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Results tagged with big-picture
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user 2284
Questions designed to get an overview of a specific subject or body of results or to understand the relations among similar definitions, techniques or concepts appearing in different sub-fields of mathematics. While such questions by their very nature sometimes cannot be made very narrow and focused, it can be helpful to keep in mind that the design of MathOverflow does not make it a good fit for questions that are too broad.
1
vote
What is the high-concept explanation on why real numbers are useful in number theory?
This has been discussed in previous answers, but I want to emphasize it. A lot of what is considered at the center of number theory and that has been so considered for centuries, if not millennia, is …
27
votes
Accepted
Are overlaps among {algebraic geometry, arithmetic geometry, algebraic number theory} growing?
I am not sure I really agree with the following quote (which is the opening paragraph of Modular forms and Galois cohomology by H.Hida) because I suspect that a mathematician valuing creativity and ve …
- 10.9k
66
votes
Why are modular forms interesting?
Your questions would require an enormous amount of work to answer properly, so let me just suggest a few modest and very partial answers to your 1)2)3).
1) Modular forms are shiny: they satisfy or ex …