**0**

votes

**2**answers

365 views

### Correct definition of the sequence of natural numbers with set theory, but without counting or measuring size [closed]

This question may appear banal, but there seems to be more than meets the eye; a common glitch is to explain numbers by the "size" of sets without saying how to measure or compare the size of sets.
...

**14**

votes

**6**answers

1k views

### Mathematical Paper That Just Links Two Different Fields of Sciences

I have a soft question that is interesting for me in some aspects. I appreciate your answers and comments about it.
Four years ago, one of my friends in MIT, in the biology lab, had working on ...

**20**

votes

**8**answers

1k views

### Self-containing structures

(This question is partly inspired by What is inter-universal geometry?.)
I have absolutely no background in Teichmuller theory or any related subject, but what I can follow of Mochizuki's description ...

**7**

votes

**4**answers

749 views

### Coboundaries and Gluing in Cech Cohomology - Intuition?

I'm trying to develop an intuition for Cech cohomology geometrically, but am currently failing. A lot of people seem to say that the groups $H^n$ measure obstructions to gluing local sections to get ...

**8**

votes

**1**answer

882 views

### How many proofs of the Weil conjectures are there?

I hope this this is not seen as too much as jumping on the band-wagon, but here goes.
Deligne's proof of the last of the Weil conjectures is well-known and just part of a huge body of work that has ...

**28**

votes

**0**answers

2k views

### The Work of Pierre Deligne

In this biography of Pierre Deligne, there is a quote of Jacques Tits which says that "quite a few of his best ideas have never been written!".
What are some of his best ideas that you have heard of ...

**1**

vote

**1**answer

800 views

### PhD in operator algebras and non-commutative geometry [closed]

I do not know whether it is a good place to ask this question or not.
I want to PhD in operator algebras and non-commutative geometry. What are the best places in the world for that? I want a good ...

**8**

votes

**1**answer

658 views

### Topology, the board game

Edit: I am reposting this question fom math.stackexchange.com; there may be some professors here who have more experience teaching topology.
This is a math education question that I've been thinking ...

**9**

votes

**1**answer

381 views

### New research on coding in reverse mathematics?

Coding is obviously a fundamental tool in reverse mathematics, and practitioners take care to both demonstrate the correctness of their coding mechanisms and point out their limitations. Harvey ...

**4**

votes

**2**answers

908 views

### How long should one wait for a report before asking about its status? [closed]

I apologize if this question is too soft or if its answers would be too subjective for this site. However, I would find it highly useful to have such a question answered on this site, and I believe ...

**0**

votes

**1**answer

253 views

### If X is a Haussdorf topological space and R and equivalence relation on X, when is X/R Haussdorf?

I was wondering if there are some necessary and sufficient conditions for the quotient space to be Haussdorf. I have been trying a little for a while, but I only got very restrictive sufficient ...

**13**

votes

**3**answers

574 views

### Is there an editors checklist for mathematics?

I always have trouble with editing math papers for publication. I know there are plenty of checklists for English exposition but is there one for math specific exposition errors?

**9**

votes

**4**answers

1k views

### Role of applications in modern mathematics [closed]

Older days scientists were universalists and philosophy, physics and mathematics were a part the same question - understanding the world.
Nowadays one may get feeling that the role of applications ...

**7**

votes

**3**answers

596 views

### Formal writing: numbers under 10

I've been tasked with proofreading an Engineering/Mathematics thesis paper. I was always told that numbers under 10 should be spelled out (one, two, three, ...) but I was wondering if this rule holds ...

**5**

votes

**2**answers

640 views

### Faculty Handbook: Mentoring Undergraduates in Research and Scholarship

A few days ago I was asked by the director of the Center for Undergraduate Research and Scholarship at Georgia Regents University (formerly known as MCG and Augusta State) to contribute an article for ...

**3**

votes

**0**answers

711 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: ...

**22**

votes

**7**answers

2k views

### Should one attack hard problems?

When I applied for a PhD student position I had an interview with two professors. Somehow we touched the problem if $P$ is $NP$ and, once we got there, for some reason both professors made it clear ...

