All Questions
27 questions
196
votes
12
answers
31k
views
Do you know important theorems that remain unknown?
Do you know of any very important theorems that remain unknown? I mean results that could easily make into textbooks or research monographs, but almost
nobody knows about them. If you provide an ...
195
votes
18
answers
17k
views
Great graduate courses that went online recently
In 09.2020 by pure chance I discovered the YouTube channel of Richard Borcherds where he gives graduate courses in Group Theory, Algebraic Geometry, Schemes, Commutative Algebra, Galois Theory, Lie ...
132
votes
22
answers
11k
views
Books that teach other subjects, written for a mathematician
Say I am a mathematician who doesn't know any chemistry but would like to learn it. What books should I read?
Or say I want to learn about Einstein's theory of relativity, but I don't even know much ...
96
votes
36
answers
17k
views
The concept of duality
I have been thinking for sometime about asking this question, but because I did not want to have two "big-list" questions open at the same time, I did not ask this one. Now its time has come....
84
votes
11
answers
12k
views
What are examples of (collections of) papers which "close" a field?
There is sometimes talk of fields of mathematics being "closed", "ended", or "completed" by a paper or collection of papers. It seems as though this could happen in two ways:
A total characterisation,...
81
votes
18
answers
25k
views
What programming language should a professional mathematician know? [closed]
More and more I am becoming convinced that one should know at least one programming language very well as a mathematician of this century. Is my conviction justified, or not applicable?
If I am right,...
77
votes
30
answers
6k
views
Atlas-like websites on specific areas of mathematics
In this post, we look for the existing atlas-like websites providing well-presented classifications or database about some specific areas of mathematics. Here are some examples:
GroupNames: https://...
75
votes
22
answers
19k
views
Essays and thoughts on mathematics
Many distinguished mathematicians, at some point of their career,
collected their thoughts on mathematics (its aesthetic, purposes,
methods, etc.) and on the work of a mathematician in written ...
49
votes
2
answers
5k
views
Well known theorems that have not been proved
I believe that there are numerous challenging theorems in mathematics for which only a sketch of a proof exists. To meet the standards of rigor, a complete proof of these theorems has yet to be ...
40
votes
29
answers
8k
views
Autobiographies of mathematicians
According to Wikipedia, an autobiography is an account of the life of a person, written by that person sometimes with a collaborator.
An autobiography offers the author the ability to recreate history....
37
votes
11
answers
8k
views
"Must read" papers in numerical analysis
In 1993, Prof. L.N. Trefethen published a NA-net posting with a list of thirteen paper he used for teaching the seminar Classic Papers in Numerical Analysis.
In Trefethen's words, ... this course ...
25
votes
11
answers
5k
views
Learning through guided discovery
I have been working through Kenneth P. Bogart's "Combinatorics Through Guided Discovery". You can download it from this page: http://www.math.dartmouth.edu/news-resources/electronic/kpbogart/
I've ...
25
votes
7
answers
7k
views
What are some good resources for mathematical translation?
I am currently in the process of translating a lecture on the étale topology by John Hubbard from French into English (and from transparencies into Beamer). For the most part, the translation is ...
23
votes
7
answers
7k
views
What are some Applications of Teichmüller Theory?
I'm trying to collect some specific examples of applications of Teichmüller Theory. Here are some things I have collected thus far:
No-wandering-domain Theorem (Sullivan)
Theorems of Thurston (...
21
votes
6
answers
2k
views
Online high quality colloquium talks
In my department we're thinking about showing online lectures one day per week at lunch, as sort of a virtual colloquium appropriate to mathematics undergraduates as well as faculty. To start with we'...
17
votes
3
answers
2k
views
Theoretical results on neural networks
With this question I'd like to have a recollection of theoretical rigorous results on neural networks.
I'd like to have results that have been settled, as opposed to hypothesis. As an example, this ...
14
votes
29
answers
7k
views
Which great mathematicians had great political commitments? [closed]
Some mathematicians claim that their field has nothing to do with political concerns; others are deeply involved in political life.
Are there many great mathematicians with great political commitments?...
14
votes
5
answers
5k
views
Who says understanding physics helps mathematicians? (A reference request) [Take the word "who" literally.]
If I wanted to make a somewhat bold and rather vague claim in print that it is widely acknowledged among mathematicians that knowledge of mechanics (in the sense in which physicists understand that ...
14
votes
2
answers
1k
views
Famous papers published in annotated form?
I very much enjoyed reading through The Annotated Turing which goes through Turing's "On Computable Numbers, with an Application to the Entscheidungsproblem" in careful detail. I saw this ...
- 323
13
votes
2
answers
2k
views
New research and re-discovering classic results in "basic" real analysis
Sometimes, it happens that researchers publish a new proof of an old well-known result in "basic real analysis" (I'm referring to what some American people may call "honors calculus"). For instance, ...
11
votes
3
answers
1k
views
Examples in ergodic theory and topological dynamics
I am currently studying basic ergodic theory:
Invariant measures
Poincaré recurrence theorem
Invariant measure for continuous transformations
The ergodic theorems and applications
Ergodic ...
10
votes
10
answers
4k
views
Music: mathematical point of view (revised) [closed]
Mathematical analysis of music started when Pythagoras made his observations about consonant intervals and ratios of string lengths.
ADDED:
In the paper Mathematical Music Theory -- Status Quo 2000, ...
9
votes
0
answers
3k
views
"Must read "papers on analytic number theory
Question: What would be some must-read
papers for an aspiring analytic number
theorist? In other words, what are the papers that any analytic number theorist would have read? (Background: Someone ...
7
votes
8
answers
4k
views
Mathematical Advice for Interested Highschool Students
This may not be a research level math question, but I believe it is still relevant to Math Overflow.
What general resources exist for students in highschool who are very interested in Mathematics?...
4
votes
3
answers
665
views
Quotations about the power of simple ideas [closed]
I'm looking for quotations about how very simple mathematical ideas can be very powerful. I know of a few, but they're not quite what I'm looking for insofar as they contain criticism of other ...
4
votes
2
answers
1k
views
Papers whose title defines a new terminology [duplicate]
To explain a new signal processing technique based on Fourier Transform, Bogert et al went on to define a new vocabulary. The new terminology was published in a paper with the title:
The Quefrency ...
1
vote
1
answer
1k
views
Do mathematicians ignore mathematical works from non-mathematicians? [closed]
Is it true that mathematicians ignore and do not like to take a look at or comment on any mathematical work or manuscript from a person outside the field of mathematics (meaning is not a professional ...