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Results tagged with soft-question
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user 11260
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 …
- 188k
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 …
- 188k
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 …
- 188k
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Q1: Can someone provide historical references for it?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 …
- 188k
14
votes
Accepted
What kind of computer tools topologists/geometers use to visualize the objects they deal with?
Here is one case study:
An impressive animation of the Hopf fibration created by Niles Johnson using only open-source tools, available for all platforms: The Python-based mathematics program Sage was …
- 4,713
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 …
- 188k
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 …
- 188k
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 …
- 188k
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 …
- 188k
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 …
- 188k
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 …
- 188k
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 …
- 188k
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.
- 188k
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 …
- 188k
6
votes
Source for analysis of identification of structures in learner's mind and mathematical struc...
A much-cited attempt to analyze Piaget's ideas and carry them further has been given by Ed Dubinsky in Reflective abstraction in advanced mathematical thinking (1991).
Reflective abstraction is a con …
- 3,065