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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.

1 vote

Has mathoverflow yet led to mathematical breakthroughs?

Chris's answer to my first question definitely cleaned up some statements in my current project.
62 votes

How to respond to "I was never much good at maths at school."

well someone has to make the sudoku puzzles http://spikedmath.net/comics/033-why-math.png
9 votes

Taking lecture notes in lectures

I do not take many notes in colloquia, seminars, etc., although I always have a pad of paper handy to jot down ideas or to doodle. But for roughly one course per semester, I take detailed notes and p …
9 votes

Impact of LHC on math ?

I am not an expert on the following aspect of LHC, so I'll bring it up but hope others will elaborate (feel free to use the community wiki features!): One of the major contributions of LHC has been t …
5 votes

Isn't a graph to be considered isomorphic to its complement, actually?

OK, I'll bite. I've never liked the word "graph". Some people use it to mean "set $V$ of 'vertices' a collection $E$ of size-two subsets of $V$". Some mean "set $V$ and a symmetric $V\times V$ matr …
Theo Johnson-Freyd's user avatar
17 votes

When and why did the postdoctoral position originate?

In know that there is some variation among fields for when post-docs became popular. My understanding is that the "post-doc" institution as a whole began around the beginning of the last century, but …
4 votes

How should I find a tutor for math-overflow level mathematics?

To find a "tutor" for MO-level math is easy: go to graduate school.
Theo Johnson-Freyd's user avatar
8 votes

What do people mean by "subcategory"?

If I want a "full subcategory", I say simply say so.
Theo Johnson-Freyd's user avatar
9 votes

How should one present calculations?

I think that in all writing, and especially in mathematical writing, signposting is extremely important. So a calculation-heavy proof should include a short summary, and then the calculations should …
2 votes

2-morphisms in structured 2-categories

Let me focus in on your third example, but I'll also wave at your other two. Here's everything in full: A symmetric strong monoidal category consists of: 0-morphisms: a category $C$. 1-morphisms: …
Theo Johnson-Freyd's user avatar
0 votes

Jordan Curve Theorem for Manifolds

Alexander's horned sphere (Wikipedia) shows that even when the first part of your conjecture (1) holds, you cannot expect the second part to. The horned sphere is a continuous embedding $\mathbb S^2 …
Theo Johnson-Freyd's user avatar
0 votes

What are the most overloaded words in mathematics?

Well-defined. Overused not because it has too many definitions but because it has too few.
2 votes

Should the "L" in the term latin/Latin square be capitalized?

A close mathematician friend of mine used to try to stick to the rule of capitalizing any word that derives from a person's name: Noetherian (not "noetherian") ring, Abelian (not "abelian") group, etc …
10 votes

Making sure that you have comprehended a concept

You cannot, because you never will. There is always more to understand about any given topic.
4 votes

When and how is it appropriate for an undergraduate to email a professor out of the blue?

I think the "when" part of the question has been well-answered, so I will only comment on formatting and style, some of which has also been addressed. One thing I have trouble with when emailing peop …

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