Potentates and plutocrats get their names plastered all over the landscape, but as far as I know you can’t yet buy the naming rights to a theorem in mathematics. You’ve got to actually do the math.

I’ve just (belatedly) discovered a thoughtful catalog and discussion of some mathematical eponyms. Dave Rusin of Northern Illlinois University has sifted through the Mathematical Subject Classification—a list of some 5,000 topics—and extracted all names of persons mentioned there. Rusin’s analysis was first posted to the Usenet newsgroup sci.math in 1998; the latest revision (updated in 2005) is available at Rusin’s web site.

Working with the 1991 version of the MSC, Rusin identified 357 terms that seem to refer to persons, and he put considerable effort into identifying *which* persons. It’s not always obvious. There’s only one Euclid in this crowd, but Hopf algebras and Weiner-Hopf operators are named for different Hopfs. And it’s always a nightmare sorting out the Bernouilli brothers—and cousins and uncles.

Many prominent mathematicians have their names attached to multiple concepts and so are mentioned more than once in the MSC ontology. Rusin’s top-ten list of mathematicians with the most MSC citations reveals some surprises. Riemann and Hilbert make the cut, but not Euler or Gauss, Archimedes or Newton. The No. 1 spot, with 54 citations, is occupied by Sophus Lie, a Norwegian best known for his contributions to group theory and algebra. Niels Henrik Abel, another Norwegian algebraist and group theorist, is at No. 6. And at No. 8 we find Evariste Galois, who, though not Norwegian, worked in some of the same areas. Perhaps there is some career advice in this cluster for those seeking mathematical immortality?

It so happens that I stumbled upon Rusin’s list while googling about for information on Ernst Jacobsthal, whom I have twice (link 1 and link 2) mentioned here recently. Jacobsthal’s name is indeed present in the MSC (Subject 11L10: “Jacobsthal and Brewer sums; other complete character sums”), and I think I know how he got there. When he was driven out of Germany by Nazi persecution, where did he take refuge? In **Norway** of course! But he made the strategic mistake of studying number theory rather than algebra or group theory and thus has only one entry in the MSC.

“You can’t yet buy the naming rights to a theorem in mathematics.”

That’s only mostly true.

One apparent exception is l’Hospital’s rule. Here is a relevant clip from l’Hospital’s Wikipedia entry:

“In 1694 he forged a deal with Johann Bernoulli. The deal was that L’Hôpital paid Bernoulli 300 Francs a year to tell him of his discoveries, which L’Hôpital described in his book. In 1704, after L’Hôpital’s death, Bernoulli revealed the deal to the world, claiming that many of the results in L’Hôpital’s book were due to him. In 1922 texts were found that give support for Bernoulli. The widespread story that L’Hôpital tried to get credit for inventing de L’Hôpital’s rule is false: he published his book anonymously, acknowleged Bernoulli’s help in the introduction, and never claimed to be responsible for the rule.”