**8**

votes

**3**answers

633 views

### “Epicycles” (Ptolemy style) in math theory?

By analogy:
The epicycles of Ptolemy explained the known facts in the sun system and in this sense were not "wrong". But they distracted from a better insight. From another viewpoint, everything fell ...

**3**

votes

**0**answers

144 views

### Have topographs been studied before?

This is my first post on MO so I hope this question is suitable. I have quite a few definitions which I will need to state before my questions at the end of this post. Please let me know if anything ...

**-5**

votes

**0**answers

171 views

### Are numbers fundamental mathematical entities? [on hold]

This question came to my mind after seeing Vi Hart's video on YouTube about the "number" Wau and the answer I gave there to the question "what is the number Wau?". As far as I know, numbers have ...

**8**

votes

**4**answers

840 views

### number theory which is close to analysis

I have basic training in Fourier and Harmonic analysis. And wanting to enter and work in area of number theory(and which is of some interest for current researcher) which is close to analysis.
...

**2**

votes

**1**answer

127 views

### Two equivalent descriptions of a physical system yielding a non-trivial mathematical formula

First I would like to admit that this question may not be entirely appropriate for this site, but I will give it a go none the less.
One often hears stories about how string dualities lead to highly ...

**11**

votes

**2**answers

612 views

### Which way for reading the proofs?

I am a master student in mathematics. For me a large part of doing mathematics is thinking about, reading and verifying the proof of theorems that I find them in my field of study. I can do this ...

**27**

votes

**8**answers

5k views

### Uninteresting questions with interesting answers [closed]

What are best examples of questions in mathematics that are not interesting until one knows the answers, whose answers themselves are what is interesting?
The thing that prompts me to post this is ...

**3**

votes

**3**answers

167 views

### Are linearizations of involutive PDEs locally solvable?

A possibly soft question for you guys and gals. Say a system of analytic PDEs has been completed to involution (in the sense that it's geometric symbol has a Pommaret basis, or has vanishing ...

**0**

votes

**0**answers

95 views

### seminar about the strong multiplicity one for the Selberg class

Very recently, a seminar took place in Seoul with Haseo Ki as an invited speaker to talk about the strong multiplicity one theorem for the whole Selberg class that he did manage to prove. I would like ...

**1**

vote

**1**answer

1k views

### Famous examples of PhD advisors younger than their student [closed]

What are the most famous examples of PhD advisors in mathematics, younger than their student?
(if possible put the date of birth and/or the difference in age).

**1**

vote

**1**answer

151 views

### soft copy of Ottmar loos's book on “symmetric spaces”

Is anyone in posssesion of the Ottmar Loos's old books on "Symmetric Spaces" . I have consulted Ottmar Loos himself as well as other experts like Prof.Parameshwaran Shankaran about the book. In their ...

**0**

votes

**0**answers

24 views

### Explicit Solution of Bessel Process

I am trying to write an find an explicit solution (Bessel process) of following SDE:
for $S\ge 0$,
$df(S)=\mu dt+\sqrt{1+\alpha f(S)}dW_t$, $\alpha>0$, and $1+\alpha f(S)\ge 0$ and $W_t$ is the ...

**1**

vote

**0**answers

127 views

### How the exceptional simple Lie groups/ algebras were first discovered and by whom?

I am wondering whether exceptional simple Lie groups/ algebras were first discovered in order to obtain a complete list of such objects, or they appeared as answers to completely different questions.
...

**46**

votes

**17**answers

9k views

### Parodies of abstruse mathematical writing

Perhaps under the influence of a recent question
on perverse sheaves,
in conjunction with the impending $\pi$-day (3/14/15 at 9:26:53),
I recalled a long-ago parody of abstruse mathematical language
...

**2**

votes

**0**answers

100 views

### algorithm to find a new point of small height in a number field extension

By the height of an algebraic number $\alpha$, I mean the absolute, logarithmic (additive) Weil height $h(\alpha)$; e.g. $h(2^{1/n}) = (\log 2)/n.$
If $K$ is a number field, let $\delta(K)$ denote ...

**7**

votes

**0**answers

223 views

### Use of an appendix in a long paper

I am writing a long paper (around 100 pages). I would consider 50 pages of it interesting in that it solves a problem of some significance in my field and contains an number of difficult ideas in the ...

