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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.
14
votes
Why the triangle inequality?
From a conceptual standpoint, the triangle inequality per se is NOT what you really need. What I always emphasize when I teach metric spaces is that what gets used over and over again is that "two thi …
72
votes
Theorems that are 'obvious' but hard to prove
How about the fact that a sphere is the surface of minimal area that bounds a given volume? (BTW, if it isn't geometrically obvious to you, and you understand a little physics and about surface tensio …
41
votes
What is an integrable system?
The simple answer is that a $2n$-dimensional Hamiltonian system of ODE is integrable if it has $n$ (functionally) independent constants of the motion that are "in involution". (Functionally independen …