Questions that ask about some aspect of mathematical research or study which doesn't involve the actual mathematics. In general, soft questions can be answered without using mathematical reasoning.
3
votes
0answers
104 views
Stable homotopy of spheres non-locally
Are there any results/conjectures about the stable homotopy groups of spheres that relate the picture at different primes? Something like Gauss's reciprocity law in number theory?
I know about the ...
7
votes
5answers
706 views
Advice on choosing an area of specialization
I'm not sure if this is an appropriate question for MO, but I figured it couldn't hurt to ask. I'm a second year graduate student, currently gearing up to construct a committee and syllabus for my ...
2
votes
2answers
421 views
Have axioms / axiom schemata of this flavour been proposed or otherwise considered?
With the exception of a few miscellaneous cases, the axioms (and/or schemeta) of ZFC can roughly be divided into two kinds:
Those that guarantee the existence of more complicated sets, given that ...
1
vote
0answers
187 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
1answer
119 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
4answers
859 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 ...
2
votes
2answers
288 views
Beautiful constructions in algebraic topology that facilitate one's understanding of homotopy theory [closed]
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
0answers
123 views
What are the areas of modern math? [closed]
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
1answer
163 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 ...
12
votes
2answers
492 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
0answers
395 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
0answers
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
11answers
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
0answers
140 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
1answer
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
0answers
88 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
0answers
78 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
1answer
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
4answers
352 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
0answers
168 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
4answers
311 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
0answers
276 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
9answers
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
0answers
361 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
1answer
274 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
3answers
729 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
1answer
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
0answers
278 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
0answers
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
1answer
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
2answers
426 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
1answer
197 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
3answers
543 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
2answers
956 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
0answers
270 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
1answer
343 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
1answer
319 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
1answer
466 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
1answer
377 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
4answers
845 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
6answers
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
1answer
176 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
1answer
331 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
1answer
362 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
2answers
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
2answers
487 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
0answers
83 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
2answers
538 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
4answers
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
1answer
482 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
...
