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Jan 19, 2021 at 3:18 answer added Nick S timeline score: 0
Jan 11, 2021 at 5:07 comment added Yaakov Baruch Well, after checking the Number Theory tag here in MO, sorting by votes, and scrolling a few pages of questions I got tired, with no sighting of really interesting answers to the question. Of course there are many good ones below, but maybe there is something of restricted nature about them that leaves one wanting.
Jul 22, 2020 at 18:39 comment added PrimeRibeyeDeal I would highly recommend Minhyong Kim's essay "Why everyone should know number theory" people.maths.ox.ac.uk/kimm/lectures/numbers.pdf
Jul 14, 2020 at 21:14 comment added Nate Eldredge I recently wanted to know how to find the dimension of a free nilpotent real Lie algebra of step $s$ on $n$ generators; I didn't expect for Möbius functions to show up in the answer. Maybe that's not "real" number theory, but it's more like it than one tends to find in geometric analysis.
Aug 31, 2019 at 2:11 history edited Gerry Myerson
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Aug 30, 2019 at 13:58 answer added Tom Copeland timeline score: 0
Apr 6, 2015 at 15:02 answer added Alexey Ustinov timeline score: 4
Aug 22, 2012 at 8:43 comment added Tom Leinster I'm curious about the vote to close. I think this question is still getting interesting new answers. Can the voter-to-close explain their reasons?
Aug 22, 2012 at 0:51 comment added Ian Agol I know of theorems in which number theory does not appear in the statement, but appears at some point in the proof. Also, there are classification theorems (such as Freedman's classification of simply-connected 4-manifolds) in which there is given a bijection between one class of objects and another class of number-theoretic objects.
Aug 21, 2012 at 17:08 answer added kjetil b halvorsen timeline score: 2
Aug 21, 2012 at 15:45 answer added user25309 timeline score: 10
Aug 21, 2012 at 15:04 answer added Todd Trimble timeline score: 13
Aug 21, 2012 at 13:42 answer added not all wrong timeline score: 5
May 11, 2012 at 9:57 answer added Tom De Medts timeline score: 5
May 11, 2012 at 2:02 answer added Eugene timeline score: 6
Mar 16, 2012 at 18:00 answer added Orr Shalit timeline score: 10
Mar 14, 2012 at 2:37 answer added Vamsi timeline score: 6
Mar 14, 2012 at 1:56 answer added Yemon Choi timeline score: 7
Mar 14, 2012 at 1:13 answer added Terry Tao timeline score: 17
Mar 11, 2012 at 10:47 answer added myself timeline score: 11
Mar 11, 2012 at 9:25 answer added Chandan Singh Dalawat timeline score: 13
Mar 10, 2012 at 20:48 comment added Tom Leinster @Terry: Jim's answer is compelling, but it does seem to presuppose a particular point of view on what mathematics is for.
Mar 10, 2012 at 19:10 answer added Terry Tao timeline score: 20
Mar 10, 2012 at 19:01 comment added Terry Tao I think this answer to the analogous question in algebraic geometry is also applicable here: mathoverflow.net/questions/77195/…
Mar 10, 2012 at 14:47 answer added Joël timeline score: 18
Mar 10, 2012 at 8:58 answer added Vladimir Dotsenko timeline score: 6
Mar 10, 2012 at 1:00 answer added Neal timeline score: 13
Mar 9, 2012 at 22:22 answer added GH from MO timeline score: 10
Mar 9, 2012 at 22:05 answer added Robert Kucharczyk timeline score: 16
Mar 9, 2012 at 21:40 answer added Robert Kucharczyk timeline score: 26
Mar 9, 2012 at 19:10 answer added Shahrooz timeline score: 20
Mar 9, 2012 at 18:37 answer added Marc Palm timeline score: 11
Mar 9, 2012 at 18:23 answer added Franz Lemmermeyer timeline score: 52
Mar 9, 2012 at 18:10 answer added KConrad timeline score: 79
Mar 9, 2012 at 17:37 comment added Grant Rotskoff Number theory is used in the representation theory of finite groups to address rationality questions. Algebraic integrality seems to come up just about everywhere.
