<story><title>Lost in Math?</title><url>https://cacm.acm.org/magazines/2019/3/234913-lost-in-math/fulltext</url></story><parent_chain></parent_chain><comment><author>throwawaymath</author><text>&lt;i&gt;&amp;gt; About 10 years ago, in the wake of the 2008 financial crisis, the Nobel Laureate economist Paul Krugman made the same point with respect to economics and mathematics in an influential article titled &amp;quot;How Did Economists Get It So Wrong?&amp;quot; His main answer was: mistaking mathematical beauty for truth. &amp;quot;As I see it,&amp;quot; wrote Krugman, &amp;quot;the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.&amp;quot;&lt;/i&gt;&lt;p&gt;I appreciate the point the article is trying to make, but I think this example is shoehorned in. You can misuse math without it being because you&amp;#x27;re &amp;quot;seduced by the beauty&amp;quot; of it.&lt;p&gt;I do agree with the author&amp;#x27;s example in physics. I have seen a lot of beautiful math in physics; look at lie algebras, monstrous moonshine and representation theory. Quite a bit of modern physics PhD dissertations are actually just math dissertations, and the same holds for a significant amount of new research in the field.&lt;p&gt;On the other hand I haven&amp;#x27;t seen that in finance. Highly exotic (read: &amp;quot;beautiful&amp;quot;) mathematics is extremely rarely used in financial engineering. Pricing derivatives is decidedly mundane work compared to the brain-meltingly abstract mathematics deployed in high energy particle physics research. That&amp;#x27;s not to say it isn&amp;#x27;t difficult - it is difficult! But difficulty is better described by the word &amp;quot;complex&amp;quot; rather than &amp;quot;beautiful&amp;quot;, and then &lt;i&gt;of course&lt;/i&gt; financial engineering is complex. Then we should be talking about how getting mired in complexity can be bad for accountability and transparency.&lt;p&gt;This is a different thesis than the one presented by the author. Being led astray because you&amp;#x27;ve built extremely brittle financial products using layers of complicated math is &lt;i&gt;not&lt;/i&gt; the same as being more preoccupied with the elegance of a grand unifying theory than its agreement with reality.&lt;p&gt;But hey, maybe I&amp;#x27;m just being pedantic. You can misuse mathematics in a lot of ways.</text></comment>
<story><title>Lost in Math?</title><url>https://cacm.acm.org/magazines/2019/3/234913-lost-in-math/fulltext</url></story><parent_chain></parent_chain><comment><author>dkarl</author><text>&lt;i&gt;But complexity theory aims at describing the performance of A over the space of all problem instances and it does so by abstracting away from individual problem instances.&lt;/i&gt;&lt;p&gt;I appreciate the effort to extend the story into CS, but I wonder if you have to be familiar with the particular work he&amp;#x27;s alluding to.  The charge (as leveled against theoretical physics) is not that some people do pure mathematical work for the sake of beauty.  The charge is that people who are &lt;i&gt;supposed&lt;/i&gt; to be applying mathematics to reality are instead prioritizing mathematics and neglecting reality.  To extend the analogy to CS, he must be talking about researchers supposedly trying to model real systems but instead just chasing beautiful math, but he isn&amp;#x27;t specific.  Is it obvious to people in the know who or what he&amp;#x27;s talking about?&lt;p&gt;For practical programmers, I think the problem is the reverse of being &amp;quot;lost in math.&amp;quot;  Practical programmers use extremely general theoretical results because they &lt;i&gt;don&amp;#x27;t want to do&lt;/i&gt; math, not because the math is more beautiful.  If they applied the information they know about their particular problem, they could get more useful mathematical results, but since they want to stay as far away from (doing) theory as possible, they use whatever facts they remember from class, which are ironically the most purely theoretical ideas because those are the simplest and easiest to remember.</text></comment>