Questions tagged [soft-question]

Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

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Who is Mrs. Gerber?

This question on a theorem in information theory called Mrs. Gerber's lemma piqued my curiosity. Who is this individual, and why the "mrs." ? A quick Google search was not informative, ...
Carlo Beenakker's user avatar
3 votes
1 answer
2k views

What's the point of differential geometry? [closed]

I've been self studying differential geometry for a little while now (4-6 months). I am learning from Lee's Introduction to Smooth Manifolds, and I just don't quite get the point of the subject. Why ...
Daniel Waters's user avatar
6 votes
1 answer
688 views

Quantum mechanics outside $L^{2}$ spaces

To this day, it is known that a satisfying mathematical formulation of quantum field theory is far from sight, even though some noninteracting theories can be described in rigorous mathematical ...
MathMath's user avatar
  • 1,255
53 votes
6 answers
5k views

Siegel zeros and other "illusory worlds": building theories around hypotheses believed to be false

What are some examples of serious mathematical theory-building around hypotheses that are believed or known to be false? One interesting example, and the impetus for this question, is work in number ...
7 votes
1 answer
768 views

Does there exist a "citation distance" calculator for papers or authors?

This question is not directly a mathematical question, but I am interested in whether there exists a calculator akin to an Erdős number calculator. The main difference is that I am not interested in ...
8 votes
6 answers
767 views

Papers on history and philosophy of mathematics suitable for master's students

In the fall, I will give a course called "Perspectives in Mathematics". This is a mandatory course at our master's program in mathematics (including applied mathematics and statistics). The ...
2 votes
0 answers
182 views

Are there some algorithms which have high consistency strength?

Are there some algorithms, their time complexity is relatively good, for example polynomial time. And the correctness of them has high consistency strength. And these algorithms shouldn't able to ...
Reflecting_Ordinal's user avatar
-2 votes
1 answer
548 views

Can mathematics help in defining free-will? [closed]

In the celebrated Free Will Theorem of Conway and Kochen it is made use of "free will" without giving a "mathematical definition" of it. The definition of the experimenter is the &...
mathoverflowUser's user avatar
1 vote
0 answers
260 views

The most simple proof of projective determinacy

I want to read the proof of projective determinacy. But every proof I could find (martin-steel original, koepke's, the proof in schindler's book, martin's new book) is too long. Are there a simple ...
Reflecting_Ordinal's user avatar
1 vote
0 answers
38 views

Choice of splitting in domain decomposition algorithms

When solving a PDE numerically by domain decomposition methods, what is the "optimal way" to split the domain? Are there any results stating that a particular partition of the domain yields &...
user298455's user avatar
17 votes
6 answers
6k views

Revisiting the unreasonable effectiveness of mathematics

Question: On balance, with theoretical advances in algorithmic information theory and Quantum Computation it appears that the remarkable effectiveness of mathematics in the natural sciences is quite ...
4 votes
1 answer
2k views

Summary of “Almost All Orbits of the Collatz Map Attain Almost Bounded Values”

Terence Tao's 2019 paper ``Almost all Orbits of the Collatz map attain almost bounded values" is pretty famous. However, it's also long and complicated. I think there are useful techniques to ...
user144527's user avatar
9 votes
1 answer
769 views

Practical Benefits of HTT/univalent foundations for assisted proofs

I'm trying to understand what the claimed practical benefits of HTT/univalent foundations are for doing computer assisted proofs and while I've seen a lot of claims of benefits they all seem to be ...
Peter Gerdes's user avatar
  • 2,551
95 votes
6 answers
6k views

Peer review 2.0

I have an idea for a website that could improve some well-known difficulties around peer review system and "hidden knowledge" in mathematics. It seems like a low hanging fruit that many ...
22 votes
2 answers
2k views

sci.math.research archive?

Does there exist an archive somewhere of posts to the USENET newsgroup sci.math.research? The best approximation I'm aware of is Google Groups. However, despite ...
53 votes
10 answers
7k views

Changes forced by the pandemic

The Covid-19 pandemic has changed our work-lives in ways few of us could have anticipated. These exceptional circumstances have forced each one of us and each one of our institutions to adapt, ...
6 votes
3 answers
548 views

Anomalous phenomena [closed]

What are examples of strikingly anomalous phenomena in mathematics, where just one or a rather small number of cases stand out because they don't fit a general pattern? This is most interesting when ...
2 votes
1 answer
254 views

What do shortest-path algorithms actually calculate?

