**12**

votes

**1**answer

238 views

### Okounkov-Vershik approach to representation theory of $S_n$

This is a rather soft question. I was wondering if someone could explain on a fundamental and intuitive level, what the Okounkov-Vershik approach to representation theory of $S_n$ is all about. It's ...

**6**

votes

**2**answers

472 views

### A new result on the Diophantine equation $x^3 + y^3 +z^3 = 3$

The above Diophantine equation is unknown to have any further integer solutions other than $(x, y, z) = (1, 1, 1)$ and $(4, 4, -5)$.
I am a prospective undergraduate mathematics student in Zimbabwe ...

**3**

votes

**0**answers

131 views

### Does the reference letter writer know which school his/her letter is sent to? [on hold]

I am using AMS Mathjob. I am wondering:
If a reference letter writer could write different letters for different schools.
To do that, He/She needs to know which school his/her letter is sent to. Can ...

**29**

votes

**3**answers

1k views

### When is an erratum necessary?

A typo, a spelling error etc., in a published article, is definitely not enough for issuing an erratum.
If a mistake destroys a main result, then an erratum is definitely necessary, and the proof ...

**74**

votes

**53**answers

24k views

### Which popular games are the most mathematical?

I consider a game to be mathematical if there is interesting mathematics (to a mathematician) involved in
the game's structure,
optimal strategies,
practical strategies,
analysis of the game ...

**17**

votes

**21**answers

11k views

### Textbook recommendations for undergraduate proof-writing class

I am teaching the proof-writing class (for the 3rd time) in the Fall and plan to buck the party line and use a different text than the default Bond and Keane. My parameters are as follows:
Logic, ...

**-6**

votes

**1**answer

284 views

### Quintic Equation [closed]

Can we solve the following polynomial quintic equation by radicals
x^5 + x^4 = 1
I found one real root which is algebraic solution (no approximation method ...

**7**

votes

**1**answer

215 views

### Base schemes and Bayesian priors

One of Grothendieck's dicta about algebraic geometry is to consider "the relative situation", where one doesn't consider the category of schemes but of schemes over a fixed base scheme.
In Bayesian ...

**-2**

votes

**0**answers

55 views

### Research topics involving advanced level usage of mathematics and computer algorithms? [closed]

The question might look general but I'm looking for an answer which could help me further my research in the particular subject until my graduation (1.5 years left) as I plan to study outside India. ...

**52**

votes

**3**answers

4k views

### What was Hilbert's view of Gödel's Incompleteness Theorems?

According to Solomon Feferman, in his slide presentation "Three Problems for Mathematics", Hilbert wrote (in regards to Gödel's second incompleteness theorem):
...the end goal [is] to establish as ...

**34**

votes

**29**answers

7k views

### Most intriguing mathematical epigraphs

Good epigraphs may attract more readers. Sometimes it is necessary.
Usually epigraphs are interesting but not intriguing.
To pick up an epigraph is some kind of nearly mathematical problem: it ...

**99**

votes

**27**answers

14k views

### How To Present Mathematics To Non-Mathematicians?

(Added an epilogue)
I started a job as a TA, and it requires me to take a five sessions workshop about better teaching in which we have to present a 10 minutes lecture (micro-teaching).
In the last ...

**63**

votes

**28**answers

9k views

### What are some very important papers published in non-top journals?

There has already been a question about important papers that were initially rejected. Many of the answers were very interesting. The question is here.
My concern in this question is slightly ...

**6**

votes

**0**answers

160 views

### Authorship and the exact wording of a quote about mathematics

This has been troubling me for a few days now and I just can't seem to bring Google to reveal the truth. Which brings me here despite the risk of this question being closed as off-topic.
A few years ...

**68**

votes

**26**answers

10k views

### What are some famous rejections of correct mathematics?

Dick Lipton has a blog post that motivated this question. He recalled the Stark-Heegner
Theorem: There are only a finite
number of imaginary quadratic fields
that have unique factorization. ...

**1**

vote

**0**answers

34 views

### Mathematical difference between broad and narrow band Spectral estimation [closed]

Is there different mathematical formulation behind spectral estimation of narrow band and wide band? By spectral estimation I mean estimating the frequencies in a given signal. Fourier transform is ...

