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Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
17
votes
What do you do when you're stuck?
The only generic advice that can be offered here is that deciding what to do in this situation is quite a difficult skill, but one that you are expected to develop as a PhD student. You ultimately mig …
13
votes
Each mathematician has only a few tricks
Tao has recently submitted a preprint on exactly this topic in the case of the mathematician Jean Bourgain. The tricks in question are quantification of qualitative estimates, dyadic pigeonholing, ra …
5
votes
Books containing new results
This is a physics example and I think the first edition was in 1995, but if I remember rightly there are some important results derived in Weinberg's textbook The Quantum Theory of Fields: Volume I. …
5
votes
Is amateur research in mathematics viable?
Even most low-grade office jobs outside of academia these days are surprisingly high pressure and stressful. Your performance is constantly monitored and analysed. I would be surprised if jobs in indu …
3
votes
Small ideas that became big
Another possibility could be the problem of the brachistochrone, a famous but one might think relatively innocent problem, which then led to the development of the calculus of variations.