**7**

votes

**2**answers

1k views

### How should a professor feel peace of mind when a student leaves academia? [closed]

I apologize if this is the wrong forum for this question -- if so, could somebody please point me to the correct one?
I'm a professor who recently started advising graduate students, and I'm trying ...

**7**

votes

**0**answers

143 views

### Tangent space, metrics etc. on simplicial sets

Is there a way to attach some sensible notion of tangent space to a simplicial set? If yes, is it possible to transfer typical local data from differential geometry such as metrics to this setting?
...

**49**

votes

**5**answers

1k views

### Math Annotate Platform?

Suppose most mathematical research papers were freely accessible online.
Suppose a well-organized platform existed where responsible users could write comments on any paper (linking to its doi, ...

**15**

votes

**1**answer

527 views

### Mendelson's *Mathematical Logic* and the missing Appendix on the consistency of PA

A very soft question, but I hope not out of order here.
In the first edition of Elliott Mendelson's classic Introduction to Mathematical Logic (1964) there is an appendix, giving a version of ...

**4**

votes

**0**answers

340 views

### dreams of mathematics(ramannujan) others? [closed]

"Ramanujan credited his acumen to his family Goddess, Namagiri of Namakkal. He looked to her for inspiration in his work,[84] and claimed to dream of blood drops that symbolised her male consort, ...

**3**

votes

**1**answer

608 views

### Math major at 36 [closed]

I decided to go for math at 36. Is this idea possible? I studied literature, political science and international relations and still I am not really sure what I am doing.
Since I was kid, I was not ...

**34**

votes

**19**answers

5k views

### Mathematicians whose works were criticized by contemporaries but became widely accepted later

Gauss famously discarded Abel's proof that an algebraic equation of degree five or more cannot have a general solution (Abel himself had rejected divergent series as the work of the devil). Cantor's ...

**5**

votes

**3**answers

724 views

### group of diffeomorphisms of a manifold

How much has been the group of diffeomorphisms of a manifold " been studied.
I got this information from wiki.
" Quite a lot is known about the group of diffeomorphisms of the circle. Its Lie algebra ...

**3**

votes

**2**answers

399 views

### To what extent should a pure mathematician care about the meaning of things? [closed]

I have asked this on SE before, But i DO hope that you kindly give me more insight about this question since it's very important to me
Having come from engineering background, I am kinda obsessed ...

**1**

vote

**1**answer

215 views

### Bounds for conjugacy classes of subgroups

My question is rather general and the reason for this is that I am primarily interested in finding sources where I can read more about this type of problems. So here goes:
To begin with, I want to ...

**35**

votes

**10**answers

2k views

### Why is Set, and not Rel, so ubiquitous in mathematics?

The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations.
Why was there the necessity of singling ...

**32**

votes

**31**answers

5k views

### Trichotomies in mathematics

Added. Thanks to all who participated! Let me humbly apologize to those who were annoyed (quite understandably) by this thread, deeming it nothing more than an exercise in futility. If you thought the ...

**23**

votes

**9**answers

2k views

### Is the empty graph a tree?

This is a boring, technical question that I stumbled upon while making a contribution to Sage. I would still like to hear a constructive answer so hopefully the question does not get closed.
The ...

**6**

votes

**4**answers

841 views

### fourier analytic proofs

While searching through Mathoverflow, I found out a fourier analytic proof of the Isoperimetric Inequality.Also, by google search I found a fourier analytic proof of Quadratic Reciprocity theorem.I ...

**3**

votes

**1**answer

394 views

### Integral representation of the modified Bessel functions of the second kind and asymptotic expansion

The modified Bessel function (Macdonald function) $K_\alpha(z)$ is known to have the following asymptotic expansion for large positive $z$:
$$
K_\alpha(z)=\sqrt{\frac{\pi}{2z}}e^{-z}\sum_{k=0}^\infty ...

**22**

votes

**13**answers

1k views

### Discovering and selecting conferences

Last summer, there were several excellent summer schools in my field that I learned of only after the application date. The events I did attend were chosen without too much care. I'm planning for the ...

