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Results tagged with soft-question
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user 25510
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.
17
votes
Publishing alone may be counterproductive?
According to my experience (50 years in academia) it works in just the opposite way. A PhD whose all papers are joint with her adviser raises a suspicion that she cannot work independently. It is good …
14
votes
Publishing corollaries of previously published results
There is a famous paper where the main result is derived as a simple corollary of a result of another author published 23 years before:
J. Milnor, Eigenvalues of the Laplace operator on certain manif …
- 91.8k
2
votes
Questions about some parallel between polynomial and differential equation
The answer to Q2 is provided by Differential algebra
created by Joseph Fels Ritt. He studied differential-algebraic varieties by analogy with algebraic ones.
See Ritt, Joseph Fels, Differential algebr …
- 91.8k
14
votes
Who says understanding physics helps mathematicians? (A reference request) [Take the word "w...
Perhaps it is correct that this opinion is "widely acknowledged" but it is not unanimous.
Here I collected some statements of some prominent mathematicians related to this question.
Some of those stat …
10
votes
What are journal rankings that employers look at?
Unfortunately, this practice spreads. Especially in the universities outside of USA. The databases most commonly used are ISI (Inst. of Sci. Information) Journal Citation reports and Scopus. Both of t …
10
votes
How can I (semi-formally) convince myself that Euclidean geometry comports with visual intui...
To the sources mentioned by @Carlo Beenakker, I would like to add the works of Soviet physicist Boris Rauschenbach, most of them are in Russian, but there are some in English:
Perspective Pictures and …
- 91.8k
3
votes
History of Gauss theorems that say "it clearly follows that" but it did not clearly follow
This could be related to the "Gauss problem" on the limit distribution of remainders of partial fractions. Gauss found this distribution, and in a letter to Laplace, claimed that he proved it. The fir …
- 91.8k
9
votes
What is an important mathematical question?
It is indeed somewhat subjective. A discussion of this, with examples, is contained in Hardy's book Mathematician's Apology. But mathematicians frequently disagree on many questions whether they are i …
19
votes
What should one do before submitting a paper?
First of all, upload to the arxiv. Then you can write to the experts you know, and inform them that you uploaded your new paper. Then wait a little to give them opportunity to send you comments. If th …
10
votes
Should one state the sharpest version of a Lemma even if only a weaker version is needed?
In each individual case, it is a question of opinion and of the author's judgement about the importance of the lemma.
There is no logical distinction between a lemma and a theorem.
Could Hermann Amand …
26
votes
Accepted
Fourier's proof of reality of all roots of Bessel function $J_0(x)$
Fourier proof was incomplete. Fourier used the following
Statement. A real entire function has only real zeros if
its derivatives have the following property:
If $x$ is a real root of $f^{(n)}$ then $ …
- 91.8k
62
votes
Accepted
Is spherical trigonometry a dead research area?
It is not. As a proof, I will mention three relatively recent papers where I am a co-author:
M. Bonk and A. Eremenko, Covering properties of meromorphic functions, negative curvature and spherical geo …
- 91.8k
61
votes
Is St. Petersburg a good place for the 2022 Int. Congress of Mathematicians
The real question is not about the Congress. There will be no ICM in Petersburg. Maximum what they can stage is a Russian-Chinese conference. Which decent Russians and Chinese will not attend anyway.
…
4
votes
Mathematical journals that accept long papers (up to 100 pages)
Publishing a paper 50-100 pages long can indeed be a problem.
However many journals actually like long papers (they are likely to have
higher citation rate:-) though they do not advertise this. Specif …
23
votes
Ideas for introducing Galois theory to advanced high school students
There is a nice book, specially written for high school students:
V. B. Alekseev, Abel's theorem in problems and solutions. Based on the lectures of V. I. Arnold (to high school students), and also fr …