What's in a (mathematical) name? The uncreative and un-critical process of naming mathematical objects/thoughts

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Why is an "eigenvalue" called an "eigenvalue"? Why should the "the Birkhoff–Grothendieck theorem" be called "the Birkhoff–Grothendieck theorem"?

As a philosopher, I feel opposed to the obscure non-clarifying namings of mathematical objects/thoughts.

I am not experienced enough with mathematics to know, but it seems to me that mathematics has a lot to learn from philosophy here.

You might object this, and say: "look, the philosophical community is equally backwards: it seems like there is something called 'the Socratic Method'". But I don't agree with that objection completely, as it is only partially (and perhaps more for the layman) backwards in its naming conventions: 'the Socratic Method' is only one name given to the method, and people have come up with better and more thought-through names, such as:
  • maieutics;
  • method of elenchus;
  • elenctic method.
All of these have much more interesting and enlightening etymological roots, which focus not so much on the simply less fundamental fact of the name of the person who popularized the method.

Therefor, I am hoping to team up with a (group of) mathematician(s), to try to re-name mathematical objects, so that the relation between mathematical thoughts can be hinted at, just by looking at an object's/thought's name.

Please contact me if you were interested to do this. I am looking for a (group of) mathematician(s) to live with for many months or even years. I can fly to any country in the world.

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