"Why Mathematicians Should Stop Naming Things After Each Other"

Why Mathematicians Should Stop Naming Things After Each Other

Interesting piece in Nautilus about mathematics and the lack of accessibility that comes from using mathematician’s names to describe their results:

When everything is named for its discoverer, it can be impossible even to track the outline of a debate without months of rote memorization. The discoverer’s name doesn’t tell you anything about what the landscape is like, any more than the “Ackerman” in Ackerman’s Island helps to convey a sandbar in downtown Wichita.

This nesting of proper nouns helps to make higher math impenetrable not just to outsiders, but also to working mathematicians trying to read their way from one subfield into another. The venerable Bill Thurston was known to complain about the perversity which, by the end of his career, had produced Thurston’s theorem, which says that Thurston maps are Thurston-equivalent to polynomials, unless they have Thurston obstructions. Every field has terms of art, but when those terms are descriptive, they are easier to memorize. Imagine how much steeper the learning curve would be in medicine or law if they used the same naming conventions, with the same number of layers to peel back:

This seems sensible to me, but there’s a catch. How else can you name abstract results? When the results are “pure” you often have no intuition upon which to anchor your name, and physically intuitive names can be misleading. Yes, it hurts accessibility, but by the time you reach the frontier of mathematics, you are already pushing to the extremes of human understanding.

A mix of naming styles is likely the best option. Results in mathematics, like science, undergo a kind of evolutionary selection, with important and understandable results bubbling up and less important results fading away. A good choice of name is one way to increase an idea’s “fitness”.

I also feel that it’s important to celebrate and humanize our heroes, and naming results after people is one way to do it. Learning the histories of past generations of mathematicians and scientists is fascinating and, at least for me, knowing personal biographies helps me remember results. There’s a lot of bias in these histories, though, and using surnames to memorialize results marginalizes women, so there is still work to be done.