Well, unless Hairy Ball Theorem is called after her, I don't think it's up to her to decide, what mathematicians "should" do. Jeez, these journalists researching "computational morality"...
To be fair, I do actually think some math jargon is unnecessarily complex and we could do better, and that it is something that actually matters. And I do think, for instance, that "commutative group" is better than "abelian group", since it is descriptive, unlike the latter. But this rarely is the culprit. Kähler manifold is called after Kähler, because he is the one who introduced such a thing, and we don't really have any better name to describe it. (And it wasn't Kähler who named it after himself too.) Can she propose a better name? I'm curious to hear it, but she conveniently skips that issue in her musings. If not, this whole argument of hers is just silly, as is thinking that "monster group" is a "cool name". It is not cool, it's rather awful, it's called that precisely because we don't have a clue WTF this thing is, and I sincerely hope that some 300 years later we'll have a much better understanding of group theory to rewrite all that stuff and to see that "monster group" is not such a "monster" after all, but quite a natural thing, that can be described conveniently and assigned some proper name.
So if we want to improve the landscape, let's rather start small, by abandoning π in favor of ½τ. Let's see how many centuries that will take.
As a contrarian: We should just teach everybody addition is Abelian. (And ignore all questions about the capitalisation). Think about the pros: no more conjugation (commut-es, -ing, -ative, -ed...) shorter (saves a lot of bits), respecting the elders, easier to translate, automatic referencing (unless they're Erdős or Bernouilli). And everything is easier to name, just find the closest word and define it!
Also, let's not talk about the LaTeX-fraction hell we enter when using τ. (π/3, π/4... are bad enough but don't appear all that often in core formulae).
In fact, let's use δ=π/180. Then Eulers formula becomes a nice e^(180δi)=-1! This also solves the degrees/radians problem, use the constant °=δ=π/180. sin(180°) is then 0.
A Kahler manifold is just a complex manifold with both a Riemann metric and a sympletic (Hamiltonian) form. It's not a rare class of manifolds and while the "adjective" Kahler has come to mean those properties. Why not call it a Reimann-Hamilton manifold if we care so much about the "history"?
I'm not suggesting that name. I'd prefer it was called a symplectic smooth inner product manifold. I'm merely pointing out the hypocrisy of the "name it after the discoverer argument"
To be fair, I do actually think some math jargon is unnecessarily complex and we could do better, and that it is something that actually matters. And I do think, for instance, that "commutative group" is better than "abelian group", since it is descriptive, unlike the latter. But this rarely is the culprit. Kähler manifold is called after Kähler, because he is the one who introduced such a thing, and we don't really have any better name to describe it. (And it wasn't Kähler who named it after himself too.) Can she propose a better name? I'm curious to hear it, but she conveniently skips that issue in her musings. If not, this whole argument of hers is just silly, as is thinking that "monster group" is a "cool name". It is not cool, it's rather awful, it's called that precisely because we don't have a clue WTF this thing is, and I sincerely hope that some 300 years later we'll have a much better understanding of group theory to rewrite all that stuff and to see that "monster group" is not such a "monster" after all, but quite a natural thing, that can be described conveniently and assigned some proper name.
So if we want to improve the landscape, let's rather start small, by abandoning π in favor of ½τ. Let's see how many centuries that will take.