**3**

votes

**0**answers

78 views

### Looking for a natural definition of certain polynomials associated with skew Young diagrams

Consider a connected skew Young diagram in the English notation and then rotate it counterclockwise by $\pi/4$. This rotation can be avoided by simply replacing "rows" by "diagonals" in the below, but ...

**1**

vote

**2**answers

332 views

### More recently published comprehensive reference on inequalities in the spirit of Hardy-Littlewood-Pólya

Is there a comprehensive reference book on inequalities in the
spirit of the one written by G.H. Hardy, J.E. Littlewood, and G. Pólya(*), but more up-to-date (i.e., published in more recent years and ...

**17**

votes

**1**answer

1k views

### Philosophical arguments in defense (or against) large cardinals

The question is essentially what is asked in the title. I split it into two parts
(A) (Arguments supporting the existence of large cardinals) What are the main philosophical arguments in defense ...

**1**

vote

**2**answers

520 views

### Numbers greater than Skewes's whose existence can be found in number theoretic proofs

Skewes has proved (without assuming RH) that $\pi(x)<Li(x)$ is violated below $e^{e^{e^{e^{7.705}}}}$ which is clearly a very large number.I was wondering if somewhere else some greater number than ...

**1**

vote

**0**answers

44 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 ...

**1**

vote

**0**answers

146 views

### “For sufficiently large” vs. “For all sufficiently large” [closed]

A purely grammatical question: Do people generally prefer:
"For sufficiently large x,..." or
"For all sufficiently large x,..."
or not care? Or might you use either according to context? The meaning ...

**1**

vote

**1**answer

150 views

### Yang-Mills Functional and Energy

I have a question about the meaning of Yang-Mills Functional.
It is stated everywhere that the Yang-Mills Functional is a measure of energy. But the formal definition of the Yang-Mills Functional is:
...

**6**

votes

**2**answers

724 views

### Publication in proceedings

Why and how publishing a paper in proceedings?
What are the difference with a "classical" journal?
What's the list of the main proceedings in which one can publish?
Do proceedings papers (never, ...

**8**

votes

**3**answers

230 views

### How do small central extensions drop the dimension of a faithful representation?

Apologies in advance that this is a very soft question. I might be talking complete nonsense. But I hope I am talking about something that has even been studied...
I am interested in the phenomenon ...

**27**

votes

**2**answers

668 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.
...

**1**

vote

**0**answers

180 views

### Intuitive Approach to Sheaf and Cech Cohomology [closed]

Sheaf and Cech cohomology $H^*(X,\mathcal{F})$ (which give the same result when applied to good enough topological spaces) are a useful generalisation of the concepts of de Rham and Dolbeault ...

**5**

votes

**2**answers

329 views

### Applications of cohomology to probability and statistics

Are there interesting/useful applications of cohomology (and homological algebra in general) to probability and statistics, or information theory?
By "interesting/useful", I mean "not merely ...

**4**

votes

**3**answers

318 views

### Need examples of homotopy orbit and fixed points

I am no expert in equivariant homotopy theory. Let's say, I am planing to give a talk on homotopy fixed points and orbits. My audience will be graduate students who are doing algebraic topology or ...

**1**

vote

**1**answer

251 views

### How to decide whether the journal is pure or applied?

I am a beginner in research and have draft ready for my first article. I have a little confusion about the pure and applied journal in Mathematics. My work belongs to pure mathematics(I think). And ...

**8**

votes

**0**answers

543 views

### How to approach the stigma of not having a math degree? [closed]

I am a faculty member in a department that is not mathematics, but is highly-ranked in my field. I greatly enjoy working with mathematicians, and have had a number of successful collaborations.
...

**3**

votes

**1**answer

415 views

### Mathematics of Computer science and AI [closed]

Computer science and Artificial Intelligence have been fertile grounds for research for decades, not only for Engineers but particularly for Mathematicians. What kinds of Mathematics have emerged ...

**3**

votes

**3**answers

329 views

### Reference request: a guide through quantum probability

Could you point out a comprehensive reference book (or more than one, if it is the case) on Quantum Probability that introduces the subject and then gradually builds up to the edges of contemporary ...

**2**

votes

**2**answers

234 views

### Heuristics for 2-morphisms of (algebraic) stacks

For topological spaces and simplicial sets one can consider each pair of parallel morphisms $f,g:X\rightrightarrows Y$ as equipped with a set of 2-morphisms given by homotopies $H:f\simeq g$ (let's ...

