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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.

12 votes

Cocktail party math

There are some good ones in topology (or maybe I just know these examples because it's my field). People always seem to think the hairy ball theorem (already mentioned) is interesting because it ex …
13 votes
7 answers
35k views

Real analysis has no applications?

I'm teaching an undergrad course in real analysis this Fall and we are using the text "Real Mathematical Analysis" by Charles Pugh. On the back it states that real analysis involves no "applications t …
12 votes
4 answers
1k views

Cite articles or book where I first found the result?

I'm writing up a paper and I'm not sure how to cite a few things. It concerns a conjecture made by Quillen. Some work has been done showing it's true in some cases, false in others. These results I fo …
49 votes
11 answers
8k views

Cures for mathematician's block (as in writer's block) [closed]

What kind of things do you find that help you get the "creative juices flowing," to use a tired cliche, when you're stuck or burnt out on a problem? I've read about some studies that suggest listening …
4 votes

Textbook recommendations for undergraduate proof-writing class

A "book" that satisfies all of your criteria is a set of notes from the Journal of Inquiry Based Mathematics called "Introduction to Proof" by Ron Taylor. linky The chapters are Symbolic Logic Pr …
8 votes
4 answers
583 views

Examples of the varying strengths of topological invariants

In my first algebraic topology class, I remember being told that the simplest reason for homology was to distinguish spaces. For example, if is X=circle and a Y= wedge of a circle and a 2-sphere then …