**31**

votes

**7**answers

3k views

### The Unreasonable Effectiveness of Physics in Mathematics. Why ? What/how to catch?

Starting from 80-ies the ideas either coming from physics, or by physicists themselves (e.g. Witten) are shaping many directions in mathematics. It is tempting to paraphrase E. Wigner, saying about ...

**13**

votes

**2**answers

1k views

### The non-traveling mathematician problem

This is a career question. I have just begun a research postdoc position in Southern California. It has been hard, but I've enjoyed teaching my first graduate courses and working on research and ...

**4**

votes

**2**answers

2k views

### Does Bourbaki's (and Grothendieck's) approach to mathematics survive today? [closed]

I am curious if the "Bourbaki's approach" to mathematics is still a viable point of view in modern mathematics, despite the fact that Bourbaki is vilified by many.
Even more specifically, does anyone ...

**26**

votes

**3**answers

972 views

### “Softness” vs “rigidity” in Geometry

According to common wisdom, there are structures in Geometry that have a more "topological" flavor, others that are more "geometrical", and others that are halfway between. Usually, geometries${}^*$ ...

**0**

votes

**1**answer

52 views

### Continuity of an extension map

Suppose $\delta\in (0,1)$ and $r<1+\delta.$ Suppose moreover we are given a sequence of functions $u_m\in H^{1/2,2}(\partial B_r(0))$, where $B_r(0)$ denotes the euclidean $n-$dimensional ball. ...

**22**

votes

**1**answer

1k views

### How should a number theorist learn a modest amount of algebraic geometry?

A little bit vague, but I hope useful for the entire community.
I am, by training, an analytic number theorist. I have managed to learn some algebraic geometry, by reading parts of Silverman's ...

**2**

votes

**0**answers

231 views

### Descriptive set theory on $\mathbb{R}^\mathbb{N}$

The short version of my question is, What is a good source for learning about descriptive set theory on the space $\mathbb{R}^\mathbb{N}$, under the product topology coming from the discrete topology ...

**0**

votes

**2**answers

204 views

### Algebraic maximal extension and algebraic closure

Let $K$ be a valued field. We say that $K$ is algebraic maximal if any algebraic extension of $K$ has either a bigger value group or a bigger residue field.
Under which condition is an algebraic ...

**6**

votes

**2**answers

742 views

### Research in topology for a master student [closed]

I hope here is the best place to ask this, I will begin my master degree very soon, I've already attended the regular undergraduate courses included Real Analysis, Analysis on manifolds, Abstract ...

**11**

votes

**7**answers

1k 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 ...

**69**

votes

**16**answers

4k views

### Does Physics need non-analytic smooth functions?

Observing the behaviour of a few physicists "in nature", I had the impression that among the mathematical tools they use a lot (along with possibly much more sofisticated maths, of course), there is ...

**2**

votes

**0**answers

324 views

### From complexity to topology after a CS PhD

Let me start by apologizing for the soft and lengthy nature of the question.
I am a third year graduate student (in India) working in complexity theory. Early this year, I developed an interest for ...

**7**

votes

**9**answers

981 views

### Examples where adding complexity made a problem simpler

I can think of a few situations in math where a problem becomes easier or an object becomes simpler when some complexity is added. Examples:
$S^n$ is never contractible, but $S^{\infty}$ is.
The ...

**4**

votes

**1**answer

456 views

### Impact of LHC on math ? [closed]

LHC (Large Hadron Collider) "... remains one of the largest and most complex experimental facilities ever built". May be it is even the most complex project in humankind's history(?).
Such projects ...

**10**

votes

**7**answers

3k views

### 13 months and not even one report. what would you do?

I submitted a 24 pages paper to a good journal - say usually in the top 10-20 - of pure maths, and after 14 months from the submission I haven't received any report. The last news I had from the ...

**3**

votes

**0**answers

229 views

### A Question Regarding Boolean-valued Models

What were the intuitions motivating the creation (or discovery, if you will) of Boolean-valued models? I have searched for the Scott-Solovay paper on the subject, but to no avail. There also seems to ...