The motivation for this question is a statement about the Bellman-Ford algorithm, that doesn't agree with the definition of what a path in a graph is. On wikipedia's description of the Bellman-Ford ...
Manfred Weis's user avatar
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8 votes
2 answers
554 views

Books/References for Inequalities that take advantage of orders

Are there any good references/papers/books that specifically address inequalities that take advantage of orders or monotonicity? I have already browsed through the classical Cauchy-Schwarz Master ...
rianko's user avatar
  • 81
2 votes
3 answers
2k views

What kind of jobs are available for a quantum logician?

What kind of jobs are there for someone with a strong, research-level theoretical background in the topic? I'm especially interested in the industry rather than academic jobs.
qk11's user avatar
  • 505
2 votes
0 answers
188 views

Small abelian categories and module categories - preservation of injective and projective objects

A soft question on small abelian categories: https://en.wikipedia.org/wiki/Grothendieck%27s_T%C3%B4hoku_paper Wikipedia: "The article "Sur quelques points d'algèbre homologique" by ...
user avatar
35 votes
15 answers
9k views

Is pure mathematics useful outside of mathematics itself? [closed]

From time to time Mathoverflow allows soft questions because they are arguably best answered by active mathematicians and they can benefit other mathematicians/PhD students/math undergraduates. I ...
7 votes
1 answer
312 views

What are some good practices which help researchers to contextualize their research?

From talks and lectures to paper writing, when researchers communicate their research, it is often very important to motivate the reader with some background information about that topic. Some of this ...
IamWill's user avatar
  • 3,151
33 votes
5 answers
3k views

Shapes for category theory

Most texts on category theory define a (small) diagram in a category $\mathcal{A}$ as a functor $D : \mathcal{I} \to \mathcal{A}$ on a (small) category $\mathcal{I}$, called the shape of the diagram. ...
0 votes
2 answers
444 views

mathematics around ranking [closed]

Is there interesting mathematics around ranking? (I mean ranking as reputation points here at mathoverflow.) It looks obvious that there is no way to make adequate ranking --- is it a theorem, at ...
Anton Petrunin's user avatar
4 votes
1 answer
949 views

Non-induced analytic structures in complex-analytic case

In Lectures on Analytic Geometry, for complex-analytic geometry, seemingly one only considers maps $(\mathbb C,\mathcal M_{<p})\to(\mathcal A,\mathcal M)$ of analytic rings for $0<p\le1$ where $...
Z. M's user avatar
  • 1,948
5 votes
1 answer
1k views

Can/should I cite some Stack projects Tag in a paper

According to Stack project, when referring to them I should use the Tag system https://stacks.math.columbia.edu/tags since “The tag system provides stable references to definitions, lemmas, ...
user12770's user avatar
  • 325
35 votes
12 answers
3k views

No canonical isomorphism [duplicate]

I thought that it would be interesting to collect into a big list various instances of isomorphic structures with no preferred isomorphism between them. I expect the examples to be interesting since ...
1 vote
1 answer
538 views

I want to enter graduate school in pure math. Is doing REU in “mathematical modeling” a good idea? Is it an essential skill to learn?

(please let me know if this question is not suitable here) Hello! I'm an undergraduate rising senior majoring in mathematics and it seems that I got rejected by an REU that is held in my university ...
jk001's user avatar
  • 129
5 votes
1 answer
336 views

Art supplies for a mathematician [closed]

These days the best tool for visualizing math is probably a computer. Nevertheless, I find it helpful/fun/nice-break-from-the-computer to sometimes make physical objects or drawings by hand. The ...
90 votes
11 answers
13k views

What are possible applications of deep learning to research mathematics?

With no doubt everyone here has heard of deep learning, even if they don't know what it is or what it is good for. I myself am a former mathematician turned data scientist who is quite interested in ...
8 votes
1 answer
515 views

Exposition of concrete constructions

I am frequently interested to find less technical proofs of results which already appear in the literature, at least in some special cases of these results. Sometimes a published proof shows that an ...
-2 votes
5 answers
2k views

Funny names of mathematical objects? [closed]

What are funny names of mathematical objects? For example Mouse (set theory)
-2 votes
1 answer
373 views

Soft Question: Asking for advice: how to study math? [closed]

(I am aware that some people might frown on this question, but I had no place to ask; this will definitely be voted to be closed in SE. I apologize in advance.) I am currently a 1st year grad student ...
James C's user avatar
  • 105
10 votes
2 answers
1k views

How professional mathematicians deal with discouragement? [closed]

