**0**

votes

**0**answers

114 views

### How to prepare a radical change of research field after the PhD [duplicate]

I am in the middle of my PhD in functional analysis. My undergraduate studies were focused on pure theory and so it was logical to continue in this direction. However, recently I got into contact with ...

**0**

votes

**0**answers

178 views

### Getting back into advanced mathematics [on hold]

I hope that this is the correct forum to post my question on. I'm a 37 year old IT professional working in the Banking Sector who previously studied for a PhD in Computattional Fluid dynamics back in ...

**18**

votes

**2**answers

812 views

### History of Geometric Analogies in Number Theory

My question, put simply, is: When did mathematicians/number theorists begin viewing questions in number theory through a geometric lens?
For example, was it before Grothendieck introduced schemes to ...

**0**

votes

**0**answers

171 views

### Non-university jobs suited for pure mathematician turned computational neuroscientists, with coding experience [on hold]

I also asked this question on academia stack exchange,
http://academia.stackexchange.com/questions/48057/type-of-non-university-research-jobs-suitable-for-a-mathematician-turned-comput
but asking ...

**12**

votes

**0**answers

466 views

### “To operate the machine, it is not necessary to raise the bonnet.”

The quotation in the title is attributed to Frank Adams and appears in several places:
In the preface of [2002, Operads in algebra, topology and physics]: "to operate the machine, it is not ...

**11**

votes

**3**answers

539 views

### How to write an abstract for a math paper? [closed]

How would you go about writing an abstract for a Math paper? I know that an abstract is supposed to "advertise" the paper. However, I do not really know how to get started. Could someone tell me how ...

**2**

votes

**1**answer

389 views

### Mathematics equivalent of Feynman's Lectures in Physics? [closed]

I'm looking for an equivalent of "Feynman's Lectures in Physics" in mathematics. I'm specifically looking for book/books that delve into, using Feynman's words, "the meaning of things".

**-3**

votes

**0**answers

226 views

### Mathematical theories of changes - except from calculus? [closed]

Unfortunately motion is regarded as displacement in geometry:
By a motion or displacement in the general sense is not meant a change
of position of a single point or any bounded figure, but a
...

**5**

votes

**2**answers

186 views

### Do computational geometers use Lagrange multipliers?

Can anyone point me to an example of a problem that (more or less) originated in computational geometry whose solution requires the use of Lagrange multipliers (or Kuhn-Tucker conditions, or dual ...

**7**

votes

**0**answers

255 views

### What would you do if you improve your own result that is submitted but not publishied?

Here is a hypothetical situation:
You have proved a result and written up a paper about it. You have submitted your article to some journal and it is being reviewed.
While you are waiting, you have ...

**17**

votes

**3**answers

2k views

### Style of mathematical writing vs. too many lemmas

I work in PDEs. I have now written 3 papers. I find my style is of the form: introduction, statement of results, paragraphs to introduce something, lemma, more text, lemma, more text, lemma, more ...

**1**

vote

**0**answers

45 views

### Precise statement of Gersho's conjecture

Here is the Gersho's conjecture from his paper "Asymptotically optiaml block qunatization"
"For $N$ sufficiently large the optimal(distortion-minimizing) quantizer for a random vector uniformly ...

**5**

votes

**2**answers

133 views

### Separable coordinate systems for the Laplace and Helmholtz equations?

According to Mathworld, in three dimensions there are 13 coordinate systems in which Laplace's equation is separable, and 11 for the Helmholtz equation. I've read the relevant chapters of the book by ...

**5**

votes

**3**answers

620 views

### “Family Tree” of Theorems

Is anyone aware of any attempt to describe the dependencies of theorems (perhaps in mathematics generally, perhaps in some limited areas) in the form of a "family tree"? That is, each node on the ...

**9**

votes

**2**answers

1k views

### Should we post on arXiv only papers in publishable shape (or very close)?

Question: Should we post on arXiv only papers in publishable shape (or very close)?
This question should be distinguished from the following:
Should one post a paper on the arXiv if it is not ...