**19**

votes

**3**answers

649 views

### What classification theorems have been improved by re-categorizing?

Many classification theorems (e.g. of the finite subgroups of $SO(3)$, or the finite-dimensional complex simple Lie algebras, or the finite simple groups) have some infinite lists, plus some ...

**4**

votes

**3**answers

566 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 ...

**2**

votes

**0**answers

120 views

### Is there something interesting in the uniqueness condition for a sheaf?

After digesting the Presheaf definition by the very first time, one feels (at least I felt) a strange sensation noticing the existence and uniqueness conditions to graduate that Presheaf as a sheaf, ...

**4**

votes

**2**answers

254 views

### Is the generalized Baire space complete?

I want to see whether the fact that the Baire space $\omega^\omega$ is a complete (metrizable) space generalizes to $\kappa^\kappa$ being a complete (topological) space. I think this is an easy ...

**8**

votes

**2**answers

999 views

### What conjectures in anabelian geometry are false?

Proving things suspected to be true in anabelian geometry is usually very hard. Maybe it is easier to disprove things suspected to be false?
In particular, I am interested in false generalizations of ...

**10**

votes

**4**answers

1k views

### How Many 4-Manifolds are Symplectic?

As an honest question (probably with some subjectivity), how many smooth oriented 4-manifolds are actually symplectic? Can I say half (perhaps under some mild assumptions)? I ask this question because ...

**7**

votes

**2**answers

2k views

### Question on “publication List” for applying to post-doctoral jobs

1) Many Mathematics departments ask to send a "list of publications" while applying for research postdoctoral jobs. My question is: how important is it to post my papers in arXiv. I know, posting on ...

**0**

votes

**2**answers

485 views

### What constitutes the division between discrete and non-discrete math? Are there any math subject where it's being blurred? [closed]

I often heard about this division but always in a non-formal manner. What constitutes it? Is it a limit operation? Or a fundamental distinction between countable and uncountable sets? And what math ...

**50**

votes

**7**answers

7k views

### Lost soul: loneliness in pursing math. Advice needed. [closed]

This is a atypical question for the forum. I'd like to get some advice on whether I should keep pursuing Math in the traditional route, i.e. get a PhD, do research & teach, etc.
Due to financial ...

**19**

votes

**2**answers

2k views

### Publication and Career as a fresh Ph.D

This may be a little off topic.
But as new Ph.D in geometry/topology area, I have a feeling that it is relatively harder to publish a descent paper. However after seeing some peers who study PDE or ...

**3**

votes

**1**answer

444 views

### Request: Kato's article “Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions.” Part II

Hello,
The question (similar to MO.96531) is about the article by Professor Kazuya Kato in this book.
In this article, Professor Kato indicates the contents of the second part.
MathSciNet does not ...

**7**

votes

**3**answers

497 views

### Intuition Behind a Decimal Representation with Catalan Numbers

From $0 = 0.5 - 0.5 = 0.5 - \sqrt{0.25}$, we can adjust the subtrahend slightly to obtain
$$0.5 - \sqrt{0.249} = 0.001\ 001\ 002\ 005\ 014\ 042\ldots$$
where the decimal representation contains the ...

**13**

votes

**1**answer

2k views

### Is it common practice to publish parts of a PhD thesis in advance? [closed]

I'm interested in publishing parts of my PhD thesis in advance and I'm wondering wether or not this will result in problems later on. One of the problems I'm thinking of is that usually the copyright ...

**6**

votes

**9**answers

1k views

### Beautiful theorems with short proof [closed]

I like to ask for beautiful mathematical theorems with short proof. A proof is short in my sense if it is at most one page assuming basic notations and very basic results a second year student will ...

**3**

votes

**2**answers

424 views

### proper quoting of theorems

Dear collegues, I am writing an overview paper for an academic journal, where I also need to state theorems proved by other authors. Usually I cite the source and then rephrase the theorem. However in ...

**3**

votes

**1**answer

533 views

### Convenient definition of “category of Riemannian manifolds”?

Has a notion of "category of Riemannian manifolds" been defined and used in the literature?
For which reasons is it or would it (not) be a useful notion?
I think the objects should be all (perhaps ...

**1**

vote

**1**answer

321 views

### Why is the physical space equivalent to $\mathbb{R}^3$ [closed]

I am trying to understand what would be the logical reasons behind our assumption that our physical space is equivalent to $\mathbb{R}^3$ or 'physical straight line' is equivalent to $\mathbb{R}$.
...

