-50000-investment-funds)

</comment></comment></comment><comment><USER20> Good to know that I'll be able to make it to the one in London during my trip to Europe. Anyone knows the invitation rate or how they assess the attendees?

</comment><comment><USER21> Montreal is a beautiful city to have a Startup School in...

</comment><comment><USER22> Just applied for the London event. For a second I was surprised to see that "going global" meant "New York" until another second later I've read "London", which still isn't global but a step forward. Very happy to see you guys coming around!

</comment><comment><USER23> I've made the trip out to Startup School for the past few years. I'll still go to the original one, but now that I'm back on the east coast, it'll be nice to hang out in a similar event with a different crowd. Excited!

</comment><comment><USER24> What's the recommendation on applying to multiple Startup Schools? I've been to the last two, but I live in NYC. Do you consider it rude to apply to NYC now, and the Valley one in the fall, and take up two spots?

<comment><USER25> I'd recommend limiting your attendance to one. Our goal with SUS has always been to share a lot of useful and inspirational advice from startup experts. We'd like to keep as many seats open as possible for people who've never been.

<comment><USER26> Is it OK to apply to both? I'm living in NY but am from London so I checked both on the off chance that one was full.

</comment></comment></comment><comment><USER27> It's worth noting that it's a national holiday in the UK today so many of the local HN regulars are likely to miss this announcement so it might be worth making another one at some point prior to the deadline.

<comment><USER19> It worked out for us — it's 10am the next day and it's prominently placed, so we won't have missed it!

</comment></comment><comment><USER28> Stepping out of your hometown to do a one day workshop is going global ... yay.

</comment><comment><USER29> It seems like it's aimed purely at developers & designers, but from past sessions, this would be useful for any kind of founder.

What's the deal for technically minded founders that aren't devs/designers?

<comment><USER10> Just apply. The form is pretty simple and will only take a few mins to fill out. There's no need to 'pre-reject' yourself.

</comment></comment><comment><USER30> Thanks for the update! is there a list to get on for other countries?

<comment><AUTHOR> You'd likely hear the news here first. But you can sign up for YC's mailing list: [http://eepurl.com/G3Aiz](http://eepurl.com/G3Aiz)

<comment><USER30> Just did , Thnx!

</comment></comment></comment><comment><USER31> This is great news for us in Europe. Thank you!!!

</comment><comment><USER32> I never new about this, but I would love to go. And they are coming to NY which is awesome because that is where I am, except for about 4 days in June (one of which is the 18th) when I'll of course be in Mountain View. Maybe next year :(.

</comment><comment><USER33> are videos from previous startup schools available online?

<comment><AUTHOR> Videos from SUS 2012 and 2013 are on YouTube. Playlists for each are here: [https://www.youtube.com/channel/UCcefcZRL2oaA_uBNeo5UOWg/pla...](https://www.youtube.com/channel/UCcefcZRL2oaA_uBNeo5UOWg/playlists)

</comment></comment><comment><USER34> Right during the Europython for the London one.

That's annoying.

</comment><comment><USER35> Wow. This will be interesting to watch. :)

</comment><comment><USER36> Please come to Cape Town! :)

</comment><comment><USER37> Interesting that Silicon Valley believes that going to NYC is "going international"!

<comment><USER22> Watch out mate, I've been voted down into oblivion for saying the same (and adding that with London it's okayish to say "global").

Obviously the idea is to attract European and Middle East attendance in the London event and I think it is a good choice. Pretty much any airport in Europe flies to London and there are plenty of low cost flights (Ryanair, Wizzair, Vueling, Norwegian, Easyjet, etc) as opposed to e.g. Berlin.

<comment><USER37> Yes, a post like mine, intended to be comedy, can be too close to the line of nasty criticism and look mean. But it was fun to take the opportunity to crack a joke suggesting that Silicon Valley is so insular that they regard NYC as going international!

That's a lot of air traffic just for warm beer! But, where do people in London live? I mean with all the Russian and Mideast money buying up all the properties, a little one room condo goes for, what, $20 million?

And, England is a huge step down from where it was when Di was alive.

</comment></comment></comment><comment><USER38> 95% of the best founders are outside the US? Really? if that were the case we'd have seen a lot more publicly traded companies of the size of Yahoo, Microsoft, Intel, eBay, etc. If it could have happened, it would have happened. We aren't even tapping the founder set we have in the US proportionally.