**5**

votes

**2**answers

884 views

### Physicist trying to understand modern mathematics

I'm a physicist trying to gain a deep understanding of mathematics that is required for my work.I intend to specialize in string theory which is a very math intensive branch of theoretical physics ...

**2**

votes

**2**answers

425 views

### Popular books written by great mathematicians [closed]

I read:
H. Poincare. Value of science
F. Klein. Development of Mathematics in the 19th Century
J.E. Littlewood. A Mathematicians Miscellany
G.H. Hardy. A Mathematician’s Apology
R. Courant, ...

**7**

votes

**2**answers

821 views

### Surveys of the items of Erdős' “toolbox”

Could you point out some survey papers and monographs that highlight the kernel of tricks, techniques, and tools that Paul Erdős employed the most in his research work (in particular in graph theory, ...

**3**

votes

**1**answer

102 views

### Reference for exercises with solutions for affine Lie algebras

I am doing self-study of affine Lie algebras, and while I have all recommended reference material, I find it hard to prepare for the exam.
It was quite easy to study finite-dimensional simple Lie ...

**7**

votes

**2**answers

213 views

### Recent trends in effective analysis

The references listed at http://en.wikipedia.org/wiki/Computable_analysis have all been published 30-15 years ago. Are the approaches which these references expose still up-to-date and relevant to the ...

**3**

votes

**3**answers

274 views

### Survey papers of results (relevant to mathematics) produced during research on the relationship between mathematics and music theory

It is well-known that there is a relationship between music and mathematics, and there are many references that explore this topic (for example, Benson's book).
However, I would like to ask if there ...

**1**

vote

**0**answers

89 views

### Why are they called 'pernicious' numbers?

The definition of a pernicious number:
In number theory, a pernicious number is a positive integer where the Hamming weight (or digit sum) of its binary representation is prime.
The meaning of ...

**8**

votes

**1**answer

422 views

### Open access journals in number theory

I'm a phd student in number theory, and I'm required (by the funding council) to publish any article I write in open access journals. The problem is that all journals I can find are either out of my ...

**3**

votes

**1**answer

390 views

### Do hom-sets really live in the category Set?

This isn't really a research-level question (sorry!), but I asked on
math.se (link), and though the question was upvoted a few times, I didn't
get any answers. So since there may well be more ...

**13**

votes

**7**answers

786 views

### Examples of categorical adjunctions in analysis, Lie theory, and differential geometry?

In introductory texts on category theory, it seems like the majority of examples come from algebraic topology, algebra, and logic. Are there any good examples of adjunctions in analysis, Lie theory, ...

**1**

vote

**1**answer

232 views

### What would undergraduate research consist of? [closed]

For undergraduate mathematics students looking to go to grad school, what kind of opportunities are open for research? I would assume undergrads would not be under any pressure or obligations to write ...

**2**

votes

**1**answer

149 views

### Survey on functional equations and inequalities

Where can I find a comprehensive survey monograph on functional equations and inequalities from sketch to current research trends with some focus on applications (both inside and outside mathematics)?
...

**-3**

votes

**1**answer

209 views

### How many of Ramanujan's discoveries have had a practical application? [closed]

I was reading about the Indian mathematician Srinivasa Ramanujan who, before dying at the age of 32, independently compiled nearly 3900 results (this is from Wikipedia). So based on this he seems to ...

**21**

votes

**1**answer

606 views

### Which properties of a variety are detected by its derived category of coherent sheaves?

Context: I'm giving an informal seminar/reading group collection of talks on derived categories, following on from earlier talks giving the abstract definition. I am starting to talk about ...

**11**

votes

**2**answers

609 views

### What is the longest recorded gap between “proof” of a “theorem” and discovery that the result is false [duplicate]

I hope this question is not a duplicate. I am motivated by wondering when widely accepted results may be considered have a secure place in the mathematical literature. The question is intended to ...

**-5**

votes

**2**answers

314 views

### Are there any with Erdös number 1 on mathoverflow? [closed]

I learned today that one of my professors wrote a paper with Erdös and Sós back in 1985, thus granting him the honor of having his Erdös number equal 1.
I was wondering - did any of the ...