**7**

votes

**0**answers

165 views

### what's the role of $H^{p}(\mathbb{R}^{n})$ in modern (harmonic) analysis?

The classical theory of $H^p$,due to it's heavy dependence on the complex function theory(such as Blaschke products), seemed to have an insurmountable obstacle barrying its extension to several ...

**9**

votes

**1**answer

207 views

### Is there a Dedekind-Frobenius group determinant for infinite groups?

If $G$ is a finite group and $\lbrace x_{g} \rbrace_{g\in G}$ are commuting formal variables, then one can form a matrix whose $(g,h)$ entry is $x_{gh^{-1}}$. The determinant of this matrix is a ...

**4**

votes

**0**answers

262 views

### Stability conditions for coherent sheaves and GIT

I am learning stability conditions for derived categories of coherent sheaves, following Bridgeland, and coming from a vector bundles background. $\mu$-stability for vector bundles has a clear GIT ...

**2**

votes

**0**answers

305 views

### The Creative Process in Mathematics [closed]

Mathematicians usually focus on the products of their creativity:
theorems (equations and inequalities, existence-uniqueness results), algorithms, modeling,
and conjectures.
A different question: ...

**7**

votes

**2**answers

821 views

### Mathematical computer desk [closed]

D. Gibb, from the Mathematical Laboratory, University of Edinburgh,
describes a Computer Desk in his book A course in interpolation and numerical integration for the
mathematical laboratory, G. Bell ...

**6**

votes

**2**answers

670 views

### Road to Solovay's Land.

In the first semester of 2012 I took a course in General Topology and Set Theory, at undergraduate level. For topology, I was instructed to use Engelking's General Topology; albeit I had a great ...

**26**

votes

**16**answers

2k views

### Justifying/Explaining math research in a public address

I have been chosen by my university to give a 1 hour public research lecture. Every year a researcher is chosen for this honour. Traditionally people explain their own research about designing ...

**1**

vote

**0**answers

114 views

### Algebraic properties of the semiring of open subsets.

Does anyone know of a useful general topological application of the algebraic properties of the semiring of open subsets of some topological space? Or examples of any such nontrivial properties at ...

**8**

votes

**0**answers

181 views

### Fixed marginals of joint distribution: status

One of the well-known problems of classical probability theory is the determination of the set of all extreme points in the convex set of all probability distributions in a product Borel space $\left ...

**5**

votes

**3**answers

1k views

### Battle of the brains; cultural mathematics

Firstly, I apologize if my question is long.
Three years ago, I watched a video with the name Battle of the Brains. It was a wonderful video about challenging some famous peoples to solve some ...

**0**

votes

**1**answer

110 views

### Reference: DaPrato and Grisvard parabolic PDEs.

Has anyone read G. DaPrato and P. Grisvard Equations d'evolution abstraites nonlineaires de type parabolique?
It's not available in my library. I am wondering if it's worth me acquiring it: is it ...

**16**

votes

**19**answers

2k views

### History Question: AUTObiography 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 ...

**28**

votes

**11**answers

5k 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 ...

**15**

votes

**4**answers

3k views

### number of zeroes in 100 factorial.

I was on math.stackexchange the other day and i found a question that said How many zeroes are there in 100!. I quickly factored it out and said that there where 24 zeroes. However thats only the ...

**6**

votes

**7**answers

1k views

### Incidences of rigorous proofs used in legal proceedings

Motivation: Loius Pojman mentions in What Can We Know? (2001) of a certain Carneades (ca. 214-129 B.C>) who must have been a "remarkable dialectician"because " in 155BC he was sent on a diplomatic ...

**9**

votes

**1**answer

2k views

### “You can't push a rope”

"You can't push a rope" is a wisdom saying that some engineering teachers pass along to their students. Since I'm not an engineer, I can only guess at what they mean, but it sounds to me like code ...

**6**

votes

**1**answer

544 views

### Motivic proof of Weil-conjectures?

Assuming the standard conjectures (and whatever is needed in addition),
is there a nice proof of the Weil-conjectures written completely in the language of motives?