## 12 February 2009

### The Arbesman limit

Samuel Arbesman talks how to get something named after yourself. Of course, he names something after himself -- the "Arbesman limit", which is the number of things that one person can have named after themselves. (Gauss, Euler, etc. provide a lower bound for this limit.)

Supposedly Banach originally named his spaces "spaces of type B" or something like that, figuring that people would see the B, assume it standed for Banach, and start calling them Banach spaces. If that's true, it worked.

Anonymous said...

reg Stigler's Law of Eponymy, isn't there something similar in math :

The Arnold Principle. If a notion bears a personal name, then this name is not the name of the discoverer.

The Berry Principle. The Arnold Principle is applicable to itself.

Anonymous said...

That reminds of the data structure B-tree. It was invented by Rudolf Bayer and Ed McCreight, but they never explained what B stood for.

Maybe Bayer hoped it would get called a Bayer tree.

Anonymous said...

For instance, the Pythagorean theorem was known to the Egyptians.

Interesting.

Hilbert, though, was pretty successful too, right? We have Hilbert's Theorem 90, Hilbert's Nullstellensatz, Hilbert or Hilbertable spaces, the Hilbert transform, the Hilbert class field, Hilbert manifolds, the Hilbert basis theorem, the Hilbert polynomial, the Hilbert syzygy theorem, the Hilbert symbol, and Hilbert problems. Those names span analysis, algebra, number theory, and algebraic geometry.

Weierstrass, by contrast, who helped develop the foundation of analysis, has much less named after him. I believe he proved the theorem on expanding holomorphic functions locally in power series, but that theorem is not normally given a name. I can think of the Bolzano-Weierstrass theorem, the Weierstrass preparation theorem, and not much else.

Anonymous said...

Apparently Norbert Wiener claimed to have independently come up with the idea of Banach space, and tried to cement his claim by talking about Banach-Wiener spaces. It didn't catch on.

This suggests to me a rule of thumb: don't look like you're trying too hard to get something named after you. Maybe try instead to get a friend or two to do the naming for you, then sit back and bask in the glory.