**28**

votes

**5**answers

1k views

### The unpublished papers in reference to the published papers

Sometimes it happens that a published paper refers to an unpublished paper for a result used.
In this case, if we want to check this result by ourselves, we need to access to this unpublished paper.
...

**0**

votes

**0**answers

138 views

### Soft Question: Relationships Between Moduli Space and Objects They Parametrize

Apologies in advance if this question is not suitable for MO. My friend and I were wondering recently what, if any, are the relationships between the geometric properties of a moduli space and the ...

**15**

votes

**1**answer

2k views

### Why do people use “formal calculation” to describe informal calculations?

Many times, I see the word formal being used to describe a calculation that is not rigorous. I would think that such calculations should rather be termed informal than formal. What is the explanation ...

**3**

votes

**1**answer

368 views

### Formulating Kunen's inconsistency and Reinhardt cardinals in term of category theory

It is known that one can formulate certain large cardinal axioms (e.g. Vopenka's principle--see Mike Shulman's answer to Harry Gindi's mathoverflow question "Reasons to believe Vopenka's ...

**11**

votes

**2**answers

764 views

### Describe the desired features of a “Mathematics Colloquium”?

I'm now a member of my department's colloquium committee. Our task is to make a great colloquium series. I thought that the first step would be to come up with an appropriate definition of ...

**20**

votes

**2**answers

702 views

### Intuition behind the definition of quantum groups

Being far from the field of quantum groups, I have nevertheless made in the past several (unsuccessful) attempts to understand their definition and basic properties. The goal of this post is to try to ...

**6**

votes

**1**answer

392 views

### Are reduced residue systems relative primorials an active area of research? If not, why not?

As a math amateur, I am finding the study reduced residue systems relative a primorial a very interesting way to understand the distribution of primes. For example, it is fascinating to me that it is ...

**8**

votes

**2**answers

583 views

### random category theory

This question is in some sense dual to the one asked in Is there an introduction to probability theory from a structuralist/categorical perspective? since contrary to the OP who asks for references ...

**2**

votes

**0**answers

143 views

### When is it appropriate to name something a 'fundamental lemma'? [closed]

The term 'fundamental lemma' refers to many results in mathematics. I don't know too many results referred to by that name, but I am familiar with, for example, the 'fundamental lemma of sieve theory' ...

**10**

votes

**3**answers

460 views

### Mathematical difference between entropy and energy

I have a rather soft question. Let's assume that we consider the heat equation posed in $S^1$:
$$
\partial_t u=\partial_x^2u.
$$
It is well known that if we define the functionals
$$
...

**7**

votes

**2**answers

518 views

### Understanding Faltings's Theorem

I am soon to become a graduate student and so I started a personal project; I want to understand Faltings's proof of the Mordell conjecture.
I want to get into arithmetic geometry (since I always ...

**-5**

votes

**1**answer

288 views

### What's the minimum amount of knowledge to start doing research? [closed]

There are cases in which you have too much knowledge of something to do anything interesting ,and cases in which a lack of experience with a problem (and the prejudices about it) helps someone solve ...

**7**

votes

**1**answer

277 views

### “Thin film evolution” (Reference request)

Ok this is my first$^*$ question on overflow, my apologies if this is not the right place to ask what follows!
I observed the following phenomenon: I put a (vitamin) tablet into water, then after a ...

**12**

votes

**4**answers

928 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 ...

**6**

votes

**0**answers

257 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 ...

**9**

votes

**6**answers

1k 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.
...

**3**

votes

**1**answer

169 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 ...

**17**

votes

**3**answers

968 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 ...

**28**

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

191 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

113 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

2k 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).

**0**

votes

**1**answer

172 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

29 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

143 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

10k 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

108 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

253 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

86 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

357 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

**2**answers

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

555 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

53 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

157 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

184 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:
...