**3**

votes

**0**answers

104 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

274 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 ...

**13**

votes

**7**answers

4k views

### Book on Symplectic Geometry

Can someone please tell me some introductory book on symplectic geometry? I have no prior idea of the subject but I do know about Lagrangian and Hamiltonian dynamics (at the level of Landau-Lifshitz ...

**10**

votes

**1**answer

540 views

### Construction of the Lie functor: left vs. right invariant vector fields on Lie groups and Lie groupoids

When constructing the Lie algebra $L(G)$ of a Lie group $G$, one usually uses the identification of the tangent space $T_1 G$ with left invariant vector fields $\mathcal{V}^l(G)$ to construct the Lie ...

**56**

votes

**16**answers

7k views

### Contest problems with connections to deeper mathematics

I already posted this on math.stackexchange, but I'm also posting it here because I think that it might get more and better answers here! Hope this is okay.
We all know that problems from, for ...

**0**

votes

**0**answers

36 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 ...

**45**

votes

**35**answers

13k views

### Most intricate and most beautiful structures in mathematics

In the December 2010 issue of Scientific American, an article "A Geometric Theory of
Everything" by A. G. Lisi and J. O. Weatherall states "... what is arguably the most
intricate structure known to ...

**1**

vote

**0**answers

213 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

800 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 ...

**89**

votes

**26**answers

39k views

### What are the most misleading alternate definitions in taught mathematics?

I suppose this question can be interpreted in two ways. It is often the case that two or more equivalent (but not necessarily semantically equivalent) definitions of the same idea/object are used in ...

**10**

votes

**0**answers

777 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 $abc$ ...

**116**

votes

**54**answers

58k views

### Interesting mathematical documentaries

I am looking for mathematical documentaries, both technical and non-technical. They should be "interesting" in that they present either actual mathematics, mathematicians or history of mathematics. I ...

**67**

votes

**10**answers

8k views

### Have you solved problems in your sleep?

I have hit upon major (for me—relative to my trivial accomplishments)
insights in my research
in various sleep-deprived altered states of consciousness,
e.g., long solo car-drives extending ...

**1**

vote

**1**answer

98 views

### Convention on Clifford Product

When studying the Clifford Algebra associated to some $(V,Q)$, one finds two basic identities differing by a sign:
$vv=Q(v)$ (see, for instance, Wikipedia)
$vv=-Q(v)$ (see, for instance, MathWorld ...

**105**

votes

**18**answers

10k views

### How does one justify funding for mathematics research?

G. H. Hardy's A Mathematician's Apology provides an answer as to why one would do mathematics, but I'm unable to find an answer as to why mathematics deserves public funding. Mathematics can be ...

**1**

vote

**0**answers

195 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

82 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, ...

**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. ...

**5**

votes

**1**answer

264 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 ...

**37**

votes

**8**answers

5k views

### Getting nervous refereeing a paper

I am refereeing my first paper and I'm quite excited! But inexperienced and I would like to ask an advice to the Maths Community of MO. Let me tell you that I have already read Refereeing a Paper, but ...

**19**

votes

**18**answers

8k views

### What are some applications of other fields to mathematics?

It is commonplace to consider applications of mathematics to other fields, especially the exact sciences. But what I would like to know about is the converse topic, namely:
What are some ...

**121**

votes

**81**answers

97k views

### Do good math jokes exist? [closed]

Have a good joke? Share.
I know this is subjective, but the principle "should be of interest to mathematicians" trumps. (I hope.)

**1**

vote

**1**answer

376 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 ...

**67**

votes

**8**answers

11k views

### How do you not forget old math?

I am trying to not forget my old math. I finished my PhD in real algebraic geometry a few years ago and then switched to the industry for financial reasons. Now I get the feeling that I want to do a ...

**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 ...

**18**

votes

**2**answers

1k views

### Felix Klein on mean value theorem and infinitesimals

This is a reference request prompted by some intriguing comments made by Felix Klein.
In 1908, Felix Klein formulated a criterion of what it would take for a theory of infinitesimals to be ...

**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

583 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

66 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 ...

**133**

votes

**44**answers

77k views

### Magic trick based on deep mathematics

I am interested in magic tricks whose explanation requires deep mathematics. The trick should be one that would actually appeal to a layman. An example is the following: the magician asks Alice to ...

**142**

votes

**29**answers

33k views

### Examples of unexpected mathematical images

I try to generate a lot of examples in my research to get a better feel for what I am doing. Sometimes, I generate a plot, or a figure, that really surprises me, and makes my research take an ...

**144**

votes

**136**answers

31k 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 ...

**51**

votes

**47**answers

18k views

### An example of a beautiful proof that would be accessible at the high school level?

The background of my question comes from an observation that what we teach in schools does not always reflect what we practice. Beauty is part of what drives mathematicians, but we rarely talk about ...

**106**

votes

**72**answers

16k views

### Most helpful math resources on the web

What are really helpful math resources out there on the web?
Please don't only post a link but a short description of what it does and why it is helpful.
Please only one resource per answer and let ...

**82**

votes

**8**answers

9k views

### Mistakes in mathematics, false illusions about conjectures

Since long time ago I have been thinking in two problems that I have not been able to solve. It seems that one of them was recently solved. I have been thinking a lot about the motivation and its ...

**136**

votes

**28**answers

58k views

### Intuitive crutches for higher dimensional thinking

I once heard a joke (not a great one I'll admit...) about higher dimensional thinking that went as follows-
An engineer, a physicist, and a mathematician are discussing how to visualise four ...

**8**

votes

**2**answers

517 views

### Are there any organized websites for seminar/conference videos?

These days, there are many conference centers and universities recording seminars and conference talks and make them available on the web. Some examples:
http://www.fields.utoronto.ca/video-archive
...

**3**

votes

**2**answers

483 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}...

**64**

votes

**59**answers

15k 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 ...

**12**

votes

**1**answer

274 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

806 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 ...

**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 ...

**7**

votes

**0**answers

248 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 ...

**13**

votes

**2**answers

2k views

### What are examples of theorems which were once “valid”, then became “invalid” as standard definitions shifted?

That is, results established by correct proofs within some framework, yet the manner in which their author or the general mathematical community at the time would describe these results would, in ...

**155**

votes

**67**answers

53k views

### Awfully sophisticated proof for simple facts [closed]

It is sometimes the case that one can produce proofs of simple facts that are of disproportionate sophistication which, however, do not involve any circularity. For example, (I think) I gave an ...

**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

829 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 ...

**20**

votes

**2**answers

2k views

### Euler's mathematics in terms of modern theories?

Some aspects of Euler's work were formalized in terms of modern infinitesimal theories by Laugwitz, McKinzie, Tuckey, and others. Referring to the latter, G. Ferraro claims that "one can see in ...