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Results tagged with soft-question
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user 613
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.
197
votes
Why do so many textbooks have so much technical detail and so little enlightenment?
By now the advice I give to students in math courses, whether they are math majors or not, is the following:
a) The goal is to learn how to do mathematics, not to "know" it.
b) Nobody ever learned m …
98
votes
What's a great christmas present for someone with a PhD in Mathematics?
I'm surprised no one has yet suggested a lifetime supply of Hagoromo chalk.
91
votes
Accepted
Parodies of abstruse mathematical writing
Is this what you're looking for?
http://thatsmathematics.com/mathgen/
Mathgen is an random math paper generator, based on SCIgen which does the same for computer science papers. It will provide you …
63
votes
How has "what every mathematician should know" changed?
I advise against using MathOverflow as a guide to what most young mathematicians do or ought or learn. The last time I saw such a strong bias towards "abstract nonsense" was when I was a graduate stud …
60
votes
Too old for advanced mathematics?
With all this unanimous enthusiasm, I can't help but add a cautionary note. I will say, however, that what I'm about to say applies to anyone of any age trying to get a Ph.D. and pursue a career as an …
59
votes
Examples of simultaneous independent breakthroughs
One of the most entertaining seminar talks I ever attended was by Michael Atiyah on the moment map on a Lie group. As the talk progressed, the people in the front row became more and more agitated, un …
39
votes
Why are matrices ubiquitous but hypermatrices rare?
I think much of what I'm about to say has been said already, but I wanted to repeat it: I don't agree with the premise of the question at all. A "hypermatrix" is simply another name for a tensor. All …
- 27.5k
34
votes
Does Physics need non-analytic smooth functions?
It is worth noting that it is impossible to solve the initial value problem for the standard heat equation in the real analytic category. Here, there are asymptotic expansions available but no Taylor …
- 27.5k
27
votes
Major mathematical advances past age fifty
Although I concede that there is some truth to the belief that the greatest conceptual breakthroughs in mathematics are made by younger mathematicians, I think it has led to the mistaken idea that old …
26
votes
Why should I prefer bundles to (surjective) submersions?
There's no reason I can see for preferring bundles over submersions, unless you need bundles. If you don't need the extra global structure implied by a bundle, then by all means stick to submersions.
- 27.5k
25
votes
What are some applications of other fields to mathematics?
I can describe one that is still a little mysterious to me. My colleagues Erwin Lutwak and Gaoyong Zhang and I have shown how ideas arising from the continuous version of Shannon information theory (w …
24
votes
What are good non-English languages for mathematicians to know?
My impression is that the vast majority of mathematical articles written in the last 20 years are in English and that even foreign mathematicians try to write their better papers in English. It is, fo …
21
votes
What are some famous rejections of correct mathematics?
What about deBranges' proof of the Bieberbach conjecture:
https://en.wikipedia.org/wiki/Louis_de_Branges_de_Bourcia
21
votes
Switching Research Fields
Although I encourage you to pursue your strengths and passions, even if it means changing fields, I also advise some caution if you do not yet have tenure. If you feel you can still do more work in yo …
21
votes
Why should one still teach Riemann integration?
I have found most theoretical presentations of integration, whether Riemann, Lebesgue, or something else, to be overkill. I believe every mathematician should know how to construct the Riemann and Leb …