grammar - "the Poincare conjecture" but "Bolzano's theorem"

Consider these two ways of coining a name: 1) Bolzano's theorem, Rolle's theorem 2) the Poincare conjecture, the Kantorovich theorem. What is the difference between these ways, why do people choose one over the other?

My guess is that the main difference is when you put 's at the end of a name, you strictly imply that the theorem/conjecture was written by this very person (Bolzano wrote Bolzano's theorem). But when it is "the [Name] theorem/conjecture," it doesn't mean that the person which name is used actually created this thing, maybe he just inspired it (Poincare might have only inspired the Poincare conjecture but did not propose it).

Sometimes there is only one way: the hairy ball theorem; you can not call it hairy ball's theorem.

Answer

Actually, there are even more ways of turning someone's name into a term beyond making it a possessive or an adjunct. For example, you could make it into an adjective:

• Malthusian growth


• Homeric epithet


• Kafkaesque bureaucracy

These of course raise the same question: why Brownian motion and not Brown's motion or Brownite motion or Brownidic motion or Brownicious motion […]?

There are various counterexamples to your theory, particularly in the second case: James Monroe formulated the Monroe Doctrine, Dick Fosbury created the Fosbury flop, Ernst Engel described the Engel curve, and so forth. And naturally there are many phenomena which are misnamed— in accordance with Stigler's Law.

There seem to be few patterns reliable enough to generalize into a rule. Things named after multiple people never seem to take adjectival or possessive forms (e.g. Bose-Einstein condensate), but I cannot say that definitively. For the most part, each effect, number, anomaly, reduction, lemma, paradox, proof, and so on gains an idiomatic usage seemingly independent of any other, and indeed this is true even for alternative names for the same concept:

Bernoulli's principle but the Bernoulli effect

Boyle's law but the Boyle–Mariotte law

Sometimes, the term is coined in a certain way that is definitively "correct"; the Peter Principle, for example, was introduced in a book entitled The Peter Principle. In other cases, however, competing forms exist and indeed may persist. Consider how prevalent Pauli's exclusion principle remains despite the overwhelming popularity of Pauli exclusion principle: