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Results tagged with soft-question
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user 2926
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
Trichotomies in mathematics
Here is a cluster of examples with a common theme, based partly on comments here and in an MO thread on whether an empty space should be considered connected, and partly on an article in the nLab, "to …
- 4,713
14
votes
Problems where we can't make a canonical choice, solved by looking at all choices at once
General topology as found in textbooks seems to be chock-full of examples where the axiom of choice seems to be (unconsciously?) invoked, and unnecessarily if one follows Eilenberg's advice to avoid s …
- 53.3k
5
votes
Which popular games are the most mathematical?
There's also Nine Men's Morris, which is a very ancient game. My understanding is that it has been effectively solved in recent years with the help of computer analysis.
- 4,713
29
votes
Is a come back to mathematical research possible?
I hesitate to posit myself as an example, but I was out of academia from 2001 to 2019, when I decided to become a stay-at-home dad while my wife became the breadwinner. (I won't go into the details of …
- 53.3k
25
votes
Is the empty graph a tree?
The whole discussion seems to devolve on whether the empty graph (or empty space) should be considered "connected". Angelo and I are of the school that it should not, but this should be explained sinc …
- 4,713
14
votes
What are some examples of colorful language in serious mathematics papers?
From Jim Stasheff's Homotopy Associativity of H-spaces I, the magisterial-sounding
To study spaces which admit $A_n$-structures, we can work directly with the maps…. In the case of a topological gro …
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3
votes
Major mathematical advances past age fifty
Charles Sanders Peirce (born 1839) explicitly declared his Existential Graphs (all three parts: Alpha, Beta, and Gamma) to be his chef d'oeuvre. This work on graphical logic began sometime in the earl …
- 4,713
12
votes
What is your favorite proof of Tychonoff's Theorem?
I won't swear it's my absolute favorite, but today I learned of a nice proof due to Clementino and Tholen who take as their starting point the closed-projection characterization of compactness, viz. t …
- 4,713
3
votes
What's a great christmas present for someone with a PhD in Mathematics?
A book of interviews of famous mathematicians could be good. I have in mind particularly More Mathematical People, which I've gotten a lot of mileage from here at MathOverflow.
- 53.3k
8
votes
Accepted
Concise definition of subobjects
Of course it's not necessary to make this identification, but it's fairly harmless since the groupoid of monomorphisms into an object $X$ is equivalent to the discrete category of subobjects, and it c …
- 53.3k
6
votes
Would it be simpler, pedagogically speaking, if textbook writers introduced root systems as ...
You might find useful certain aspects of Alissa Crans's thesis,
Alissa Crans, Lie 2-Algebras, Dissertation, U. Cal. Riverside, 2004 (link).
For instances, Lie groups and their associated Lie algebra …
- 53.3k
24
votes
Most memorable titles
You'd think that with John H. Conway around, this should be like shooting fish in a barrel. One title that comes to mind is
The Sensual (Quadratic) Form
and there are more goodies if you look at his …
- 4,713
16
votes
A map of non-pathological topology?
I'll go ahead and say that Polish spaces are an interesting and almost sui generis class. There is a rich literature of applications to and from descriptive set theory, with layers of "pathology" hier …
- 53.3k
9
votes
Examples of notably long or difficult proofs that only improve upon existing results by a sm...
The following example is described in The Man Who Loved Only Numbers by Paul Hoffman.
There is a reasonably short proof, found by Esther Klein (later Szekeres) in 1932, that given 5 points in the pl …
- 53.3k
4
votes
Accepted
Technical term for representing object of a presheaf determined by a left-adjoint?
As requested, I'll turn my comments into an answer. There were two questions, the first being what we call the representing object if a presheaf $c \mapsto \mathcal{D}(F c, d)$ is representable, and t …
- 53.3k