**7**

votes

**1**answer

304 views

### Algebraic structure on homotopy groups of spheres

It is about a "conjecture" I heard (when I was student). There would exist an algebraic structure on the homotopy groups of spheres such that this algebraic structure would be the free algebraic ...

**3**

votes

**0**answers

126 views

### Research topics in Curves and Surfaces [on hold]

I advance that I'm not a mathematician but I'm an undergraduate student of mathematics. In my courses at university I have studied a bit of Differential Geometry, in particoular differential geometry ...

**5**

votes

**1**answer

326 views

### Why did Gödel name his constructible universe $L$?

It seems like Gödel didn't use the letter $L$ for his model before his book "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory", which is ...

**0**

votes

**0**answers

37 views

### Software for matching theorems to inputted conditions/hypotheses

Many times I find myself going through analysis books, wikipedia and papers, looking for what is known for my functions/objects at hand.
So is there any software that at least tries to move in that ...

**1**

vote

**0**answers

216 views

### On algebraic morphisms

Let given schemes $Y\subset X$ and $Z$, where $Y$ is closed subscheme of $X$. Assume that for some morphism $f:Y\to Z$, $Z = [f(Y)]$ (where [] means closure in $Z$). Is it true that there exists ...

**13**

votes

**2**answers

808 views

### Most papers ever “recalled” due to a flawed result?

Prompted by this bit of news,
http://www.wired.co.uk/article/fmri-bug-brain-scans-results
where a bug in MRI software has the potential to nullify up to 40,000 published papers. Has anything analogous ...

**10**

votes

**0**answers

796 views

### Recent progress on the verification of Mochizukis proof of the abc conjecture? [closed]

Apparently in preparation for the upcoming workshop on "Interuniversal Teichmüller Theory" in Kyoto in two weeks, which is intended to bring more light into Mochizukis proposed proof of the $abc$ ...

**1**

vote

**0**answers

198 views

### In what language do you think when doing mathemematics? [closed]

Today, nearly all important papers are written in English. People whose mother tongue is not English nevertheless have to learn English if they want to be a mathematician. My question concerns these ...

**4**

votes

**0**answers

83 views

### Is there a name for groups of the form $Sp(1)^n$?

A (compact) torus is a Lie group isomorphic to the product of finitely many circles: $T^n = S^1 \times \cdots \times S^1$. Such groups are extremely important in Lie theory, Differential Geometry, ...

**5**

votes

**1**answer

269 views

### Intuitive descriptions of some large cardinals

I was trying to formulate intuitive descriptions of some large cardinals.
Roughly something equivalent to "A manifold is an object which looks like patches of $R^n$ glued together". Not perfectly ...

**1**

vote

**1**answer

379 views

### Doing graph theory after a thesis in pure mathematics [closed]

I've just went through the 1st year of my PhD in France, it is related to Floer Homology. I didn't know what it was really about at that time, I chosed this subject because I thought it would combine ...

**3**

votes

**0**answers

149 views

### Topology on $\mathcal{C}(X,Y)$ to work with homotopy

We know that the compact open topology on $\mathcal{C}(X,Y)$ is a good choice for topology on the set of continuous maps, but this seems really efficient, both naively and with respect to existence of ...

**4**

votes

**2**answers

438 views

### How to find volunteer reviewers?

I am currently in a little dilemma about publishing a result related to general matching.
The dilemma is, that I am not associated to any research institute and thus do not have contact to ...

**5**

votes

**5**answers

585 views

### Important results with one or more than one proof [closed]

Can you give examples of deep, important results that have only one known proof, and not just because the first proof is fairly recent, or because not many people really cared to think about it? How ...

**1**

vote

**1**answer

67 views

### best known bounds for spectral radius [closed]

There are many bounds for the spectral radius of graphs in terms of no. of vertices, maximum degree, chromatic number etc. I wish to know till date what are the best lower and upper bound for the ...

**3**

votes

**2**answers

486 views

### Math and social commitment [closed]

I am a master's student and am looking for ways that link a certain social commitment with serious math. Since I have not found such an overview yet and in order to raise public awareness of such ...

**0**

votes

**0**answers

97 views

### Does the method below provide any advantages?

I completed course intro to numerical method and lately interested and trying to find special way to solve this ODE.I have try and ask in math exchange stack but do not get any respond so decided to ...

