I was musing on the fact that I have never heard a psychologically plausible account of the appeal of pure mathematics. (I say “pure” mathematics because I suspect pure and applied mathematics have different sources of appeal). By “psychologically plausible”, I mean one grounded on the psychology of individual mathematicians. Lots of mathematicians have written explanations of the appeal, but most of these are either of the form “Because mathematics is awesome.”, or “Because I’m awesome” While mathematics is awesome, and while I’m willing to grant the premise that I’m awesome pretty much any time it comes up, these explanations lack the kind of specificity I have in mind. One common explanation, for example, is that math is like music, which relies on the presupposition that music is intrinsically valuable, and that math has value by analogy. But why do we like music? What in the psychology of mathematicians makes math seem like music to them? These are harder questions than the original one. Another explanation is that math is challenging, which is a subspecies of the “I’m awesome”. But in what way is mathematics challenging to mathematicians? Mathematicians, as a group, do not strive to be Nietzschean superman endlessly trying to overcome their limitations, so why this particular challenge, rather than the Nathan’s hot dog eating contest, or climbing Everest?
There are psychological explanations floating around as stereotypes, most of which are immensely unflattering, but are least examples of the kind of explanation I have in mind. One example is that mathematicians are like the Rain Man in that they just like repetitive tasks like counting or adding. Another example is that mathematicians can’t handle the real world, and so retreat to the safety of the world of numbers. These are both wrong and insulting, but they are at least grounded in the psychology of individual mathematicians. If anyone has a non-wrong explanation, I’d be curious to hear it.