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Results tagged with soft-question
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user 6153
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.
2
votes
Some thoughts on Zeilberger's 111th opinion
That's probably not quite the right formulation of an issue. "Pure mathematics" has been defined as generating proofs, for around a century. Proofs come in various kinds: "cleaning the stables" and "i …
- 12.6k
8
votes
Proof correctness problem
First comment: see https://en.wikipedia.org/wiki/List_of_incomplete_proofs
Second comment: That page is probably enough to convince anyone that the problem as posed is not a new one. Assertion of a t …
6
votes
Consolidation: Aftermathematics of fads
One thing that comes directly to mind is the calculus of variations, in the classical sense, where the point is to get rigorous results by mathematical analysis.
Now, there are probably several typi …
7
votes
At what point in history did it become impossible for a person to understand most of mathema...
At some point between Harald Bohr's foundation of the theory of almost periodic functions, and the major paper of van der Corput that J. E. Littlewood regarded as the most technical paper in the whole …
3
votes
Do names given to math concepts have a role in common mistakes by students?
An example is French module monogène for what is "cyclic module" in English. I can't prove that the possibility that a module monogène for a given ring may not be a groupe cyclique would be a stumblin …
0
votes
How to study a math text
A more precise formulation is: "what is the role of rote learning in mathematical study?" A purist such as Pólya would say "almost none". You have learned a theorem well when you know it back-to-front …
1
vote
Helpful services based on mathoverflow API
I'm a long-term Wikipedian, and I find MO interesting for several reasons. And there is already a good measure of mutual linking going on (MO questions in some cases are suitable external links for WP …
- 12.6k
3
votes
Local methods in algebraic number theory
To start with part 3: "local-global principles" of various kinds are one of the big themes in number theory, at least. Starting with, for example, a positive integer k being a square if and only if it …
- 12.6k
4
votes
What is the difference between hard and soft analysis?
Cantor sets, then. I would expand the ternary Cantor set by a factor of three, note that this makes two disjoint copies, and conclude the measure was zero that way. A "soft" argument indeed. That does …
2
votes
0
answers
2k
views
Who will write the algebraic geometry texts that are needed? [closed]
Readers of MO are probably aware of the pedagogic need that would provoke such a query. It's around 60 years since Serre's FAC, and I imagine some people would say "you still have to read the original …
6
votes
A Learning Roadmap request: From high-school to mid-undergraduate studies
There are (today) many popular books on mathematics. I don't know any very good ones. Kac and Ulam, Mathematics and Logic, is an older style of popular book, pretty good I think, and on Google Books. …
7
votes
Why didn't Vladimir Arnold get the Fields Medal in 1974?
In 1974, also, Pierre Deligne had a Fields Medal "withheld", after his proof of the Weil conjectures. That was hypothesised to be prejudice against non-peer reviewed aspects of the proof. I wouldn't r …
1
vote
Is Galois theory necessary (in a basic graduate algebra course)?
I don't really know how to have a clarifying discussion on such topics, but perhaps I have a little distance these days. There is such a topic as "applied algebra", though I suppose it is hardly ever …
3
votes
Why are finiteness conditions important (and how to recognize them)?
Two types of points, I think. (1) Counting dimensions is usually a lot more interesting for finite-dimensional vector spaces than for the rest. (2) Where finiteness conditions can be removed, as often …
2
votes
Less-known conjectures of significant influence and the contrary
One can contrast Hilbert's 7th problem (http://en.wikipedia.org/wiki/Hilbert%27s_seventh_problem) on transcendence with his views on Fermat's last theorem. These are reported somewhere, namely that th …
- 12.6k