All professional mathematicians feel discouraged occasionally due to some issue. My question is: How do professional mathematicians deal with discouragement? In this link , Andrew Wiles say ...
0 votes
1 answer
659 views

Applying Phd directly after undergraduate [closed]

I'm a math undergraduate and I'm about to finish my second year at UCL. It's time to consider my graduate school, and I have some questions about it. In the UK, many universities provide math PhD ...
Nonenicht's user avatar
0 votes
0 answers
103 views

Dinatural adjunctions

Let $F\colon\mathcal C\to \mathcal D$ and $U\colon\mathcal D\to\mathcal C$ be two functors. The traditional notion of "$F$ being a left adjoint of $U$" is expressed by the condition that ...
user177849's user avatar
8 votes
1 answer
5k views

How to cite an article with an article number (instead of page range)

I am curious to know what is the standard way (in AMS style) to cite a journal article that has an article number and/or a page range. For instance, here is a BibTeX entry from MathSciNet of an ...
Matteo Raffaelli's user avatar
10 votes
0 answers
943 views

The "unification" of geometry via topos theory?

This question is somehow motivated by The unification of Mathematics via Topos Theory and Synthetic vs. classical differential geometry. Sorry if this is a naïve question. There has been quite a lot ...
xuq01's user avatar
  • 1,054
7 votes
0 answers
486 views

Who is Claude Morlet?

[Please delete if off-topic.] I would be curious to find out more about the life and mathematical achievements of the French topologist Claude Morlet. The internet told me he got his PhD in 1968 with ...
Jens Reinhold's user avatar
15 votes
2 answers
2k views

How to structure a proof by induction in a maths research paper?

I am 16 years old at the time of writing (so I have no supervisors to seek advice from) and I have written a mathematics research paper, which I plan on submitting to a journal for publication. I ...
A-Level Student's user avatar
0 votes
1 answer
311 views

Why is the Barban-Halberstam-Davenport theorem important?

I have a slightly open-ended question about the Barban-Halberstam-Davenport theorem and hope that it is not off-topic. The theorem itself states that for any $A>0$ and $Q$ lying the range $x\log^{-...
user avatar
24 votes
1 answer
2k views

Is an interpretation mathematics (fit for publication)?

Background I am a mathematician with two published papers. The first is based on my PhD thesis and generalised a tool to a more general setting. The thesis was cited a number of times by the time the ...
Newbie's user avatar
  • 265
5 votes
1 answer
213 views

References for Hopf Galois module theory

I am a first-year PhD student and I am really interested in Galois module theory, both in a "classical" and in a "nonclassical" sense. In the last months I have been reading about ...
Lios's user avatar
  • 213
12 votes
1 answer
967 views

Where to publish a long classification?

Suppose that the classification of some mathematical (say algebraic) notions requires (say) 70 pages. Let clarify that (say) 90% of the pages are used to write the result itself, whereas only 10% are ...
1 vote
0 answers
179 views

What are some great examples of wordsmanship in published literature? [duplicate]

David L. Goodstein begins his book on statistical mechanics, ''States of Matter'', with the following introduction: "Ludwig Boltzmann, who spent much of his life studying statistical mechanics, ...
Klangen's user avatar
  • 1,943
55 votes
9 answers
6k views

Proofs of theorems that proved more or deeper results than what was first supposed or stated as the corresponding theorem

Recently, I figured out that a colleague of mine has had published during recent years a proof of a theorem in which he was actually proving a deeper result which we both thought to be still open. ...
9 votes
1 answer
303 views

Origin and context of adjunctions inducing equivalences between full subcategories

The following is well-known. Theorem. Let $F\dashv U$ be a pair of adjoint functors $$F\colon \mathcal C\to \mathcal D, \qquad U\colon \mathcal D\to\mathcal C$$ with unit $(\eta_A\colon A\to U(F(A)))_{...
user175321's user avatar
7 votes
1 answer
188 views

Hybrid online/ in-person workshops, conferences, and summer schools

I am writing to ask if people in the community can post any noteworthy experiences they have had with hybrid online/in-person workshops. Does anyone have experience with these, as either organizer or ...
David Jordan's user avatar
  • 6,053
10 votes
1 answer
3k views

Latest "A Term of Commutative Algebra" by Altman and Kleiman? [closed]

Where can I find the latest revision of A term of Commutative Algebra by Allen B. ALTMAN and Steven L. KLEIMAN? Is my 2013 version ok? It is hard to locate the latest one; many old revisions and ...

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