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 example is made even sillier when one realizes that that "complex" and "symplectic" actually mean the same thing, but the former is Latin and the latter is Greek. It is essentially the same "everyday" description being applied two to quite different mathematical objects.
What Wikipedia says is not the best of arguments, for the simple reason that mathematics articles on Wikipedia have long suffered, as Wikipedia writers themselves have argued about for many years, from the problem of diving straight into jargon in the first sentence. It's fairly well-trodden territory by this point, and things are a lot better than they used to be, but part of the tension is between "But one has to understand these other things before one can understand this article anyway." and "An encyclopaedia is read by people who do not understand the subject, because if they understood it they wouldn't be trying to use an encyclopaedia to find out about it.".
> Let's not get rid of our ability to honor people in a failed attempt to make the communication more effective.
I think we should honor mathematicians less with eponymous theorems (prestige culture is toxic), but I agree it shouldn't be done at the expense of worse communication.
What's so toxic about honouring a long-dead mathematician? The article praises the Ancient Greeks and how they named things after their teachers. That, to me, is far more problematic. The history and the effort that went into developing the theorems of geometry presented by Euclid's Elements are all lost. Now we only know about Euclid, Pythagoras, Archimedes, and maybe a few others.
On the other hand, we know far more about the lives of Fermat, Euler, Gauss, Riemann, and Newton. While we can't owe all of the work of historians to eponymous topics, the use of their names in everyday mathematics helps to keep their memory alive so that new generations of people may be interested in learning about the history of mathematics.
To me, learning the mathematics is more important than learning the history, although the history is very interesting.
As for long-dead mathematicians... theorems are still being named to this day for living people. I think the glory we attach to discoverer of the mathematics diminishes the glory of the mathematics.
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.