In my limited experience these objects are complicated and unintuitive enough that it would be hard to come up with a short simple descriptive name for them. So then you are back to applying an arbitrary label, like a name!
But then, who better to name them than the individuals who made the breakthrough? As the article mentions, the pair of pants, hairy ball theorem, no free lunch, and refers to conway, presumably the game of life.
The creators/inventors/discoverers are in the best position to come up with a name, because they presumably understand the concept enough. Though it does require a degree of creativity.
"This nesting of proper nouns helps to make higher math impenetrable not just to outsiders, but also to working mathematicians trying to read their way from one subfield into another."
As if the biggest and only hurdle to understanding and working with advanced math was learning names... by the time you understand the concept and it's importance to a degree that you can work with it, the name becomes second nature.
The author certainly has a point. However, when he mentioned rote memorization I was reminded how easy it came to me to remember all these names. I majored in physics and minored in math, and at some point I realized how many theorems and mathematical objects I knew that were named after a person without sitting down and trying to memorize them. As soon as the concept of, say, a Taylor series, Hilbert space, Schrödinger equation, the Schwarzschild radius or the Tesla unit was introduced, the name stuck immediately.
Then again, I could add another argument as to why naming things after persons is bad: it's ridiculous how many things have been named after Euler [1] or Gauß [2]. But I'm not aware that this causes widespread confusion. Maybe it's not a problem.
In terms of memorisation, naming something after a person is very beneficial.
The ease of remembering something is a function of how many associations you can make to it. For instance, for a person you can associate with their name:
1. Where they lived.
2. What they looked like.
3. Interesting information about their life
For example you might remember Galois lived in France, he looked like a kid and he died in a duel.
If someone just makes up a word it's going to be much harder to remember because there's no attachment points for associations.
Having worked in mathematics for 10+ years, I can tell for sure, that the least problem you will face when trying to understand Calabi-Yau manifolds are the naming conventions.
Unwrapping the last term alone is a multi-year endevour if you start from scratch:
> [A] manifold is a locally ringed space, whose structure sheaf is locally isomorphic to the sheaf of continuous (or differentiable, or complex-analytic, etc.) functions on Euclidean space [IR^n]. -- https://en.wikipedia.org/wiki/Manifold#Mathematical_definiti...
Note that definition, does barely use inventor's names and is still very dense and hard to unwrap.
I never found naming conventions to be a notable problem.
Agreed. Even if a relatively short description is possible ("complete normed vector space"), if a concept is used often enough, it might be named (in the case of the example, "Banach space") - what's the problem with that?
In daily life, we don't say "Pull the horizontal surface suitable to sit on closer to the somewhat higher horizontal surface suitable to perform office tasks on", we say "Pull the chair closer to the desk", because we have given these concepts names.
Perhaps the opposite is true-- to wit, a concept given a special name makes it easier to remember, marks it distinctively, and the assignment of the name itself indicates that it is an important concept. In the case of prolific discoverers such as Thurston, or say, Euler, the second quality breaks down, but this can be obviated by choosing different descriptive names (which themselves need not even exclude giving credit to their discoverers, provided they are chosen appropriately).
People who are not smart enough to invent something that could be named after them have no business telling those who are, and should mind their own business.
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[ 2.7 ms ] story [ 43.8 ms ] threadThe creators/inventors/discoverers are in the best position to come up with a name, because they presumably understand the concept enough. Though it does require a degree of creativity.
As if the biggest and only hurdle to understanding and working with advanced math was learning names... by the time you understand the concept and it's importance to a degree that you can work with it, the name becomes second nature.
Then again, I could add another argument as to why naming things after persons is bad: it's ridiculous how many things have been named after Euler [1] or Gauß [2]. But I'm not aware that this causes widespread confusion. Maybe it's not a problem.
[1] https://en.wikipedia.org/wiki/List_of_things_named_after_Leo...
[2] https://en.wikipedia.org/wiki/List_of_things_named_after_Car...
The ease of remembering something is a function of how many associations you can make to it. For instance, for a person you can associate with their name:
1. Where they lived.
2. What they looked like.
3. Interesting information about their life
For example you might remember Galois lived in France, he looked like a kid and he died in a duel.
If someone just makes up a word it's going to be much harder to remember because there's no attachment points for associations.
Unwrapping the last term alone is a multi-year endevour if you start from scratch:
> [A] manifold is a locally ringed space, whose structure sheaf is locally isomorphic to the sheaf of continuous (or differentiable, or complex-analytic, etc.) functions on Euclidean space [IR^n]. -- https://en.wikipedia.org/wiki/Manifold#Mathematical_definiti...
Note that definition, does barely use inventor's names and is still very dense and hard to unwrap.
I never found naming conventions to be a notable problem.
In daily life, we don't say "Pull the horizontal surface suitable to sit on closer to the somewhat higher horizontal surface suitable to perform office tasks on", we say "Pull the chair closer to the desk", because we have given these concepts names.
These jobs pay like crap but require an intellectual.