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4 votes

Use of an appendix in a long paper

This is tricky, because it strikes at the tension between pressures from the publication system to keep papers short vs our collective desire to have a peer-reviewed literature with no gaps. Let's ...
11 votes

What would you do if you improve your own result that is submitted but not published?

This kind of situation is actually pretty normal in math research. The answer basically hinges on the meaning of "dramatically." If it was only a minor improvement, then the normal thing to ...
6 votes

Does anyone use non-sober topological spaces?

As suggested by @DavidWhite, I am turning my comment into an answer. One class of very naturally appearing non-sober spaces is that of Alexandroff topologies on infinite posets. An irreducible closed ...
3 votes

Where can I find a collection of new errata for EGA?

In the years since this question was asked, such a collection of errata has begun to be built, thanks to the community project https://github.com/ryankeleti/ega At the moment of writing, they have ...
David White's user avatar
  • 29.4k
4 votes

How common is it for universities to create new positions for dual hires?

This is an old question that lingers on the unanswered queue. Nowadays, it would be migrated to Academia.SE, but that site didn't exist when this was asked. Anyway, I'll try to answer, in case it ...
4 votes
Accepted

Publication Of 50 pages

This question was asked a long time ago, and never got an answer, but did receive some useful comments. The short answer is there are hundreds of journals that would publish such a paper. In some ...
10 votes

What are journal rankings that employers look at?

Unfortunately, this practice spreads. Especially in the universities outside of USA. The databases most commonly used are ISI (Inst. of Sci. Information) Journal Citation reports and Scopus. Both of ...
9 votes

What are journal rankings that employers look at?

Let me answer from the perspective of a liberal arts college that emphasizes both teaching and research. I'm going to tell you how I've seen research assessed. I don't claim that this is a good way to ...
10 votes

How can I (semi-formally) convince myself that Euclidean geometry comports with visual intuition?

To the sources mentioned by @Carlo Beenakker, I would like to add the works of Soviet physicist Boris Rauschenbach, most of them are in Russian, but there are some in English: Perspective Pictures and ...
Alexandre Eremenko's user avatar
9 votes

What are journal rankings that employers look at?

Many universities have adopted the San Francisco Declaration on Research Assessment (DORA), which forbids considering journal rankings as a proxy for research quality. What matters is the merit of an ...
10 votes
Accepted

How can I (semi-formally) convince myself that Euclidean geometry comports with visual intuition?

Patrick Suppes asked Is Visual Space Euclidean? (1977). A more recent contribution that answers the question in the negative: Is perceptual space inherently non-Euclidean? (2009). It is often assumed ...
Carlo Beenakker's user avatar
2 votes

Why does mathematics seem to have a polarity bias?

$\newcommand\Set{\mathrm{Set}}$Rather than what we use more or less than what, I've wondered at why while category theory is a completely symmetrical theory, many dual things feel very different from ...
dan l's user avatar
  • 21
0 votes

What could be some potentially useful mathematical databases?

Maybe I can post my collection of mathematical databases here (The page is in Chinese, but nowadays web translations are popular anyway.): recommended math stuffs. These resources include various ...
3 votes

How would you cite a result that it is not quite correct, but whose proof contains some useful ideas

This question was asked a long time ago, but never received an answer. I largely agree with Deane Yang's comment, but wish to expand on it, for the sake of future visitors to MO. First, several other ...
10 votes

Use of singular pronoun "I" in the acknowledgements

This question was asked some time ago, but never received an answer. It has several highly upvoted comments, but there is also disagreement in the comments. I think the question is reasonable, given ...
2 votes

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

If you want something simultaneously recent, readable, and controversial, you may want to take a look at Katz, M.; Kuhlemann, K.; Sherry, D.; Ugaglia, M.; van Atten, M. "Two-track depictions of ...
1 vote

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

For the philosophy of mathematics, I wrote my book specifically with mathematical readers in mind. Many readers have told me that they appreciate the accessible manner the book has of treating even ...
0 votes

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

If you are interested in serious combinations of history and philosophy of math, there are some collective books which have not been mentioned. To consider only books published after 1980, let me ...
1 vote

Application of higher categories in algebra

There are tons of such applications. For example, less than two years ago, they were used to prove the Redshift Conjecture, a statement about iterated algebraic $K$-theory. I previously wrote an ...
4 votes

Math graduate school applications and personal hardships

This question was asked a while ago, but never got an answer. The comments focused on how a goal of "getting into a top 6 PhD program" followed by a "top 30 professorship" was a ...
9 votes

Is it fine to correct and extend texts of a late colleague when publishing them?

I would recommend publishing such a book in a Part I + Part II format. Part I would contain the works of your late colleague with minimal edits: remove what's obviously wrong, remove the sections that ...
André Henriques's user avatar
2 votes

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?

This was asked a while ago, and never received an answer but did receive some helpful comments. Since future visitors might have the same question, I'll try to answer. First, an REU is a "...
David White's user avatar
  • 29.4k
6 votes

Advice for PhD in Algebra

This question was asked in 2020, and had a built-in five day deadline. It never received an answer but did have some helpful comments. Since this is a general question, and future users might benefit ...
2 votes

Reference on Operads

Most textbooks have a portion of the front-matter devoted to telling the reader what mathematical prerequisites are expected. Tom Leinster's excellent book has already been mentioned in an answer (and ...
David White's user avatar
  • 29.4k
0 votes

Comments and reference-request on books for KK-theory

I have both of the books you mentioned but didn't own. For sure the better one is "K-Theory for Operator Algebras" by Blackadar, if your goal is the Atiyah-Singer Index Theorem. First, this ...
David White's user avatar
  • 29.4k
13 votes

Where did the military money go?

This question is rather old, but never got an answer (though it did have some useful comments), so I'll try to answer it. First, yes, I think it's fair to say that the military funding for pure math ...
David White's user avatar
  • 29.4k
2 votes

Algebra/Algebraic geometry in statistical mechanics

The answer depends on the precise interpretation of the question. Carlo Beenakker's answer mentions a possible (general, universal) algebraic approach to the field as a whole. Let me complement this ...
Jules Lamers's user avatar
  • 1,813
6 votes
Accepted

Literature about formalization of "natural reasoning" in mathematical logic

Quantum logic might be one example of "a non-standard way of doing logic motivated by the nature of reality," as described in Quantum Logic in Historical and Philosophical Perspective.
Carlo Beenakker's user avatar
2 votes

Algebra/Algebraic geometry in statistical mechanics

An algebraic approach is used in physics to develop a rigorous theory of systems with an infinite number of degrees of freedom, as they appear in quantum field theory and in the thermodynamic limit of ...
Carlo Beenakker's user avatar
4 votes

Examples of conjectures that were widely believed to be true but later proved false

The Connes embedding conjecture, formulated in 1976, asserts that every type II₁ von Neumann factor embeds into an ultrapower of the hyperfinite II₁ factor. Even though it is sometimes known as the ...
1 vote

What are some examples of colorful language in serious mathematics papers?

From Andretta's "Large cardinals and iteration trees of height $\omega$" (Annals of Pure and Applied Logic vol. 54, 1990): We have tried to make this paper self-contained but we could not ...

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