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John D. Cook's user avatar
John D. Cook's user avatar
John D. Cook's user avatar
John D. Cook
  • Member for 15 years, 2 months
  • Last seen more than 1 year ago
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What are some deep theorems, and why are they considered deep?
I saw a nice talk once that worked its way up to the Atiyah-Singer index theorem starting with the angles in a triangle adding up to pi. Then generalize to sphere, then to Gauss-Bonnet, then ...
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Spectral theory of graph Laplacian besides $\lambda_2$
Thanks! I am not familiar with those references.
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Binomial distribution conjecture
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Binomial distribution conjecture
Yes. I'll edit the question to make that clearer.
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Research topics restricted to students at top universities?
The correctness of a math paper is objective, but the importance of a paper is not. If you're not sure how much of a contribution a paper is, but it's written by someone respected in the field, you give them the benefit of a doubt. An outsider doesn't get that benefit. That's another reason a young researcher needs to ride the coattails of a more established researcher, writing papers and grants together until he or she develops some name recognition.
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