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.
0
votes
0answers
2 views
Reference on Infinite Dimensional Manifold
I am studying manifold. For comprehension, I read the site http://en.wikipedia.org/wiki/Manifold, and there is some information about infinite dimensional manifold.
Now I have two questions or ...
18
votes
1answer
4k 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
245 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
175 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 ...
1
vote
1answer
56 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
391 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
168 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
487 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 ...
-1
votes
0answers
70 views
what is the Erdos Discrepancy Problem connection(s) to (T)CS? [migrated]
recently there are some new results on computer-based empirical/experimental study of the Erdos Discrepancy Problem (via SAT solvers, cited below). this problem has been cited & studied by several ...
6
votes
2answers
916 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 ...
-1
votes
0answers
153 views
What's the software mathematician usually use? [duplicate]
As research mathematicians, what kind of software can aid us?
7
votes
0answers
235 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
0answers
181 views
Relation: Modular Forms and hyperbolic geometry, or, why do they map from $\mathbb{H}$? [migrated]
In my very young mathematical career, I have worked a lot with modular forms. Recently, I worked as a teaching assistant in a course about geometry. At the end of the course, we dealt with hyperbolic ...
3
votes
1answer
325 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
285 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
446 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
356 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
821 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 ...
11
votes
6answers
942 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
166 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) ...
-6
votes
1answer
281 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
341 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
471 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
71 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
517 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
471 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
1answer
186 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
1answer
421 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
0answers
155 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 ...
4
votes
0answers
135 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 ...
22
votes
5answers
1k 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
0answers
198 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 ...
4
votes
2answers
313 views
Mazur's torsion theorem on elliptic curves and its generalisations
I want to study Mazur's torsion theorem for elliptic curves over $Q$ and its generalizations for number fields, i.e., papers by Kamienny, Kenku & Momose, Filip Najman. So please suggest to me what ...
38
votes
18answers
4k 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
1answer
136 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
7answers
2k 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
1answer
374 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
1answer
131 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 ...
5
votes
1answer
293 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 ...
8
votes
2answers
973 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 ...
2
votes
1answer
277 views
Examples of Quot schemes
I'm studying Quot schemes, that I denote with $Quot_{N,X,P}$, with $N \in \mathbb{Z}$, $X \subset \mathbb{P}^d$ and $P \in \mathbb{Q}[t]$. So, I'm looking for explicit examples of Quot schemes. Could ...
7
votes
1answer
291 views
Model structure for cooperads and for coalgebras
I am studying the homotopy theory of (algebraic) operads and I came up with several questions I am unable to answer to. I would like to stress that I don't have applications in mind, I just would like ...
5
votes
1answer
366 views
Is Logic/Set Theory necessary for studying Topos Theory?
I have just completed a postgraduate course, in which I studied Category Theory, without having a background in Set Theory and Logic - this probably already sounds absurd to many. This did not seem to ...
10
votes
5answers
578 views
Accessible proofs of contemporary results in mathematics
Are there strong results in contemporary mathematical research (last 20 years) which have a proof which every mathematician (holding a PhD) can completely understand within a few days? -- If yes, ...
2
votes
0answers
231 views
Equal signs with fancy marks
Some people use $\stackrel{\mathrm{def}}{=}$, $:=$ or $\stackrel{\Delta}{=}$ for definitions.
In more informal contexts, I have also seen $\stackrel{?}{=}$, for "I wish to prove this equality, which ...
36
votes
8answers
2k views
What is entropy, really?
I first saw the term "entropy" in a chemistry course while studying thermodynamics.
During my graduate studies I encountered the term in many different areas of mathematics.
Can anyone explain why ...
1
vote
0answers
309 views
On Mathematicians Who Did Their Masterworks After 40 Years Old [duplicate]
Remark: The idea of this soft question is adopted from the following interesting book.
Timothy Gowers, Mathematics: A Very Short Introduction, Oxford University Press, 2002.
...
7
votes
2answers
188 views
Natural $\Pi^1_2$ (or worse) classes of structures?
(To clarify, my interest is mainly lightface, that is, $\Pi^1_2$ instead of $\bf \Pi^1_2$, although it doesn't particularly matter.)
This is just an idle curiosity. In logic, I find myself frequently ...
