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Results tagged with soft-question
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user 9896
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
4
votes
Blackbox Theorems
The Lovasz Local Lemma gives a very simple criterion for when certain random events have positive probability. Almost all applications of the Lemma automatically have an algorithm to find such events. …
3
votes
Graduate School
I was in a similar position: I worked in a technical, mathematically sophisticated but very specialized job for ten years out of undergraduate before applying to an applied math PhD program. I am curr …
1
vote
Demystifying complex numbers
Complex numbers make working with polynomials much easier, including purely real-valued questions about polynomials.
For example, prove every real polynomial factors into linear and quadratics. With …
33
votes
18
answers
6k
views
Non-rigorous reasoning in rigorous mathematics
I was wondering what role non-rigorous, heuristic type arguments play in rigorous math. Are there examples of rigorous, formal proofs in which a non-rigorous reasoning still plays a central part?
Her …
9
votes
What notions are used but not clearly defined in modern mathematics?
Infinitesimals are almost in this category.
Technically, calculus generally uses limits instead of infinitesimals. And there are logical systems (e.g. nonstandard analysis) in which genuine infinites …