Opinion 158: The American Mathematical Society Should not Force People to Stop using The Historical Names of Mathematical Theorems, Conjectures, Theories, Etc. and Replace Them by their AMS-ID-numbers: Galois Theory Should NOT become Theory001040 and the Riemann Hypothesis Should NOT become Conj011400

By Doron Zeilberger

Written: April 1(!), 2017

The American Mathematical Society (henceforth AMS) has recently created the position of Diversity Officer, a full-time position, womanned by a prominent female mathematician. That's a good thing! Women and minorities should be encouraged. But it went too far when it proposed, effective Jan. 2019, to prohibit the use of the traditional names of the numerous programs (e.g. Erlangen, Langlands, ...), theories (e.g. Galois, Iwasawa, and dozens of others), theorems (e.g. Pythagoras, Lagrange, and thousands of others), polynomials (e.g. Legendre, Jacobi, and hundreds of other), conjectures (e.g. Riemann and many others), inequalities (e.g. Cauchy-Schwartz, Holder, and dozens of others), groups (e.g. Conway, O' Nan, Lyons, Sims, Thompson, ...), algorithms (e.g. Dijkstra, Buchberger, Robinson-Schenstead-Knuth, and thousands of others) etc. etc.

The well-intentioned, but misguided, rationale is that with very few exceptions (e.g. Noetherian rings, Cauchy-Kowalevsky theorem, Moufang loop, Sister Celine's Technique, Daubechies wavelets) all the names are those of men, and this sends an unfair, subliminal message, and a reminder of the great historical injustice where, until recently, only men could do mathematics. Even besides that , Mathematics is discovered, not invented, and Pythagoras' theorem belongs to all of us, and it is just a historical coincidence that someone called Pythagoras happened to be the first one to discover it (and, in fact, at least in this case, it is very debatable, and there are lots of mis-attributions in the history of mathematics).

The proposal was inspired by Neil Sloane's amazing OEIS, where every sequence has an "A-number", so one no longer has to say "the Fibonacci sequence", but rather `Sequence A000045', and instead of `Catalan Numbers' one says `Sequence A000108'. According to this proposal, the AMS would create analogous databases for theories, theorems, conjectures, functions, polynomials, inequalities, identities, formulas, rules, lemmas, sieves, and even programs, and assign an id to them, and state them each with references to proofs and their traditional names, that should only be used in historical articles. Every article published in one of their prestigious journals should only use the standard IDs of theorems, conjectures, theories, etc.

So brace yourself. In two years, you would open-up an AMS journal, and read an abstract that looks like this:

"Using Theory T1014, and Theorems Th100154, Th54135, and Th87651, as well as inequalities In54312, and In34567, we prove Conjecture C84231."

Please! Mathematics papers are hard enough to read the way they are written now, and this new policy would make reading them so much harder. It is true that few people read papers any more, and eventually, only computers will write and read papers, and for them using numbered-theorems would be preferred, so let's postpone this reform for another fifty years, when humans will no longer care how unreadable a mathematics paper is, since no huamn will be stupid enough to read them.

Opinions of Doron Zeilberger