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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.

5 votes
5 answers
3k views

Easy and Hard problems in Mathematics [closed]

Modified question: I would like to know some examples of problems in Mathematics, for pedagogical purposes, which do not involve difficult techiques to solve the problem but with a change of context …
8 votes

Excellent uses of induction and recursion

1)Proof of Euler's formula, V-E+F=2, with induction on F (number of faces). 2)Backward induction proof of generalized AM-GM inequality. 3)Proof of Heine-Borel theorem using Transfinite Topological …
Uday's user avatar
  • 2,239
4 votes

Collection of conjectures and open problems in graph theory

A list of about 60 algorithmic problems pertaining to trees are given in the paper by Stephen T. Hedetniemi (Wayback Machine, journal website). Some of the discussion in the paper can be extended to q …
Uday's user avatar
  • 2,239
23 votes
8 answers
8k views

Grothendieck on topological vector spaces

In a short biography article on Alexander Grothendieck, it is mentioned that after Grothendieck submitted his first thesis on topological vector spaces (TVS), apparently, he told Bernard Malgrange tha …