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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 …
- 91.8k
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
73
votes
Good "casual" advanced math books
What's one person's "higher level topics" is another person's "elementary math", so you should be more specific about the desired level.
But still you may try these books:
Michio Kuga, Galois' dream, …
- 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 …
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 …
- 101
34
votes
Theorems with many distinct proofs
"what is worth proving
is worth proving again" (Attributed to N. Katz in D. Ruelle's paper, The nature of properly human mathematics.)
You are asking for a very long list: most deep and important th …
- 91.8k
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
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 …
- 91.8k
56
votes
How can a mathematician handle the pressure to discover something new?
I can share my own experience: similar considerations always disturbed me too.
To deal with this, I always considered mathematics research as a hobby. From the very beginning I thought that my main jo …
- 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
33
votes
Diplomacy when reporting errors
Of course, reporting an error benefits the author, so I advise to write to him/her. A polite form is: Dear X, I am reading your interesting paper Y, and I have difficulty in understanding why A implie …
- 91.8k
32
votes
Accepted
Access to journals during pandemic
Let me try to summarize this long discussion in the comments. There are many free resources.
arXiv. It is true that not all mathematicians post their papers on the arXiv, for various reasons. But som …
- 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 …
- 91.8k
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 …
- 91.8k