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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.
96
votes
Examples of interesting false proofs
$$e^i = (e^i)^{(2\pi/2\pi)} = (e^{2\pi i})^{1/2\pi} = 1^{1/2\pi} = 1.$$
I first saw this one many years ago, written on the wall of a bathroom stall in the Princeton University math department.
45
votes
Endless controversy about the correctness of significant papers
Stanley Yao Xiao's comment has been upvoted so highly that it seems worth posting as an answer.
There is a currently unresolved controversy over Shinichi Mochizuki's claimed proof of the abc conjectur …
43
votes
Accepted
Changing field of study post-PhD
Speaking as someone whose thesis was also in algebraic graph theory but who has later gone on to do research in other areas, I would say that it is definitely possible to switch fields. The main skil …
34
votes
Is data science mathematically interesting?
The Mathematics of Data may go some way towards answering your question. As one example of a mathematically interesting topic that is motivated by data science, you might want to look at the concept …
32
votes
Endless controversy about the correctness of significant papers
As far as I know, Wu-Yi Hsiang still maintains that his proof of the Kepler conjecture is complete and correct. Perhaps this does not quite meet your criteria because it seems that nobody other than …
32
votes
Are there any fields of academic mathematics whose epistemic status as math is controversial...
There are several possible dimensions to the question, "Is it math?"
Does it belong in the mathematics department? I think you mostly want to exclude this dimension, because of your comment about pur …
29
votes
Sophisticated treatments of topics in school mathematics
Wilkie's solution to the so-called Tarski high-school algebra problem shows that not all identities involving addition, multiplication, and exponentiation that are true for all positive integers are p …
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 …
27
votes
Conceptual reason why the sign of a permutation is well-defined?
This is an elaboration of Will Brian's comment. As I understand it, the goal isn't to find the simplest possible proof or a proof that is most palatable to students; the goal is to make things seem " …
- 82.7k
26
votes
What are possible applications of deep learning to research mathematics?
In the category of guessing, there is the Ramanujan Machine. This project got off on the wrong foot with the research mathematics community because their initial announcement made overblown claims (su …
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 …
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 …
19
votes
Special rational numbers that appear as answers to natural questions
An adventitious quadrangle is a (convex) quadrilateral with the property that if its two diagonals are drawn in, all angles formed are rational multiples of $\pi$. A classification of all such quadri …
16
votes
Math talk for all ages
My inclination would be to convey that it's fun to be a professional mathematician.
How many people in the world have a fun job that they love doing? Only a small percentage. I feel privileged to be i …
16
votes
Examples of theorems where numerical bounds on $\pi$ played a role
In the paper, Space vectors forming rational angles, by Kiran S. Kedlaya, Alexander Kolpakov, Bjorn Poonen, and Michael Rubinstein, the authors classify all sets of nonzero vectors in $\mathbb{R}^3$ s …
- 82.7k