**2**

votes

**1**answer

414 views

### Hilbert style axiomatic proof or sequent Calculus?

I am puzzling with the question which of the two proof systems (Hilbert style axiomatic proofs or substructural Sequent Calculi) is the most discriminatory?
With discriminatory I mean is which proof ...

**33**

votes

**17**answers

4k views

### What are some deep theorems, and why are they considered deep?

All mathematicians are used to thinking that certain theorems are deep, and we would probably all point to examples such as Dirichlet's theorem on primes in arithmetic progressions, the prime number ...

**5**

votes

**1**answer

437 views

### Naive question on adelic groups

The ever-reliable Wikipedia says:
... an adelic algebraic group is a semitopological group defined by...
No more details are given, and I was wondering if the multiplication only being ...

**18**

votes

**5**answers

629 views

### Online high quality colloquium talks

In my department we're thinking about showing online lectures one day per week at lunch, as sort of a virtual colloquium appropriate to mathematics undergraduates as well as faculty. To start with ...

**23**

votes

**3**answers

2k views

### Contemporary mathematical themes

The presence of fruitful mathematical themes suggests the unity of mathematics. What I mean by a mathematical theme here is a basic idea or guiding principle that motivates or directs the central ...

**2**

votes

**5**answers

251 views

### Equivalence relations not associated with a group

This is a vague question; so vague that I wonder if anyone will get it. Many, perhaps most, equivalence relations that are regularly used in mathematics correspond to the orbits of some group action ...

**6**

votes

**1**answer

619 views

### What are current trends/questions in algebraic logic?

What are current trends/questions in algebraic logic? I mean the research developed by Paul Halmos.
Could anyone give some references for the overview of its history? Any overview of its application ...

**5**

votes

**1**answer

367 views

### What are good ways to present proofs of theorems requiring auxiliary lemmas? [closed]

I am writing an academic paper for submission to a journal. One of my co-authors wrote the following:
Theorem Statement of the theorem
Proof of theorem We first show the following result
...

**9**

votes

**2**answers

653 views

### Rigid analytic spaces vs Berkovich spaces vs Formal schemes

I wonder if someone could explain briefly what is the relation between these 3 formal models, of a Berkovich space, a rigid analytic space and a formal scheme?
I have been working with formal schemes ...

**20**

votes

**4**answers

1k views

### Why Cohen-Macaulay rings have become important in commutative algebra?

I want to know the historic reasons behind singling out Cohen-Macaulay rings as interesting algebraic objects.
I'm reviewing my previous lecture notes about Cohen-Macaulay rings because now I'm ...

**14**

votes

**10**answers

2k views

### An example of a proof that is explanatory but not beautiful? (or vice versa)

This question has a philosophical bent, but hopefully it will evoke straightforward, mathematical answers that would be appropriate for this list (like my earlier question about beautiful proofs ...

**5**

votes

**1**answer

251 views

### Origins of Axiomatic Reasoning

Is there any evidence that axiomatic reasoning has been used prior to Thales of Milet (624-547BC), who is generally credited for the "invention" of axioms.
In this context I understand axioms in the ...

**36**

votes

**15**answers

3k views

### How does the work of a pure mathematician impact society? [closed]

First, I will explain my situation.
In my University most of the careers are doing videos to explain what we do and try to attract more people to our careers.
I am in a really bad position, because ...

**1**

vote

**4**answers

455 views

### What is the meaning of “algebraic construction”, and how could this be used in algebraic geometry

I try to make my question clear:
When reading a paper or listening a seminar talk, people showed me some set, and claim it to be a scheme; or some map, and claim it to be a morphism. I query why this ...

**32**

votes

**9**answers

2k views

### Homotopy as a general organizing principle

One of the realizations that led to the development of Homotopy Type Theory (HoTT) is that the ideas of homotopy theory have very broad applicability in mathematics. Indeed, Quillen model categories ...

**7**

votes

**1**answer

392 views

### Number theory underlying Euler's theory of music

I've recently been studying Euler's theories on music, and I came across Euler's concept of gradus suavitatis or 'degree of pleasure' of a rational number representing the ratio of two tones. (I found ...

**8**

votes

**7**answers

1k views

### Review papers in mathematics

Are there review papers, literature reviews in mathematics that describe the recent developments in various fields for a newcomer? Or is the prerequisite knowledge always provided in research ...

