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Results tagged with big-picture
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user 934
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.
8
votes
Surprising and Useful Physical Intuition for Mathematical Objects
I remember from Folland's PDE book an anecdote about Green convincing himself of the existence of a Green's Function:
Let $\Omega$ be a vacuum and $S$ a perfectly conducting shell grounded to zero po …
36
votes
Your favorite surprising connections in mathematics
The pair correlation function between Riemann zeta function zeros is the same as the pair correlation function between eigenvalues of random Hermitian matrices.
19
votes
Describe a topic in one sentence.
Analytic Number Theory: log log log log log...
Did I see that quote in Havil's book Gamma?
94
votes
Collection of equivalent forms of Riemann Hypothesis
I like Lagarias "elementary" reformulation of Robin's theorem: that RH is true iff
$\sigma(n)\leq H_n+e^{H_n}\log(H_n)$
holds for every $n\geq 1$, where $\sigma(n)$ is the sum of divisors function a …