**1**

vote

**2**answers

108 views

### classical typed higher order logic natural deduction

Has somebody worked out a typed higher order logic? I mean something like type theory but not with this intuitionistic touch.
Is there a natural deduction system for this logic?

**11**

votes

**1**answer

2k views

### Mathematical writing : using an “out-of-date” notation

When I wrote my master's thesis, a professor who read it said that I should not use the phrase "A function of class $k$." but instead "A function of class $C^k$". I am not an expert about mathematical ...

**3**

votes

**1**answer

211 views

### Lecture notes on Invariant theory of finite groups [closed]

I am looking for a book or lecture notes on invariant theory of finite groups. I am a beginner in this subject. Any basic references or lecture notes will be very helpful.

**0**

votes

**1**answer

189 views

### A question regarding models of $ZF+I_0$ [Revised]

In his answer to user42090's mathoverflow question"Minimal Generalized Contnuum Hypothesis & Axiom of Choice", Prof. Hamkins writes:
"...one can build the analogue of the symmetric models for ...

**14**

votes

**3**answers

1k views

### Current Research in Numeric Mathematics

To me, as an non-expert in the field, it seems as if numeric mathematics should have lost its importance because nowadays symbolic calculations or calculations with unlimited precision are generally ...

**18**

votes

**2**answers

2k views

### Derived algebraic geometry: how to reach research level math?

I know the question "how to study math" has been asked dozens of times before in many variations, but (I hope) this one is different.
My goal is to study derived algebraic geometry, where derived ...

**-3**

votes

**1**answer

137 views

### Encyclopedia of Mathematics?(non-Alphabetical) [closed]

Do you know any Encyclopedia of Mathematics which is in non-alphabetical order, like it starts from basic mathematics and then goes up to very advanced level.
And what's the difference between say, ...

**13**

votes

**0**answers

316 views

### Research situation in the field of Information Geometry

I am now doing an article survey on the field of information geometry started by S.Amari and Barndorff-Nielson. I want to know some research situation in this field.
I have read (4) and parts of (3). ...

**10**

votes

**1**answer

240 views

### Finding combinatorial models / statistics

In many cases in combinatorics and especially algebraic combinatorics with some representation theory, the main problem is about finding the correct statistic on a mathematical object.
For example, ...

**28**

votes

**5**answers

2k views

### Why should we care about “higher infinities” outside of set theory?

Let's say you are a prospective mathematician with some addled ideas about cardinality.
If you assumed that the natural numbers were finite, you'd quickly vanish in a puff of logic. :)
If you ...

**3**

votes

**0**answers

67 views

### Can Mumford-Shah functional be adapted to lower $L^1$ space?

The well know Mumford-Shah functional functional
$$
F(u)=\int_\Omega|\nabla u|^2+\mathcal H^{N-1}(S_u) \tag 1
$$
where $u\in SBV(\Omega)$ and $\nabla u$ is the absolutely continuous part of ...

**1**

vote

**0**answers

128 views

### Importance and intuition of global sections in sheaf cohomology

I am trying to understand why global sections of a sheaf are "important" or interesting objects of study. Perhaps I have too weak of a background to appreciate it (and that is certainly an acceptable ...

**3**

votes

**0**answers

66 views

### Families of trigonal curves with hyperelliptic limit

Suppose I have a family of trigonal curves $C\to D$ over a closed disk $D$ where the central fiber $C_0$ is hyperelliptic (this is of course possible since the hyperelliptic locus is in the closure of ...

**0**

votes

**1**answer

105 views

### Is there relation between vector valued RKHS and interpolation space?

Vector valued RKHS which is covered extensively in the book "Pick Interpolation and Hilbert function spaces" . In a different context interpolation space is defined in the wikipedia link: ...

**1**

vote

**0**answers

81 views

### Can we have extension of Mercer theorem to interpolation? [closed]

This question is related to Mercer theorem, Reproducible kernel Hilbert space(RKHS) and interpolation. The wikipedia links are https://en.wikipedia.org/wiki/Mercer%27s_theorem and ...

