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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

7 votes

Making an intuition precise

In addition to the other answers...experiment! Write SAGE (or other) code to look at a hundred or a thousand examples of what you're trying to say something about. You'll probably see the pattern mo …
12 votes

Which mathematical ideas have done most to change history?

Can you say something about the audience of this course? Popular math? Undergrads? grads? That might set some appropriate response parameters. If this were a graduate-level course (I suspect not, …
11 votes

Particular problem solved by solving a more general problem.

The only way to prove that there's at least one prime in every arithmetic progression is by proving that there are infinitely many primes in every arithmetic progression. This is intuitively a fairly …
11 votes

What out-of-print books would you like to see re-printed?

After a quick pop over to my Amazon wish list, the following 4 have been pretty unattainable to me for as long as I've been looking: Galois Cohomology of Algebraic Number Fields, by Haberland Class F …
29 votes

Would Euler's proofs get published in a modern math Journal, especially considering his trea...

I think the answer to your question is pretty well-addressed by Gerald in the comments. Let me just throw in a couple of points that wouldn't fit in a comment. 1) Euler knew what he was doing. He …
Cam McLeman's user avatar
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10 votes

Tips on cohomology for number theory

"Do people just remember all the rules and go through the formal manipulations of the cohomology groups of class field theory mechanically, or are people actually "feeling" what is going on here. If i …
45 votes

Have any long-suspected irrational numbers turned out to be rational?

This certainly doesn't answer the question, but I can't help but mention Conway's constant: http://mathworld.wolfram.com/ConwaysConstant.html It relates to Pete's comment about "bumping" it up a not …
168 votes
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Most helpful math resources on the web

I occasionally find mathoverflow.net rather helpful. In particular, there's a good list of answers to your specific question here.