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Results tagged with gm.general-mathematics
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user 3106
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.
4
votes
Accepted
Is the solution to this trig function known to be algebraic or transcendental?
It should be possible to show that $x$ is irrational using Theorem 7 of Trigonometric diophantine equations (On vanishing sums of roots of unity) by J. H. Conway and A. J. Jones, Acta Arithmetica 30 ( …
- 82.7k
24
votes
Is amateur research in mathematics viable?
While I agree with others that it is possible to pursue mathematical research as an amateur, and I don't think you'll be "ostracized," I do think that there are some potential sociological obstacles t …
6
votes
Fascinating moments: equivalent mathematical discoveries
There may be a distinction between what you're talking about and the closely related phenomenon of the same result being rediscovered independently multiple times, and the following may be more illust …
5
votes
Accessible proofs of contemporary results in mathematics
There are a number of such results in combinatorics. The Wilf–Zeilberger method is perhaps the "strongest" one that I can think of off the top of my head. It is strong by any reasonable definition of …
5
votes
Accessible proofs of contemporary results in mathematics
Manjul Bhargava's proof of the 15 theorem (in Quadratic Forms and Their Applications, Contemp. Math. 272, 1999) is strikingly simple, especially when contrasted with Conway and Schneeberger's original …
12
votes
Can pure mathematics harness citizen science?
There are two obvious classes of problems that are amenable to this sort of thing.
Converting human-readable proofs into machine-checkable proofs that are verifiable using something like Mizar, HOL …
6
votes
Golden ratio in contemporary mathematics
Here is an example which on the surface has nothing at all to do with Fibonacci numbers or continued fractions. Theorem 1.1 of Itai Dinur's 2021 SODA paper Improved algorithms for solving polynomial …
15
votes
A search for theorems which appear to have very few, if any hypotheses
The Feit-Thompson theorem. Every group of odd order is solvable.
7
votes
Oddities of evenness
The special orthogonal group $SO_n$ behaves quite differently depending on whether $n$ is even or odd. In the Cartan–Killing classification, the odd case is type $B$ and the even case is type $D$. The …
27
votes
Situations where “naturally occurring” mathematical objects behave very differently from “ty...
The example mentioned in a comment by Martin M. W. seems worth posting as an answer. Naturally occurring theorems and conjectures tend not to be unprovable (relative to one of the standard axiomatic s …
1
vote
Oddities of evenness
There are a lot of results that are more difficult, or at least different, in characteristic 2 compared to odd characteristic. See for example the math.SE question, What's so special about characteris …
6
votes
Oddities of evenness
The biggest little polygon is a regular polygon if the number of sides is odd, but is an unexpectedly interesting shape when the number of sides is even (and at least 6).
20
votes
Demonstrating that rigour is important
Many examples that have been given are of statements that one could at least formulate, and conjecture, without rigorous proof. However, one of the most important benefits of rigorous proof is that i …
6
votes
Demonstrating that rigour is important
The answer to another MO question What did Ramanujan get wrong? cites Bruce Berndt (Ramanujan's Notebooks, Part IV) for a discussion of some cases where Ramanujan's legendary intuition went astray and …
3
votes
Demonstrating that rigour is important
Gowers is particularly interested in cases in which a "proof of a statement that was widely believed to be true and was true gave us much more than just a certificate of truth." Reading through the an …