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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.

7 votes

Why are some heuristics successful?

The Weil conjectures could qualify as a set of heuristics developed into a rigorous proof by Deligne and others: What was really eye-catching, from the point of view of other mathematical areas, was …
1 vote

Rigorous statistical mechanics: difficulty of realistic models

General remark on why one would study simple models: In the statistical mechanics of phase transitions one distinguishes relevant and irrelevant variables. A phase transition is associated with a dive …
Carlo Beenakker's user avatar
4 votes

Accessible literature on fractional dimensions of subsets of $\mathbb R^n$

Erin Pearse's Introduction to dimension theory and fractal geometry may well be suited for this purpose. It introduces the various ways to define and measure a fractional dimension (box counting, Mink …
Carlo Beenakker's user avatar
4 votes

Hilbert's approach to Riemann hypothesis using Fredholm's work

Since this question was bumped to the front page, I might address Q1: Can someone provide historical references for it? This goes back to André Weil, who writes in [1] that Ernst Hellinger, a student …
Carlo Beenakker's user avatar
6 votes
Accepted

Current state of the art in geometric complexity theory

As explained by Scott Aaronson, in his 2017 overview of Geometric Complexity Theory, the core problem it tries to solve is to prove Valiant's conjecture VP$\neq$VNP that the permanent requires exponen …
Carlo Beenakker's user avatar
12 votes
Accepted

Mathematical emails

See https://wiki.archivematica.org/Email_preservation My own practice is to collect individual messages in a single mbox file, I do this twice a year so that the file is not too big. There are many ro …
21 votes

Who says understanding physics helps mathematicians? (A reference request) [Take the word "w...

Michael Atiyah, On the Work of Edward Witten: In his hands physics is once again providing a rich source of inspiration and insight in mathematics. Of course physical insight does not always lead to …
4 votes

Math conference-organizing checklist?

A detailed checklist is here. We organize many smaller conferences/workshops, where the participation of the participants is the key thing. No idea if that applies to this situation, but you might wan …
2 votes

Examples of games developed purposely to analyze players' strategies for mathematics research

This meets your criterion of a "game developed purposely to analyze players' strategies for mathematics research," if I am allowed to consider a branch of mathematics, optimal control theory, at the i …
Carlo Beenakker'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 intui...

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
5 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

Zentralblatt MATH volume numbering

The numbering is sequential in the order in which a review is entered, so not strictly tied to a particular year of publication. For example, volume 1430 has mainly papers published in 2019 and 2020, …
Carlo Beenakker's user avatar
11 votes

AI tools for editing and re-generating old math documents

Since you ask specifically about LLM's: A customized version of ChatGPT is available for this functionality, see Document to LaTeX Custom GPT. Here is a promotional. I have not tried it, you need a pa …

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