**6**

votes

**3**answers

752 views

### How to Discover Counterexamples and Required Objects [closed]

What are strategies or tips, which research mathematicians have discovered through their work and experience, that would help undergraduates learn how to discover counterexamples or find an object on ...

**-1**

votes

**1**answer

325 views

### collective slide-hosting for Mathematics [closed]

Has anyone considered using SlideShare to host slides from talks? In much the same way arXiv hosts papers.
Truth be told, the slides are often much easier to absorb than the papers.
Sometimes I will ...

**2**

votes

**4**answers

950 views

### When did you “meet Polya”? [closed]

I guess most of us didn't meet Polya in person (this is the answer to the title)! Perhaps, it is much easier to guess that most of us have met one of his writings (or alike) on problem solving, and ...

**4**

votes

**1**answer

878 views

### Preparing for Set Theory Research

Is reading Jech's text on Set Theory too little, just enough, or overkill to prepare oneself to do independent research in set theory? This would be my first attempt at doing independent research ...

**19**

votes

**2**answers

744 views

### Strict applications of deformation theory in which to dip one's toe

I hesitate to ask a question like this, but I really have tried finding answers to this question on my own and seemed to come up short. I readily admit this is due to my ignorance of algebraic ...

**16**

votes

**3**answers

1k views

### Is there a scheme corresponding to the unit interval?

Can someone complete the following table?
$\begin{array}{cc} \text{Topology over } \mathbb{R} & \text{Topology over } \mathbb{C} & \text{Algebraic Geometry} \\\\ \hline \mathbb{R} & ...

**18**

votes

**21**answers

2k views

### What are some examples of mathematicians who had an unconventional education? [duplicate]

Possible Duplicate:
Famous mathematicians with background in arts/humanities/law etc
What are some examples of mathematicians who had an unconventional education and yet, went on to make an ...

**21**

votes

**7**answers

1k views

### Pros and cons of math teaching using smartboards

Currently, there is some talk in my university concerning a change in our lecture rooms from blackboards to smartboards (or other alternatives, such as a smart podium). For that reason, I'm interested ...

**9**

votes

**0**answers

305 views

### State of research in moduli space of flat connections

I am a recent PhD student trying to settle into a research topic. Even though I have a current project I am working on, I am not particularly enjoying it and would like to switch. Before braving the ...

**21**

votes

**9**answers

3k views

### Research topics restricted to students at top universities?

Hello everybody.
I am a Ph.D student in North America looking for advice about my prospective research area.
My supervisor works in a research area, let's say area A, so as soon as I was accepted as ...

**5**

votes

**1**answer

820 views

### How to find a topic to do research with as a Post-Doc? [closed]

I will soon finish my PhD in arithmetic geometry. My advisor told me that I will have to find my next research topic on my own. How do I do that? (Except for "continue where the PhD thesis ends") Can ...

**19**

votes

**3**answers

761 views

### Where to look for corrections of papers?

When I start reading a paper, is there some easy way to find a list of corrections for that paper?
For example, it happens occasionally that some result of a paper turns out to be wrong, or at least ...

**6**

votes

**0**answers

206 views

### History of the characterization of commutative Artin rings

When it comes to the world of "classical" (pre-homological) Noetherian commutative algebra, I tend to think of most of the results (Krull's intersection theorem, the principal ideal theorem, etc.) as ...

**21**

votes

**3**answers

2k views

### Is there an RSS reader for mathematicians?

For a while, I have used Google Reader to stay on top of several math blogs. Unfortunately, Google will pull the plug on Reader one month from today, so I need to find an alternative fast. I was ...

**6**

votes

**7**answers

917 views

### famous papers/results by non professional mathematicians [duplicate]

Possible Duplicate:
What recent discoveries have amateur mathematicians made?
Dear overflowers
Out of curiosity: do you know any famous papers and/or results by non professional ...

**-1**

votes

**1**answer

407 views

### A question concerning how mathematicians feel about theorems and their proofs. [closed]

Must one of my favorite geometrical theorems come to be regarded as "trivial" or "obvious", when it is
shown to have a really short and easy proof? Let C denote any closed unbounded subset of the ...