I applaud the concept of adding diversity to the pool (even-gasp! people with accents--) but I have a sneaking suspicion this is really about finding cheaper labor for the us based companies in the end. What investors are really going to put money into companies in countries in Africa and Asia where property rights, IP, and other laws don't protect companies as well as the US? What about places that demand even more corporate taxes? Color me skeptical.

<comment><USER39> US Population: 317,987,522 World Population: 7,164,066,667

Source: United States Census Bureau - [http://www.census.gov/popclock/](http://www.census.gov/popclock/)

By those estimates, the United States accounts for less than 4.44% of the world's population. Or, to put it another way, more than 95% of the world's population is outside the US.

So, unless you believe that there is something special about people in the United States that makes them better founders than people from other countries, it's not a massive stretch of the imagination to conclude that there are 19x as many good founders outside the US as there are inside it.

<comment><USER32> Actually I would argue that it is a big stretch of the imagination that there are 19x as many good founders outside the US. The problem is by the opportunity provided of where people live, their status is society, and a variety of other factors such as available education, access to technology etc. For that reason the multiplier has to be much less.

</comment></comment></comment><comment><USER40> So yes, I would like to join "SC Europe" but I won't be able to make it to "London". Maybe call it "SC London"?</comment>


Show HN: Light Flip – A cell inversion puzzle game - <AUTHOR> https://play.google.com/store/apps/details?id=com.rmal30.lightflip&hl=en <comment><USER8> Why is this one different from the hundreds of similar clones?

<comment><AUTHOR> Lights Out flips the neighbouring cells, this game flips all cells in the same row or column

<comment><USER9> You should probably make this really clear. I probably wouldn't download either version, however without any clear difference from the other 1000s of clones I instantly dismissed it after not seeing anything new.

<comment><AUTHOR> Added a note

</comment></comment></comment></comment><comment><USER10> On even board to flip a square, hit square and hit all other squares in the same row and all other squares in the same column.

To flip 4 squares in a 2 x 2 arrangement, hit all of those 4 squares.

What makes the bigger grids hard is the size of my little finger.

</comment><comment><USER11> This reminds me of a puzzle in an old point-and-click adventure with a Fridge with a lock like this...

[http://questgame.ru/images/pilots/2.jpg](http://questgame.ru/images/pilots/2.jpg)

</comment><comment><USER12> I had fun playing this game for a while. Eventually I discovered some fairly reliable algorithms which enabled me to collect all the achievements. I'd like some bigger boards to have a go with now!

<comment><AUTHOR> Glad to hear that you're enjoying the game! I've added the 8x8 board. In the average case, it can be solved in around 32 moves using the most optimal algorithm.

<comment><USER12> Thanks :-)

</comment></comment></comment><comment><USER13> I haven't downloaded the app, so maybe this makes sense somehow, but the following text from the app description confused me:

Difficulty ratings:

\- 2x2 board - <USER3>

\- 3x3 board - <USER3>

\- 4x4 board - <USER7>

\- 5x5 board - <USER5>

\- 6x6 board - <USER6>

\- 7x7 board - <USER7>

Shouldn't the difficulty rating increase with increasing board size?

<comment><USER14> Solving an even square might be inherently harder than an odd square. I haven't played the game though.

<comment><AUTHOR> Yep, it requires n^2 moves for even boards while odd boards require less moves (no formula found yet). Using a computer, I found, by brute force, that the 5x5 can be solved in 8 moves at most, the problem quickly becomes intractable for 7x7 and above. It looks like this might be NP hard according to another post: [http://stackoverflow.com/questions/27436275/how-can-i- furthe...](http://stackoverflow.com/questions/27436275/how-can-i-further- optimize-this-solver-of-a-variant-of-lights-out)

</comment></comment></comment><comment><USER15> Strategy that seems to be pretty effective: click all the squares that are originally yellow

</comment><comment><USER16> Why would anyone play this game when he could just diagonalize (nxm)x(nxm) matrix in F2 and get a basis? (in case of non-singular, otherwise impossible) upd: misunderstood the game, it's about solving Ax=b in F2, so Gauss elimination.

<comment><USER17> Yeah, that's what the rest of us were thinking as well.</comment></comment>