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Ars Mathematica

Dedicated to the mathematical arts.

The Art of MumfordDecember 21 2008

The language of schemes relies on a dramatic extension of the notion of points. David Mumford’s Red Book on Varieties and Schemes is full of drawings that try to communicate these exotic new sorts of points. Lieven Le Bruyn explains.

Your Vocabulary LessonDecember 9 2008

Aimless websurfing has taught me that mathematics is apodictic. Now you know.

The Appeal of MathematicsDecember 8 2008

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 stereotyp

Thanks for Spin-Statistics TheoremNovember 29 2008

Cosmic Variance has a cute little tradition where for each Thanksgiving Day they pick a physics result to be thankful for. This year they pick the spin-statistics theorem, which explains why elementary particles with half-integer spins satisfy the Pauli exclusion principle.

Physics Books for a Math Ph.D. StudentNovember 19 2008

Slashdot has a thread discussing physics books recommendations for a math Ph.D. student who would like more physical intution into partial differential equations. There are some good suggestions, and many comments that come dangerously close to “You’re a math Ph.D. student and you don’t know what a PDE is?”