**1**

vote

**0**answers

446 views

### Is it possible to give a fair assessment of the influence of Bourbaki's “Eléments de mathématique”? [closed]

Well, I apologize if this "soft-question" (related to the "Arnold-Serre" debate) is considered as irrelevant for MO, and for possible misunderstandings in the two earlier versions of this post (which ...

**42**

votes

**11**answers

10k views

### What areas of pure mathematics research are best for a post-PhD transition to industry?

I have a student who is looking to start a PhD in pure mathematics. She is talented and motivated, and will do quite well. She is still in a phase of her development where she is still open to the ...

**3**

votes

**0**answers

162 views

### Looking for author of calculus quote

When I was a lowly calculus student many many years ago, my calculus teacher quoted some famous mathemtician: "Calculus is the last course in arithmetic and the first course in mathematics that one ...

**0**

votes

**1**answer

89 views

### Inserting maple or macaulay script in a paper [closed]

I see many wonderful papers where the authors include some script written in Maple, Macaulay or other software that are needed for their proof. How do you insert that in your tex file?

**6**

votes

**0**answers

112 views

### Duality between large and small scale structures

A rather immediate reaction to seeing the definition of a coarse structure, at least to me, is to be reminded of a uniform structure. The axioms for a coarse structure $\mathcal{C}$ (defined by a ...

**14**

votes

**1**answer

2k views

### What have simplicial complexes ever done for graph theory?

(I am asking in a somewhat tongue-in-cheek fashion, of course, but nevertheless...)
Are there examples of results in "classical" [*] graph theory that have
been achieved by using simplicial ...

**3**

votes

**4**answers

469 views

### Understanding reasons for best constants in inequalities

Why, in functional analysis, is so important to calculate best constant in an embedding inequality?
Cross-posted from ...

**0**

votes

**0**answers

196 views

### Game Theory - need references on analysis of particular game

My hobby AI research have led me to a thorethical game of particular design. As design is pretty simple, I was sure that such game has well-known name. But my question on math.stackexchange, where I ...

**4**

votes

**4**answers

465 views

### Determine if a graph has a large clique

This question is quite specific and practical. I hope it is still relevant for MO and will not be removed.
I have a collection $\mathcal{C}$ of graphs having from 5000-6000 vertices and edge density ...

**7**

votes

**0**answers

413 views

### Is there a theory of abuse of notation? [closed]

Is there any theory about the different ways notation can be abused and which abuses are ineliminable without complicating the notation in some essential way? We can define "abuse of notation" as any ...

**72**

votes

**9**answers

8k views

### Analogues of P vs. NP in the history of mathematics

Recently I wrote a blog post entitled "The Scientific Case for P≠NP". The argument I tried to articulate there is that there seems to be an "invisible electric fence" separating the problems in P ...

**3**

votes

**0**answers

477 views

### Does Pure Mathematics glue Science together? [closed]

A little while ago, I was reading Cathy O'Neil's post Why is math research important (subtext: why does Pure Math deserve funding), where she discusses 3 possible answers. One of these is the usual ...

**6**

votes

**1**answer

415 views

### Sources of Theorem drafts by the original author

When I look at first time to a theorem and I try to understand it or when I try to memorise a useful theorem I always have difficulties (I am not the only one. For example: I read a question: I always ...

**22**

votes

**3**answers

952 views

### “Paradoxes” in $\mathbb{R}^n$

One may think of this question as a duplicate of this one. I see it more like an extension.
The "inscribed sphere paradox" discussed in the aforementioned question states that if you inscribe a ...

**24**

votes

**1**answer

5k views

### Who made the famous error in calculation that 'wasted' the final years of his life?

Sorry, I am merely a Middle School maths teacher at an Australian secondary school. I remember reading years ago about a famous mathematician (18th or 19th Century?) who calculated table upon table of ...

**3**

votes

**0**answers

209 views

### A paper by Elashvili (translation request)

I would like to know if there is an English version of a paper by Elashvili called "Centralizers of nilpotent elements in semisimple Lie algebras".
If not, is there atleast an online version of the ...

**2**

votes

**1**answer

151 views

### Reference to complete derivation of Kossakowski–Lindblad equation and its steady solutions

Are there recommended textbook or good intro-reference to explain with complete stretch of Kossakowski–Lindblad equation especially how is the idea to derive it from ground?
...

