Comment by Tainnor
2 days ago
I don't know anybody who first learns about new mathematical ideas from Wikipedia. Mathematics is a body of knowledge, not just simple isolated theorems or definitions. You learn new mathematics from textbooks.
Even for reference purposes there are often better resources. E.g. proofwiki is usually better for looking up proofs because the proofs and definitions are interconnected.
If I run across a term like "bialgebra" while doing work, I don't always have the leisure time to derail my life and sign up for a 4 month class at a local university. Sometimes, I just need to move on with my task at hand and get something working.
I'm familiar with the mathematician response to this, I've heard it before and I fundamentally disagree with it. At work last week I gave someone a crash course in the simplex method and linear programming in about 30 minutes and it was a good-enough explanation that I came back in a few hours and the code was right.
This isn't impossible. There's just some wild apprehension that I'll never understand which insists everything is a grueling 1,000 hour journey to some kind of valhalla of enlightenment so you can bask in some aesthetic beauty of how perfect math is, as tears drip down from your cheeks, or something like that.
I mean come on now. Sometimes all you want is the cliff notes.
Well, you're comparing a concrete algorithm from applied mathematics (simplex) to a term from abstract algebra. I'm not exactly sure how you'd expect such a general concept to be described. Where in your work do terms like "bialgebra" regularly come up and is "it's some sort of algebraic structure" not enough of an understanding to continue without digging into the details? Maybe your problem is with people who put abstract mathematics into applied material without motivation or explanation and not with research mathematicians themselves?
Would you expect to be able to read the "cliff notes" on French and then be able to read Camus in the original? That's what I mean by "body of knowledge" as opposed to individual facts.