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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.

7 votes
1 answer
742 views

Intuition on Log-Concave Sequences

A sequence $(a_n)$ is said to be log-concave provided $a_i^2 \geq a_{i-1}a_{i+1}$ for all $i$. What sorts of intuition can one have about log-concave sequences? In particular, what kind of "picture" …
14 votes
6 answers
28k views

Induction vs. Strong Induction

Is there ever a practical difference between the notions induction and strong induction? Edit: More to the point, does anything change if we take strong induction rather than induction in the Peano ax …
3 votes

Best online mathematics videos?

Timothy Gowers' "The Importance of Mathematics" never fails to instill a sense of purpose in my work, even when I feel I'm doing "useless" mathematics.