**1**

vote

**2**answers

588 views

### What are trivial objects, in general?

Trivial objects show up in most every branch of mathematics, and we all know lots of examples: the trivial group, ring, vector space, module over a ring, graph, knot, homomorphism from one object to ...

**0**

votes

**1**answer

444 views

### Why do we change the order of summation? [closed]

Alexander the Great is staring at the Gordian Knot, bewildered. Absentmindedly he fingers the hilt of his trusty sword. On the sword is inscribed the words: "Change the order of summation".
...

**2**

votes

**3**answers

918 views

### Assessing effectiveness of (epsilon, delta) definitions [closed]

There is much discussion both in the education community and the mathematics community concerning the challenge of (epsilon, delta) type definitions in calculus and the student reception of them. The ...

**7**

votes

**2**answers

1k views

### Is Turing degree actually useful in real life? [closed]

In theoretical computer science, we classify problems according to their Turing degree. Is there any practical application of this?
Edit: Given that we cannot explicitly and mechanically understand ...

**12**

votes

**2**answers

568 views

### Riemann's quote cited by Lakatos: what is the context?

"If only I had the theorems! Then I should find the proofs easily enough."
This quote is generally attributed to Bernhard Riemann. In particular,
on page 9 in Proofs and refutations by Imre ...

**4**

votes

**1**answer

461 views

### What is the correct preposition? (And is there one?)

I just stumbled upon a linguistic problem I wasn't able to resolve via web search. Suppose we're given some geometric set $A$ and subset $B\subset A$. Isn't there a compact way of saying that there ...

**4**

votes

**1**answer

551 views

### Basics on anabelian geometry and Grothendieck's section conjecture

Even I can find similar questions and some answers on that questions, most of them are not quite unsatisfactory to me. Maybe this is a very stupid question, but there is no other place that I can ask ...

**17**

votes

**1**answer

527 views

### Is Grothendieck classification of tensor norms and Kuratowski's 14 sets theorem somehow related?

It is known that there are only 14 reasonable tensor norms in $Ban$. On the other hand it is well known fact for topologists that one can obtain only 14 different sets from a given set applying ...

**4**

votes

**1**answer

443 views

### Examples of “nice” properties of algebraic extensions of $\mathbb{Q}$

I am writing a short survey of some "nice'' properties of algebraic extensions of $\mathbb{Q}$. Let's say a property (P) is nice if
every finite extension of $\mathbb{Q}$ satisfies (P), and
if $K ...

**22**

votes

**4**answers

1k views

### What is the definition of a large cardinal axiom?

In different books one can find different implicit definitions for a large cardinal axiom.
My question is that which one of these definitions are more popular or standard amongst set theorists?
Any ...

**13**

votes

**6**answers

1k views

### Text for Algebraic Number Theory

I have the privilege of teaching an algebraic number theory course next fall, a rare treat for an algebraic topologist, and have been pondering the choice of text. The students will know some ...

**4**

votes

**1**answer

192 views

### An intutive reason why a “distance” metric may be a poor one for a procedure where we attempt to modify a string (mutating 0 OR 1 bits)

If I'm attempting to mutate one arbitrarily chosen binary string $s_a$, to another arbitrarily chosen binary string $s_b$, in the smallest number of steps (i.e. with the smallest number of mutations) ...

**-5**

votes

**1**answer

530 views

### First PhD in pure math and the second PhD in applied math [closed]

Assume that someone has PhD in mathematics, and the dissertation was in Pure Mathematics. Is he eligible to apply to PhD program in Applied Mathematics? There are universities where the department of ...

**6**

votes

**1**answer

428 views

### Origin of the term “weight” in representation theory

In representation theory, there are the related concepts of weights and roots. Since both are kinds of generalised eigenvalues, and eigenvalues are roots of e.g. the characteristic polynomial, the ...

**18**

votes

**2**answers

2k views

### Where are Georg Cantor's Original Manuscripts?

Georg Cantor is famous for introducing transfinite numbers and set theory.
A main part of his mathematical point of view about this new type of "numbers" and this new "realm of mathematics" cannot be ...

**2**

votes

**2**answers

545 views

### Authorship, and order of authors [duplicate]

Currently I am writing a paper with several collaborators; although I am the primary author to this (I have done a large (>85%) majority of the work and have actually written the paper) my last name ...

**2**

votes

**1**answer

207 views

### On non-unital ring and algebraic geometry

When I learned abstract algebra many years ago,I noticed the author deals with commutative ring say,$A$ has the proposition:$A^2=A$(without assuming it has identity).It seems that many proposition of ...