**8**

votes

**2**answers

1k views

### How quickly did Gödel's Incompleteness Theorem become known and heeded throughout mathematics

Does anyone know how news of Gödel's incompleteness theorem spread? Did it do so little by little, or was it shouted in dramatic headlines throughout mathematical literature? If anyone can point me to ...

**58**

votes

**53**answers

13k views

### Pseudonyms of famous mathematicians

Many mathematicians know that Lewis Carroll was quite a good mathematician, who wrote about logic (paradoxes) and determinants. He found an expansion formula, which bears his real name (Charles ...

**20**

votes

**4**answers

1k views

### Publication rates in Mathematics

Have there been any studies of publication rates in Mathematics?
We are trying to construct a workload model for the Faculty of Science and Engineering at my institution. Part of this involves ...

**30**

votes

**4**answers

1k views

### Intuition behind the definition of quantum groups

Being far from the field of quantum groups, I have nevertheless made in the past several (unsuccessful) attempts to understand their definition and basic properties. The goal of this post is to try to ...

**125**

votes

**76**answers

40k views

### Best online mathematics videos?

I know of two good mathematics videos available online, namely:
Sphere inside out (part I and part II)
Moebius transformation revealed
Do you know of any other good math videos? Share.

**177**

votes

**109**answers

45k views

### What are some examples of colorful language in serious mathematics papers? [closed]

The popular MO question "Famous mathematical quotes" has turned
up many examples of witty, insightful, and humorous writing by
mathematicians. Yet, with a few exceptions such as Weyl's "angel of
...

**135**

votes

**72**answers

23k views

### Your favorite surprising connections in Mathematics

There are certain things in mathematics that have caused me a pleasant surprise -- when some part of mathematics is brought to bear in a fundamental way on another, where the connection between the ...

**139**

votes

**136**answers

30k views

### Fundamental Examples

It is not unusual that a single example or a very few shape an entire mathematical discipline. Can you give examples for such examples? (One example, or few, per post, please)
I'd love to learn about ...

**162**

votes

**36**answers

43k views

### Widely accepted mathematical results that were later shown wrong?

I wonder if there are any examples in the history of mathematics of a mathematical proof that was initially reviewed and widely accepted as valid, only to be disproved a significant amount of time ...

**162**

votes

**41**answers

61k views

### A single paper everyone should read? [closed]

Different people like different things in math, but sometimes you stand in awe before a beautiful and simple, but not universally known, result that you want to share with any of your colleagues.
Do ...

**67**

votes

**16**answers

7k views

### What makes four dimensions special?

Do you know properties which distinguish four-dimensional spaces among the others?
What makes four-dimensional topological manifolds special?
What makes four-dimensional differentiable manifolds ...

**35**

votes

**6**answers

5k views

### There must be a good introductory numerical analysis course out there!

Background As a numerical analyst, I've frequently taught the 'Introductory Numerical Analysis' class. Such courses are found in many major universities; the audience typically consists of reluctant ...

**89**

votes

**55**answers

16k views

### Counterexamples in Algebra?

This is certainly related to "What are your favorite instructional counterexamples?", but I thought I would ask a more focused question. We've all seen Counterexamples in Analysis and Counterexamples ...

**31**

votes

**1**answer

2k views

### Why is there a connection between enumerative geometry and nonlinear waves?

Recently I encountered in a class the fact that there is a generating function of Gromov--Witten invariants that satisfies the Korteweg--de Vries hierarchy. Let me state the fact more precisely. ...

**139**

votes

**11**answers

42k views

### Have any long-suspected irrational numbers turned out to be rational?

The history of proving numbers irrational is full of interesting stories, from the ancient proofs for $\sqrt{2}$, to Lambert's irrationality proof for $\pi$, to Roger Apéry's surprise demonstration ...

**35**

votes

**4**answers

2k views

### Hilbert's (cancelled) 24th problem

Hilbert's 23 problems, ten of which were presented at the 1900 ICM in Paris, are too famous for any mathematician to not know. If one reads the descriptions of the problems in Hilbert's paper, one ...

