**0**

votes

**0**answers

161 views

### Recreating the wheel

I recently finished my Phd in pure maths and I am looking for open problems in my research area, functional analysis. Without going into the details, I stumbled onto an interesting problem and I ...

**4**

votes

**1**answer

106 views

### What is the early history of the concepts of probabilistic independence and conditional probability/expectation?

In the 1738 second edition of The Doctrine of Chances, de Moivre writes,
Two Events are independent, when they have no connexion one with the other, and that the happening of one neither forwards ...

**4**

votes

**4**answers

738 views

### Advice for number theory library

Hi I just got a faculty position and it comes with a generous start up funds for "office supplies", which I must use or lose. What does a pure mathematician need? I have good computers already. I ...

**3**

votes

**2**answers

268 views

### Beautiful constructions in algebraic topology that facilitate one's understanding of homotopy theory [on hold]

There is an army of interesting constructions in AT, and Understanding them are usually very helpful for appreciate the theory underneath. So I would like to invite you to share those examples that ...

**-1**

votes

**0**answers

115 views

### What are the areas of modern math? [on hold]

question:
In undergraduate mathematics there are very clearly defined areas (Calculus, Linear Algebra, Analysis, et cetera), however these are very well developed ares of mathematics that seem to not ...

**3**

votes

**1**answer

159 views

### References for von Neumann Algebras

I have some -possibly- simple but broad questions: Where to begin the study of von Neumann Algebras? Which are the important questions in the field that guide current research? I'm interested in ...

**-2**

votes

**0**answers

61 views

### Books and papers on differential equation method [closed]

I wanted to understand the differential equations method for analyzing stochastic sequences. Is there a good book/ papers that provide a gentle survey this topic with a good number of examples? A good ...

**12**

votes

**2**answers

475 views

### Applications of really large numbers

I have seen several questions here on MO regarding large numbers, (uparrow notation, etc.), and different way to construct and compare such numbers.
I am curious what the applications are for the ...

**1**

vote

**0**answers

392 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 ...

**3**

votes

**0**answers

235 views

### About Blind Mathematicians [migrated]

Since some mathematicians are blind could we talk a minute about the Access to Mathematics by blind students. How to use a tactile writing system like the Braille language on MO. I found this nice ...

**38**

votes

**11**answers

5k 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 ...

**2**

votes

**0**answers

135 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

78 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?

**1**

vote

**0**answers

87 views

### Fast-pace exposure a better idea for applied mathematician (not application but formalism for science problem)? [closed]

I don't really recall where and who said that, there a string theorist said one time more or less a joke,
"Physicists study Atiyah-Singer index theorem, then try to learn Riemannian geometry."
It ...

**6**

votes

**0**answers

73 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

1k 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 ...

**2**

votes

**4**answers

346 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

165 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

304 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

272 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 ...

**58**

votes

**9**answers

6k 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

359 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 ...

**4**

votes

**1**answer

271 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 ...

**20**

votes

**3**answers

720 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 ...

**22**

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 ...

**9**

votes

**0**answers

273 views

### What is a good poster for a math conference?

I'm going to participate to a conference and they ask me to do a poster on my research. I've never made a poster for a conference/seen a poster session in a conference. So what is important? What do ...

**3**

votes

**0**answers

187 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

63 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

422 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

194 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

541 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 ...

**6**

votes

**2**answers

952 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 ...

**8**

votes

**0**answers

269 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 ...

**3**

votes

**1**answer

340 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

312 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 ...

**16**

votes

**1**answer

464 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

373 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 ...

**21**

votes

**4**answers

835 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

175 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

324 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 ...

**5**

votes

**1**answer

360 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

485 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 ...

**0**

votes

**0**answers

82 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

537 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 ...

**37**

votes

**4**answers

2k 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?

**4**

votes

**1**answer

481 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

188 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 ...

**-5**

votes

**1**answer

444 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 ...