**2**

votes

**2**answers

619 views

### L-functions and algebraic geometry

Robert Langlands commented in a letter to Deligne that perhaps some of the deepest problems of algebraic geometry lie in L-functions. I want to understand the general philosophy and the connection ...

**42**

votes

**4**answers

3k views

### The Arnold – Serre debate

I have read (but I cannot now find where) that Arnold & Serre had a public debate on the value of Bourbaki. Does anyone have more details, or remember or know what was said?

**5**

votes

**1**answer

610 views

### Submission of papers to ArXiv or similar [closed]

This is an extension of this question and this question on MathStackExchange.
I have developed a formula for almost primes which is far more accurate asymptotically than Landau's well known
...

**1**

vote

**1**answer

241 views

### Submitting lecture purposal to conferences. (lecture about a thesis) [closed]

I wish to consult with you about something: I have recently given a lecture about my master's Thesis in a local conference organized by my advisor. The subject had a lot to do with algebraic geometry ...

**-6**

votes

**1**answer

779 views

### V.I. Arnold's high school problem [closed]

According to his interview to the Notices of the AMS, when Vladimir I. Arnold was 12 years old (in 1949) his teacher I.V. Morozkin, gave to his classroom (apparently 6th grade of a soviet primary ...

**0**

votes

**0**answers

165 views

### Examples of 'bad' notations and definitions [duplicate]

I am trying to compile a list of notations and definitions that has become ingrained in mathematical folklore, yet are still on some objective scale unsatisfactory. I offer two starting examples.
For ...

**5**

votes

**0**answers

324 views

### Design slides for presentation (conference talk) [closed]

Question: What are approved guidelines for design good slides for a
conference talk, especially with focus on mathematics?
I'm aware of the following, general best practices for holding a ...

**26**

votes

**5**answers

10k views

### Advice for pure-math Phd students [closed]

Pursuing a Phd in pure math can be a daunting task. A number of students who begin a Phd in pure math don't complete it, and there are high-quality dissertations and those which are not so high ...

**2**

votes

**0**answers

219 views

### Request for good research mailing list in Dynamical System & Chaos for notification of recent research results, conference, announcements [closed]

Are there some good research-level mathematics mailing list to be recommended in order to be notified of recent research results, news, announcements, conference, etc, particularly in Dynamical System ...

**41**

votes

**18**answers

6k views

### How can an extremely mathematically talented young person be helped to fulfill his/her potential?

Obviously, this question is not a research level mathematics question at all. But, I've just met an extremely mathematically talented 11 years old student and I don't know how I can help him. For ...

**2**

votes

**1**answer

149 views

### English translation of Gauss' “Principia generalia theoriae figurae fluidorum in statu aequilibri”

I have been unable to locate an English translation of Gauss' work, "Principia generalia theoriae figurae fluidorum in statu aequilibri".
A German translation exists (PDF), but my German is not quite ...

**29**

votes

**7**answers

3k views

### Is it worthwhile to give off-topic talks?

I am a graduate student. Occasionally for some reason I am asked to give a talk on my research at a conference whose stated purpose is almost completely unrelated to my research. To preserve my ...

**4**

votes

**1**answer

653 views

### a conjecture in sum-free sets

Let $ A $ be a set of non-zero integers. Then $A$ contains a sum-free subset $B$ of size $ |B|> \frac{|A|}{3} $ (a result of Erdős). It is conjectured that RHS can be improved to $\frac{|A|}{3} ...

**2**

votes

**1**answer

158 views

### Name of the concept “Topological boundary of A intersected with A”

In closure spaces (thus, also in topological spaces), one may define the boundary of a set A as the closure of A minus the interior of A. This set is partitioned into "the closure of A minus A" and "A ...

**4**

votes

**1**answer

348 views

### What does it mean for a Deligne-Mumford stack to have trivial generic stabilizers?

I have stumbled upon some literature on Deligne-Mumford stacks, and it seems to me, at least superficially, that there is a strong link between DM-stacks which have "trivial generic stabilizers" and ...

**10**

votes

**2**answers

1k views

### How difficult will it be for me to switch fields (details below) after my Ph.D. in pure mathematics?

I'm a first year postdoctoral researcher, working in pure areas of Riemann surfaces and differential geometry, after just finishing my Ph.D. in 2013. Recently I've also started taking interest in ...