**17**

votes

**1**answer

2k views

### Grothendieck and Non-commutative Geometry?

When Grothendieck and his followers were working on their profound progress of algebraic geometry, did they ever consider non-commutative rings? Is there anyway evidence that Grothendieck foresaw the ...

**230**

votes

**21**answers

28k views

### Thinking and Explaining

How big a gap is there between how you think about mathematics and what you say to others? Do you say what you're thinking? Please give either personal examples of how your thoughts and words ...

**44**

votes

**22**answers

12k views

### Interesting Calculus Questions/Exercises

I am in the process of redesigning the calculus course that I have taught five or six times. What I would like to know is if anyone has some really good examples or exercises that I could either do ...

**242**

votes

**72**answers

90k views

### Video lectures of mathematics courses available online for free

It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortunately, some ...

**2**

votes

**2**answers

172 views

### type theory that does not treat the terms of $\mathrm{Prop}$ as types

In type theory there is a type $\mathrm{Prop}$ that contains every proposition, so $p\colon\mathrm{Prop}$ (in words, "$p$ is of type $\mathrm{Prop}$") where $p$ is a proposition. In all type theories ...

**40**

votes

**9**answers

6k views

### How does a mathematician choose on which problem to work?

Main question:
How does a mathematician choose on which problem to work?
An example approach to framing one's answer:
What is a mathematical problem - big or small - that you solved or are ...

**12**

votes

**1**answer

966 views

### Research and exposition: how does writing “basic” books affect your “serious” research work?

I can see the benefit of writing a mathematical monograph: you revise and organize your own work and recollect the key ideas of your own research. But this applies only to books aimed at researchers ...

**11**

votes

**1**answer

289 views

### 'Updated' book in the same spirit as Dieudonné's Panorama des mathématiques pures

Today a colleague of mine asked me if I knew of any "more modern version" of J. Dieudonné's Panorama des mathématiques pures. Le choix bourbachique.
The very first thing that instantly came to my ...

**6**

votes

**3**answers

656 views

### What are the usual deadlines in paper submission procedure?

I've submitted a paper to a journal 10 days ago, and I did not yet get any news from the handling editor.
Of course, 10 days is quite short, but I hope I will not wait one year without any news for ...

**2**

votes

**1**answer

207 views

### Where does the name $NE(X)$ come from?

Why do we call the cone of curves(effective one cycles) on a variety $X$ as $NE(X)$, what does $NE$ stand for?

**44**

votes

**17**answers

4k 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 ...

**2**

votes

**0**answers

159 views

### Originality of an idea [closed]

How can I verify (ensure myself) that a research question in mathematics was not already treated ?
or at least see where a particular paper was cited ?
thank you.
PS : I hope i am posting in the ...

**3**

votes

**0**answers

243 views

### Examples of beautiful theories without applications [closed]

What are examples of beautiful theories, which have no known applications?

**28**

votes

**2**answers

966 views

### Different styles of writing/reading articles

Recently, I discovered a rather unexpected thing. We are writing an article in collaboration and we permanently have some discussions about how to write, in which order, how to organize material etc.
...

**24**

votes

**12**answers

2k views

### What math institutes offer research in pairs/research in teams?

Some math institutes offer programs in which a small number of researchers are enabled to meet at the institute for a week or more. A list seemed as if it could be useful.

**1**

vote

**0**answers

87 views

### Curve meeting an open subset

I would like a reference for the following (easy/classical?) result:
Let $X$ be a quasi-projective irreducible algebraic variety of dimension $\ge 1$, defined over an algebraically closed field $k$ ...

**105**

votes

**39**answers

31k views

### Most interesting mathematics mistake?

Some mistakes in mathematics made by extremely smart and famous people can eventually lead to interesting developments and theorems, e.g. Poincaré's 3d sphere characterization or the search to prove ...

**116**

votes

**58**answers

24k views

### What are your favorite instructional counterexamples?

Related: question #879, Most interesting mathematics mistake. But the intent of this question is more pedagogical.
In many branches of mathematics, it seems to me that a good counterexample can be ...