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Results tagged with soft-question
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user 3106
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.
137
votes
Suggestions for special lectures at next ICM
How about a lecture on proof assistants/formal proofs?
Most mathematicians are still skeptical of the value of proof assistants, and it's certainly true that proof assistants are still very difficult …
76
votes
How do you decide whether a question in abstract algebra is worth studying?
I'm going to interpret your question in the language of Gowers's "two cultures" essay as follows:
How does one get good at theory-building?
The process of developing a good theory can seem decep …
75
votes
How would you have answered Richard Feynman's challenge?
There's a certain gaming/sporting aspect to Feynman's challenge that works in his favor. First of all, as phrased, the challenge gives him a 50/50 shot at being right even if he guesses randomly. Al …
66
votes
Accepted
When is one 'ready' to make original contributions to mathematics?
It is something of a myth that everything has already been studied and that you have to master thousands of pages of prior work before you can contribute something new.
To be sure, there are some sub …
61
votes
How to write a good MathSciNet review?
I'll take a stab at this because in the past I have gotten some feedback from Mathematical Reviews saying that they like my reviews, and they did ask me to write a Featured Review once (back when ther …
59
votes
Accepted
The editor wrote the paper for me
[Comments combined into a community wiki answer.]
Copyright is the wrong word in this context; the correct word is authorship. A reasonable course of action is to propose to the editor that you and h …
58
votes
Mistakes in mathematics, false illusions about conjectures
Before Erdős and Selberg found an elementary proof of the prime number theorem, G. H. Hardy had predicted that the discovery of such a elementary proof would be cause "for the books to be cast aside a …
57
votes
Old books you would like to have reprinted with high-quality typesetting
I have some experience resurrecting old math books and I want to make a few comments about copyright.
First, it is definitely true that except for very old books, someone owns the copyright. Typicall …
55
votes
Proofs shown to be wrong after formalization with proof assistant
This question was raised on the Foundations of Mathematics mailing list back in 2014, and the short answer is no, there are no examples of this. [EDIT: Although this may have been true at the time I …
54
votes
On starting graduate school and common pitfalls...
Marie desJardins has a nice article on Surviving Graduate School that is definitely worth reading.
The top two pieces of advice I would give are:
The most important thing when choosing an advisor i …
54
votes
Publishing a bad paper?
When all else fails, try honesty.
I don't mean that you have to tell the professor to his face that you think his field is toxic and that the paper is garbage. But if your honest opinion is that the …
51
votes
Request for examples: verifying vs understanding proofs
Don Zagier has a well-known paper, A one-sentence proof that every prime $p\equiv 1\pmod 4$ is a sum of two squares. An undergraduate mathematics major should be able to verify that this proof is cor …
49
votes
Extent of “unscientific”, and of wrong, papers in research mathematics
As Kevin Buzzard himself admits in his answer, he somewhat exaggerated his point for effect.
However, I'd submit that if you were unsettled by his talk, then that's a good thing. I don't think that …
47
votes
How to read an article and make it actually useful?
Before you decide how to read a particular paper, you have to decide why you're reading that particular paper.
You said you're doing your Ph.D. You might want to take a look at a couple of other MO qu …
47
votes
In what respect are univalent foundations "better" than set theory?
This is a question that has been discussed a lot on the Foundations of Mathematics mailing list (unfortunately with more polemics than necessary IMO—though I confess that I may have been guilty of sto …