**5**

votes

**5**answers

1k views

### Financial Mathematics Books

Hi, I am looking for a good reference to start reading about Mathematical Finance/Financial Engineering. I have a good background in Math but have no idea at all in Finance.

**3**

votes

**1**answer

335 views

### Geometry and quantization

I know that lots of effort is being put into quantization of geometry(NCG).This effort of course comes with the idea of operator algebra being a powerful machinery. Has any effort been given in the ...

**19**

votes

**10**answers

1k 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 ...

**7**

votes

**4**answers

801 views

### Examples of “exotic” induction

Next week I am going to teach two lessons on induction to very motivated students from high schools. At some point I would like to talk about ordered sets, well-ordered sets, and mention the fact that ...

**7**

votes

**1**answer

246 views

### Formulating the calculus of varations with exterior calculus

I noticed that a calculus of variations problem is just an integral over a differential form. Therefore, I would think it would be possible to formulate the Euler-Lagrange equations using exterior ...

**7**

votes

**2**answers

438 views

### Examples In Ergodic Theory and Topological Dynamics

I am currently studying basic Ergodic Theory:
Invariant Measures
PoincarĂ© recurrence Theorem
Invariant Measure For Continuous Transformations
The Ergodic Theorems and Applications
Ergodic ...

**3**

votes

**3**answers

525 views

### Is there a (standard) name for $\bar{A}\setminus A$?

This is a notation question:
If $A$ is a set in a topological space and $\bar{A}$ is its closure, is there a (standard) name for $\bar{A}\setminus A$?

**4**

votes

**3**answers

582 views

### Meaning of a phrase from “The algebra of grand unified theories”.

Motivated by an answer to this mathoverflow question I've been making an effort to understand Baez and Huerta's article "The algebra of grand unified theories".
As far as I can tell, mathematically, ...

**-3**

votes

**2**answers

766 views

### Should science authors discourage / boycott the recent push for author IDs [closed]

In recent years, several organizations (publishers, arXiv, universities) started pushing for systems of a reliable author identification, gaining considerable traction with the recent launch of ORCID. ...

**9**

votes

**6**answers

2k views

### submit the second part of a paper

I couldn't find similar question being asked here. The closest one I can find is When to split/merge papers?. Here is my situation: I proved a theorem. When I try to type it, I found that it's very ...

**9**

votes

**2**answers

1k views

### Math Zeitgeist 2012 [closed]

Dear MO-fellows, Happy New Year !
Taking google as an example: https://www.google.com/zeitgeist/2012/
Why not to make a list of noted math events in 2012 ?
E.g. 15 December 2012 Museum of Math was ...

**70**

votes

**28**answers

7k views

### New grand projects in contemporary math

When I was a graduate student in math (mid-late eighties and early nineties) the arena was dominated by a few grand projects: for instance, Misha Gromov's hyperbolic groups, which spread into many ...

**6**

votes

**0**answers

266 views

### Where does the term “torsor” come from?

Is there a heuristic reason why pricipal homogeneus spaces of a group (object) $G$ (in some categories) are called $G$-torsors? Does it have anything to do with the idea of "torsion", somehow? When ...

**1**

vote

**19**answers

1k views

### Math for a cake [closed]

My wife likes to decorate birthday cakes. She told me that she will make a math cake for my birthday and I should provide her a "famous math formula" to be written on the top of the cake.
I realized ...

**16**

votes

**3**answers

1k views

### Intuitive pictures in characteristic p

This is a tough one, but does anyone know of any images that recall characteristic p geometry (over algebraically closed fields) in some sense? It is not enough if it is some picture that can be also ...

**40**

votes

**8**answers

4k views

### Publishing a bad paper?

First, I apologize if mathoverflow is a bad fit for this question, but it is the only place where I can think to get advice from professionals given my circumstance. I'm also sorry about any vagueness ...

**5**

votes

**4**answers

488 views

### Integral transform and $\frac{1}{n!}$.

Probably this is a trivial question, but I am unable to find an answer: is there a function $v(x)$ such that
$$
\int_{0}^\infty x^n e^{v(x)} dx =\frac{1}{n!}
$$
for all positiv integer n?