**3**

votes

**3**answers

301 views

### Embedding Theorem for topological spaces, and in general

There are many examples throughout mathematics of abstracting the formal properties of a "familiar" structure, but then having a theorem stating that all models of the abstract axioms embed into one ...

**43**

votes

**7**answers

2k views

### How closed-form conjectures are made?

Recently I posted a conjecture at Math.SE:
$$\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx\stackrel{?}{=}\frac{\pi}{2}(\mu^2-\nu^2),$$
where $J_\mu(x)$ and $Y_\mu(x)$ ...

**40**

votes

**13**answers

3k views

### Why don't more mathematicians improve Wikipedia articles?

Wikipedia is a widely used resource for mathematics. For example, there are hundreds of mathematics articles that average over 1000 page views per day. Here is a list of the 500 most popular math ...

**2**

votes

**2**answers

268 views

### fixedpoint or fixed point or fixed-point

I am unsure which is the right spelling (if there even is a ‘right’ spelling), but maybe native speakers can enlighten me: When should I use
fixed point
fixed-point
fixedpoint
when I refer to the ...

**4**

votes

**0**answers

94 views

### Categorical notions involving $\ell_p$ spaces.

First of all, apologies for a somewhat vague question but let me give a try. We know what the projective objects in the category of Banach spaces are: these are precisely $\ell_1(\Gamma)$-spaces. (One ...

**7**

votes

**3**answers

838 views

### Importance of separability vs. second-countability

For me second-countability always felt like to be the more important and fundamental concept from general topology than separability. I wonder whether there are any points which can be made for the ...

**2**

votes

**1**answer

535 views

### Derivation of Bessel functions

I am writing a summary on a work on Fluid Dynamics that develops irrotational flow states that appear to interact amongst each other according to the equations of Electromagnetism ...

**4**

votes

**1**answer

347 views

### Is it true that Nature promotes products?

I hope this question is not unreasonable.
We all know how to take products of numbers, this generalises to a huge amount of different types of products in mathematics. In a certain sense this notion ...

**3**

votes

**0**answers

179 views

### Is it difficult to prove that nature is chaotic?

If we have a Markov coding or another symbolic description of a dynamical system it is usually easy to prove that the system is chaotic (in the sense of of Li-York, Devaney, positive entropy of what ...

**0**

votes

**1**answer

289 views

### Do you set a one or two commas when using \mapsto?

I am currently revising a paper and I am completely confused about the commas. Is it correct English to write
1) "The canonical map $X \to Y$, $x \mapsto f(x)$, is injective."
or is it
2) "The ...

**60**

votes

**24**answers

6k views

### Modern Mathematical Achievements Accessible to Undergraduates

While there is tremendous progress happening in mathematics, most of it is just accessible to specialists. In many cases, the proofs of great results are both long and use difficult techniques. Even ...

**9**

votes

**1**answer

320 views

### Discrete Morse theory and chess

There are many mathematical objects that are similar to groups and Cayley graphs of groups but lack homogeneity in some sense. Graphs of webpages with edges corresponding to links are one example. ...

**4**

votes

**1**answer

244 views

### Alexandrov angles in Riemannian manifolds

Dear all, I am teaching a course in Riemannian geometry, and I would like to prove some comparison theorems in the next lessons, building on the well-known theory of Jacobi fields, and of Rauch ...

**13**

votes

**4**answers

1k views

### motivating geometric representation theory

I am wondering if there is a good motivation for geometric representation theory from within the questions of classical representation theory.
In other words, I'd be curious to see something using ...

**8**

votes

**6**answers

1k views

### Intuitionistic logic as quantization of classical logic?

A classically trained mathematician is more likely to be familiar (at least anecdotally) with an area of mathematical physics such as deformation quantization than with Intuitionistic logic. It is ...

**5**

votes

**5**answers

2k views

### What does a mathematician expect from mathematics education? [closed]

Consider that my question is not a personal and/or subjective question. Perhaps, you have hired a mathematics educator in your department and you are interested in finding a way to communicate with ...

**2**

votes

**2**answers

247 views

### Stronger theorem not resulting from proof analysis

Suppose that we proved $\varphi$ from a theory $T$. Often we ask whether or not we could have proved $\varphi$ with a weaker theory, to find out we usually analyze the proof and try to figure out ...