Mar 9, 2012 at 16:18 answer added Anthony Quas timeline score: 11
Mar 9, 2012 at 16:13 answer added user19475 timeline score: 25
Mar 9, 2012 at 16:09 answer added Arturo Magidin timeline score: 17
Mar 9, 2012 at 16:05 answer added Felipe Voloch timeline score: 11
Mar 9, 2012 at 16:02 answer added Denis Serre timeline score: 24
Mar 9, 2012 at 15:59 answer added Denis Serre timeline score: 4
Mar 9, 2012 at 15:38 comment added Tom Leinster @Vladimir: that's fine, I didn't think you meant it that way. Your comment was helpful. @unknown (yahoo): thanks.
Mar 9, 2012 at 15:36 comment added user19172 See also: mathoverflow.net/questions/84320/…
Mar 9, 2012 at 15:27 answer added Tom Goodwillie timeline score: 32
Mar 9, 2012 at 15:26 answer added Vladimir Dotsenko timeline score: 6
Mar 9, 2012 at 15:24 comment added Vladimir Dotsenko @Tom: just for the record, I did not mean to make the question sound pointless, it's interesting to hear what people have to say! Maybe it'd be good to formulate it in a way that encourages people to share how they ended up with stuff from number theory somewhat "unexpectedly". I mean, in the same spirit as how the n-factorial conjecture ended up being proved using quite advanced algebraic geometry. Maybe a good candidate along those lines is this result of Kanel-Belov and Kontsevich that uses reduction to char p: arxiv.org/abs/math/0512171
Mar 9, 2012 at 15:22 answer added user19475 timeline score: 14
Mar 9, 2012 at 15:20 answer added user19172 timeline score: 29
Mar 9, 2012 at 15:18 answer added Kevin Walker timeline score: 39
Mar 9, 2012 at 15:17 history edited Tom Leinster CC BY-SA 3.0
Added clarification
Mar 9, 2012 at 15:15 answer added Francesco Polizzi timeline score: 9
Mar 9, 2012 at 15:14 comment added Tom Leinster @Martin: any. Vladimir's point (2) could be the undoing of this question, because it's too easy to name things around the borders of the subject.
Mar 9, 2012 at 15:13 comment added Tom Leinster @Francesco: I guess I'd view algebraic geometry in characteristic p as being number theory already. Of course, this is along the lines of Vladimir's point (2).
Mar 9, 2012 at 15:12 comment added Martin Brandenburg @Tom: What sorts of number theory do you have in mind? (the wikipedia page lists at least 7 subbranches) I have read your question as if it refers to prime number distributions or alike, but the comments so far obviously go beyond that.
Mar 9, 2012 at 15:11 comment added Tom Leinster Thanks very much for the comments. Can I suggest that people write this kind of thing as answers rather than comments, though? That way, replies to your comments are organized more neatly.
Mar 9, 2012 at 15:06 comment added wood I guess "whenever a function appears that is also studied in number theory". One particular example comes from combinatorics. In many cases, especially the theory of partitions, the corresponding generating functions turn out to be related to modular forms. So if you are a combinatorists working in this area, at some point you will have to learn also the number theory of automorphic forms.
Mar 9, 2012 at 15:05 comment added Vladimir Dotsenko This is too empty for an answer, so I'll just type a comment. 1) For your third interpretation I have at least one relevant experience of my own - "factor systems" (some) number theorists deal with when talking about central simple algebras over number fields did contribute to the development of homological algebra in general, and learning that somehow expanded my homological algebra horizons a bit. 2) Sometimes, it's hard to say where the border between number theory, commutative algebra, and algebraic geometry lies. Around that "triple point" there should be many potential answers.
Mar 9, 2012 at 14:50 history asked Tom Leinster CC BY-SA 3.0