**10**

votes

**1**answer

388 views

### The geometric median of a solid triangle

Let $\Omega\subset \mathbb R^n$ be a compact subset of dimension $n$. Define the geometric median on $\Omega$ as the point $m_{\Omega}\in \mathbb R^n$ such that the integral $\int_{\Omega}|x-m_{\Omega}...

**12**

votes

**1**answer

276 views

### Digital physics and “Gandy-like” machines

Various physicists, famously John Wheeler, have asserted that physical information is the central object of study in physics, in the sense that an object or concept is "physically meaningful" if it ...

**7**

votes

**1**answer

810 views

### Should I quit the PhD? [closed]

I am not sure whether this is the right place to post this question.
I am at the end of my seventh year. I won't have funding neither from my department nor from my advisor next year and I do not ...

**7**

votes

**0**answers

249 views

### Partial differential equations outside of academia [closed]

I've seen a number of career/jobs questions on mathoverflow before, so I thought I would ask. Please excuse me if this isn't the best place for this specific question. Lately I've been really ...

**1**

vote

**0**answers

58 views

### Covering rough boundaries of closed sets in manifolds by charts

This question is a little vague, I'm afraid, because I'm not sure I expect there to be a complete answer; but there should be some sort of situations where it is possible.
Consider a Riemannian ...

**10**

votes

**1**answer

832 views

### What is a field [Körper] really?

The notion of a field (a commutative ring $R$ with $0\neq 1$ and $R^\times=R-\{0\}$) seems to fit uncomfortably into modern algebra. To see what I mean, consider the following statements:
The ...

**4**

votes

**1**answer

81 views

### Terminology: jointly completely bounded?

This question has a subjective component but I would like answers that try to stick to concrete observable facts, such as which papers use which terminology. However, the informed impressions of those ...

**26**

votes

**4**answers

2k views

### Is it usual for a referee to heed updated versions on arxiv?

I've put a paper on arxiv one year ago and I've submitted the version 6 to a journal seven months ago.
During these last seven months, I've given several talks about this work, which led me to ...

**-4**

votes

**2**answers

195 views

### If mathematics is logic and intuition, then [closed]

I am just wondering why Mathematics is often defined as The study of Structures, Logic and Numbers which I can concur with but still retain various questions in mind.
I am a postgraduate student of ...

**52**

votes

**4**answers

5k views

### Is it possible to have a research career while checking the proof of every theorem that you cite?

A colleague raised the above question with me; more precisely he said:
Suppose that a mathematician were resolved not to publish any theorems
unless they had checked the proof of every theorem ...

**3**

votes

**1**answer

204 views

### Early examples of problems that are easier in high dimension

In many areas of mathematics, there are problems that admit a natural formulation in any dimension. It often happens that such a problem is easier to solve in dimension $n>k$ as compared to ...

**9**

votes

**0**answers

330 views

### Why do we study symplectic geometry? [closed]

What is the motivation behind studying smooth manifolds with a non-degenerate closed two-form?
The subject certainly originated from physics, but is there a deeper reason for why it is still an ...

**1**

vote

**0**answers

113 views

### Referencing your own research paper on a conference board? [closed]

Is it considered poor etiquette to refer a viewer to a research paper while looking at a conference poster? The paper could be placed on the same table so it is readily accessible.

**21**

votes

**3**answers

2k views

### Adapting arguments and plagiarism

I'm currently working on my PhD thesis. I have several suggested problems to work on, some of them are very similar to some problems that my advisor have worked before and published already, either in ...

**3**

votes

**1**answer

231 views

### How to learn concepts of Functional Analysis which are common in PDE

I am a master student and working in PDE area. I am trying to gain deep understanding of some of the concepts in functional analysis which are common tools in PDE research, such as weak*-topology, ...

**2**

votes

**0**answers

311 views

### Do Peano curves provide a counterargument to Grothendieck's critique?

This question arose in the context of an earlier question on Grothendieck's critique of the traditional foundations of topology. Can the paper Group Invariant Peano Curves by Cannon and Thurston be ...

**8**

votes

**3**answers

364 views

### Connection between solution for Schrödinger equation and solution for heat equation

It's known, that if you write imaginary unit into a heat equation you'll get time-dependent Schrödinger equation. Recently one guy discovered a connection between solutions for these two equations (...