**10**

votes

**1**answer

401 views

### Listing ORCiD in LaTeX papers

The ORCiD unique author identifier, run by a non-profit organisation, has been around for a number of years now. Its stated goal is to become a de facto standard for uniquely identifying authors, even ...

**2**

votes

**1**answer

102 views

### Is there any parameter space of Cramér–Rao_bound

It is known that Cramér–Rao_bound is the lower bound of variance of a parameter. A useful link is https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound There is also a term called ...

**4**

votes

**2**answers

294 views

### Categories of finite objects

In my experience, category theory is very successful at providing powerful machinery to reason about large objects or objects unrestricted in size, for example (logical) models (via accessible ...

**5**

votes

**1**answer

361 views

### soft: Reference/ Suggested Read: Homological Algebraic techniques in PDEs

I was reading this article on wikipiedia and was interested by the apparent link between Homological Algebra and PDEs. What is an accessible reference which showcases the link between these topics? ...

**3**

votes

**0**answers

226 views

### Why only Normed Linear Spaces? [closed]

It is well known that "Norm on a vector space can be used to obtain a metric on that space."
I think easily we can generalize the notion of norms to groups and rings.
My questions are,
Why ...

**10**

votes

**0**answers

516 views

### Which journals publish applied mathematics with mostly pure mathematics content?

In the spirit of Which journals publish expository work? please advise:
What consistently high quality journals$^1$ today publish results that would otherwise go to a pure mathematics journal if ...

**0**

votes

**0**answers

28 views

### Characterization of complete lattices with join-incomplete lattice endomorphisms

Let $L$ be an complete lattice. A lattice homomorphism $f: L\to L$ is said to be join-incomplete if there is an infinite set $S \subseteq L$ such that $f(\bigvee_L S) > \bigvee_L f(S).$
How can ...

**33**

votes

**2**answers

1k views

### When to postpone a proof?

One possible practice in writing mathematics is to prove every theorem and lemma right after stating it.
A long, technical proof — and sometimes even a short one — can interrupt the flow ...

**1**

vote

**0**answers

158 views

### Newer list of open problems in model theory

In the book Model Theory by C. C. Chang and H. J. Keisler, there is a list of open problems in model theory. More exactly, this list is called "Open problems in classical model theory" (on page 597, ...

**12**

votes

**1**answer

458 views

### Which nice/deep elaborations on the (operators <-> sheaves) / (endomorphisms <-> objects) theme are there?

A linear operator $T:V\to V$ on a (say) vector space over a field $k$ is just a $k[T]$-module, and may be viewed as the sheaf $\mathscr F_T$ over $\mathbb A^1_k$, with fibre over $\lambda\in k$ equal ...

**22**

votes

**3**answers

877 views

### What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?

Over the years, advances in machine learning has allowed us to communicate and interact, using the same natural language, more and more semantically with computers, e.g. Google, Siri, Watson, etc. On ...

**0**

votes

**0**answers

141 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 ...

**19**

votes

**2**answers

1k 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 ...

**12**

votes

**0**answers

581 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 ...

**13**

votes

**3**answers

1k 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

592 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".

**6**

votes

**2**answers

225 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

306 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 ...

**18**

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 ...

**5**

votes

**2**answers

257 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

712 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 ...

**10**

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

2k 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.
...

**-6**

votes

**1**answer

317 views

### Quintic Equation [closed]

Can we solve the following polynomial quintic equation by radicals
x^5 + x^4 = 1
I found one real root which is algebraic solution (no approximation method ...

**1**

vote

**1**answer

329 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 ...

**17**

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

400 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 ...

**12**

votes

**2**answers

813 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 ...

**31**

votes

**4**answers

1k 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

458 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 ...

**7**

votes

**2**answers

780 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

162 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

497 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
$$
...

**9**

votes

**2**answers

757 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 ...

**-6**

votes

**1**answer

363 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 ...