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Results tagged with gm.general-mathematics
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user 25510
Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
67
votes
Useless math that became useful
The most famous example is conic sections. Conic sections were of great interest to
Greek mathematicians, and their theory was highly developed in the 2-nd century BC.
However I don't know of any appl …
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 amateur research in mathematics viable?
This is possible. I have at least two friends who studied mathematics (in the graduate school), did not defend their PhD, and found some jobs not related to mathematics. Still they do research, and pu …
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 …
31
votes
Counterexamples against all odds
The most famous example is the so-called Riemann-Hilbert problem, which has a long and complicated history which I don't explain in detail. As it happens Hilbert's own formulation was not very exact, …
30
votes
The origin(s) of the word "elliptic"
The origin of all these uses is very different. Joe Silverman explained the genesis of the sequence ellipse $\rightarrow$ elliptic integral $\rightarrow$ elliptic function $\rightarrow$ elliptic curve …
- 91.8k
29
votes
Where can square roots come from when they are not distances?
$i=\sqrt{-1}$ has no apparent relation with any distance.
Also $\int_{-\infty}^\infty e^{-x^2}dx=\sqrt{\pi}.$
23
votes
Fascinating moments: equivalent mathematical discoveries
An example which always puzzled me is J. Milnor's paper entitled
Eigenvalues of the Laplace operator on certain manifolds,
Proc. Nat. Acad. Sci. U.S.A. 51 1964, 542.
The whole paper occupies about ha …
20
votes
Is the field of q-series 'dead'?
The opinions that certain areas of mathematics are dead are frequently stated but in many cases incorrect. Some areas experience declines in activity and then revivals. Many examples can be given.
On …
16
votes
A search for theorems which appear to have very few, if any hypotheses
There are infinitely many prime numbers.
Every integer is a product of primes, in essentially unique way.
(Theorems with NO hypotheses:-)
16
votes
Can pure mathematics harness citizen science?
I have no proposal, but only want to mention a historical example of what can be called
"Citizen science" in mathematics. http://www.computer.org/portal/web/csdl/doi/10.1109/85.707573.
This is how th …
16
votes
Special rational numbers that appear as answers to natural questions
Rational number 1/4 occurs as a universal constant in several problems of Analysis.
The most famous is the "Koebe 1/4 Theorem". Let $f(z)=z+\ldots$ be an injective holomorphic function in the unit dis …
14
votes
Collaboration or acknowledgment?
No general rule can be established here. It is by mutual agreement of all involved parties that such things are usually decided. If you decide to write a paper where you use the results of
a discussio …
14
votes
What are some examples of understanding a space by studying the functions on this space?
The idea goes back to the 1930s when algebraic geometers understood that points
of an algebraic variety "are" maximal (or prime) ideals of the ring of regular functions
on it. The counterpart of this …
13
votes
When should a supervisor be a co-author?
The meaning of your question depends very much on who YOU are: a student or a supervisor:-)
My guess is that you are a student.
In which case, my advise would be: just do what your supervisor suggest …