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Results tagged with soft-question
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user 1149
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.
105
votes
Too old for advanced mathematics?
This is indeed not a typical math overflow question, but never mind that.
Of course you can learn mathematics at the age of 30 after having stopped studying it at the age of 18! Examples are abundan …
- 65.4k
85
votes
What are the most misleading alternate definitions in taught mathematics?
I increasingly abhor the introduction of the finite ring $Z_n$ not as $\mathbb{Z}/n\mathbb{Z}$ but as the set $\{0,\ldots,n-1\}$ with "clock arithmetic". (I understand that if you want to introduce m …
68
votes
Refereeing a Paper
I think your question is so important as to deserve multiple answers, even if there is a good deal of overlap among them. (Indeed, overlap indicates that various respondents feel the same way about s …
66
votes
When should a result be made into a paper?
This is a question of interest to most mathematicians who are research active and not slowly but surely knocking off important problems in their field at the rate of one per paper. (I think I could h …
55
votes
Fundamental Examples
The Fermat Equation xn + yn - zn = 0.
This has truly been much more than an example in both algebra and number theory: it was one of the main motivations to develop the theory of unique factorizati …
52
votes
Most memorable titles
Finding composite order ordinary elliptic curves using the Cocks-Pinch method, by D. Boneh, K. Rubin and A. Silverberg. (To appear in the Journal of Number Theory.)
51
votes
Famous mathematical quotes
Do not ask whether a statement is true until you know what it means. -- Errett Bishop
49
votes
Why is it a good idea to study a ring by studying its modules?
I want to answer your question twice: first with a "top-down" approach and second with a "bottom-up" approach. Let me limit myself to the first answer here and see how I do.
I claim the following an …
- 65.4k
48
votes
Top specialized journals
The following is my personal (i.e., includes all of my mathematical prejudices) ranked list of subject area journals in number theory.
From best to worst:
1) Algebra and Number Theory
2) Internatio …
47
votes
Which math paper maximizes the ratio (importance)/(length)?
Noam Elkies, The existence of infinitely many supersingular primes for every elliptic curve over Q, Invent. Math. 89 (1987), 561-568.
47
votes
Most harmful heuristic?
That there is something weird and unsavory about field extensions that are not separable and that serious contemplation of such things should be put off to the indefinite future.
(In fact, much of th …
47
votes
Why should one still teach Riemann integration?
Here are some unpolemical facts concerning the Riemann integral:
The Riemann integral has a geometric interpretation which is different than that of the Lebesgue integral and is certainly useful in s …
41
votes
How to present mathematics to non-mathematicians?
For some reason, many mathematicians have trouble with the idea that when some layman asks them about their work, the appropriate response is not to try to figure out how to describe the latest theore …
34
votes
How to know if somebody else is also working on your problem?
As others have indicated, the only 100% effective method of preventing getting "scooped" or finding out that your result already exists in the literature is that of complete abstinence: i.e., not tryi …
33
votes
Teaching undergraduate students to write proofs
This is a great question. In fact, I hope people won't think it over-dramatic if I call it one of the great math education questions of our time.
At the University of Georgia, we have decided as a de …