Mathematicians should stop naming things after each other

Not everything is easy to Google:

C, D, F, R, COM, .NET, node ...

Guess would need a different term for Markov chains of higher order. And I'm not sure if there's other concepts that could also be labeled "memoryless chains", where a distinct name might help.

It could be called Stroustrupilian ... or "The one with Turing complete templates".

This falls a little flat with me. Let's consider an example from the article- a Kähler manifold. I'm not a geometer, so I looked it up on Wikipedia, and it says that a "Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure." https://en.wikipedia.org/wiki/K%C3%A4hler_manifold

Two of those things are not named after a person, and none of them are understandable without special training. Naming something after a person doesn't make it any harder to understand unless there are multiple things named after that person and you can't figure out which they mean from the context.

In case you're wondering about those structures, here is what Wikipedia has to say about them:

- A Riemannian manifold "is a real, smooth manifold, M, equipped with a positive-definite inner product g_p on the tangent space T_p M at each point p."

- "A complex manifold is a manifold with an atlas of charts to the open unit disk in C^n, such that the transition maps are holomorphic."

- "A symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form ω, called the symplectic form."

The only thing in the above descriptions accessible to non-specialists is probably that the Riemannian manifold is probably named after that guy that they heard of in calculus class. Let's not get rid of our ability to honor people in a failed attempt to make the communication more effective. You can call a Riemannian manifold or a Kähler manifold whatever you want, but it's not going to prevent someone from having to spend years before they are able to understand them.

This is one of those articles that might sound convincing to non-mathematicians (because it is annoying to learn names for difficult concepts, and many people can relate to that experience), but will not sound all that convincing to domain experts.

It'd be hard to deny that descriptive terms are easier to memorize. Sometimes a piece of natural and/or physical intuition allows such terminology to arise.

Scientist and mathematicians do tend to think about terminology quite frequently: communicating with other scientist and mathematicians is a major part of doing science, and "the reviewers couldn't follow your argument" is a valid, and not especially rare reason for rejected articles in mathematics. Given the amount of thought put into it, "intuitive" names do tend to come about when possible (as it happened with what we now call the Ham Sandwich theorem, the concept of Fibration, the Squeeze Lemma, and countless others).

Given that mathematicians do put thought into terminology, there's often a good reason for not having more intuitive names: maybe no good common-sense intuition was available (e.g. Chu constructions are too general for this sort of thing), or the thing comes up only in highly specialized contexts where it's not worth bothering with it (e.g. Girard's paradox), or there are too many different metaphors that one would have to invoke to describe the situation appropriately, so that it's more efficient to derive a completely new term from an associated name (e.g. Abelian became such an adjective, which now has its own associations).

It's telling that the author criticizes terms like "Calabi-Yau manifold", but doesn't suggest any alternative: coming up with an insightful name that communicates the key properties of such an object, and is easier to use and remember than "Calabi-Yau" is, let's just say, very very hard.

The same phenomenon is not limited to mathematics. Would Dijkstra's algorithm, the Haber–Bosch process or the Otto cycle be easier to learn and remember if they had snappy, insightful names? Probably. But the same concerns apply. It's hard to come up with genuinely better, more descriptive names for these processes. And even if we were successful in popularizing newer, better names, we would find that the names were not the real bottlenecks that made computer science, chemistry or mechanical engineering difficult to master.