**2**

votes

**0**answers

61 views

### What does the square root sign tells us in the wave equation? [closed]

I have been reading the paper on wave equations, and I have some confusion in notations.
Consider the initial value problem(IVP)(Wave equation):
$\frac{\partial ^2 u } {\partial t^2}(x,t) = \...

**36**

votes

**5**answers

1k views

### Undergraduate ODE textbook following Rota

I imagine many people are familiar with the extremely entertaining article "Ten Lessons I Wish I Had Learned Before I Started Teaching Differential Equations" by Gian-Carlo Rota. (If you're not, do ...

**7**

votes

**0**answers

290 views

### Errata in EGA, collected

There is an extensive list of EGA's errata on the books themselves, but my question is whether new errata, that is those found by various mathematicians after the publication, are collected somewhere.
...

**44**

votes

**5**answers

3k views

### How do you mentor undergraduate research?

Lets say you had an undergraduate who wanted to do some advanced work and some research, possibly for a thesis, or things like that.
There are two slightly more specific groups of questions I have ...

**7**

votes

**2**answers

395 views

### Famous results about the value of a given limit assuming it exists

Chebyshev got famous showing that if the limit $l:=\lim_{x\to\infty}\frac{\pi(x)}{x/\log x}$ exists, then necessarily $l=1$, constituting a major breakthrough towards a proof of the famous prime ...

**9**

votes

**5**answers

590 views

### Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…) [closed]

So far, We have seen the applications of functional analysis in PDE, probability and many areas in applied mathematics. On the other hand, methods of algebraic topology are introduced to functional ...

**2**

votes

**0**answers

338 views

### First few research papers [closed]

I was planning on posting this on academia.stackexchange, but I want an answer from mathematicians who've dealt with a similar issue when they were beginning graduate students. If this site doesn't ...

**-4**

votes

**1**answer

284 views

### Proof of formula for $\pi$ [closed]

The number $\pi$ can be expressed as $\pi=\lim_{n\to\infty} \frac{n\sqrt[n]{-1}-n}{\sqrt{-1}}$ or more poetically $\pi=\frac{\infty\sqrt[\infty]{-1}-\infty}{\sqrt{-1}}$. Here we choose the principal ...

**11**

votes

**1**answer

232 views

### Multiplicative infinitesimals in q-analogs?

Risking to be downvoted, here is a very lightweight question.
In various fields - say, algebraic geometry, nonstandard analysis, synthetic differential geometry - infinitely small quantities, i. e. ...

**22**

votes

**4**answers

1k views

### Expert, Intuitive, Organizing Analogies

In learning a new area it is very helpful to have high-level intuitive analogies that keep track of the various parts of an important argument or strategy. Experts have a store of such things, and ...

**4**

votes

**1**answer

443 views

### How many papers are posted a year? [closed]

How many pure math papers are published a year? I vaguely remember seeing a figure of 10,000 but that might be old, and I may be wrong.

**1**

vote

**0**answers

57 views

### Norm-averaging reference request

(Apology in advance for the broadness of this question) I recently came across a relatively simple application where I needed to "balance" the "spreaded-out-ness" of a function with the "peaked-ness" ...

**42**

votes

**10**answers

3k views

### What advantage humans have over computers in mathematics?

Now that AlphaGo has just beaten Lee Sedol in Go and Deep Blue has beaten Garry Kasparov in chess in 1997, I wonder what advantage humans have over computers in mathematics?
More specifically, are ...

**12**

votes

**1**answer

507 views

### What is the motivation behind inner model theory?

Inner model theory aims to construct canonical inner models which captures as much of V as possible, which now is formulated more concretely as to build (fine structural) mice that contain many large ...

**8**

votes

**1**answer

298 views

### What does “game theory” cover and how should it be called?

There seems to be a huge discrepancy in what people refer to when they speak of "game theory". I tend to think of it as including, among other things:
Combinatorial game theory dealing with certain ...

**35**

votes

**13**answers

3k views

### Applications of the Cayley-Hamilton theorem

The Cayley-Hamilton theorem is usually presented in standard undergraduate courses in linear algebra as an important result. Recall that it says that any square matrix is a "root" of its own ...