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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.
19
votes
How does one justify funding for mathematics research?
A century old opinion: http://www.jstor.org/stable/2972761 (The Significance of Mathematics, by E. R. Hedrick)
Shall we not search our own house? Shall we not ask if our own collegiate and
gradu …
17
votes
Has Apéry's proof of the irrationality of $\zeta(3)$ ever been used to prove the irrationali...
As Frits Beukers writes in http://www.staff.science.uu.nl/~beuke106/caen.pdf "Ironically all generalisations tried so far did not give any new interesting results. Only through a combination of miracl …
8
votes
Companion to theoretical physics for working mathematicians
If you are not interested too much in details, the following book can play the role of a comprehensive companion: http://www.amazon.com/Unified-Grand-Theoretical-Physics-Edition/dp/1439884463 (A Unif …
8
votes
Accepted
References for von Neumann Algebras
For a rapid introduction see http://www.math.berkeley.edu/~vfr/MATH20909/VonNeumann2009.pdf (Von Neumann Algebras, by Vaughan F.R. Jones -- "The purpose of these notes is to provide a rapid introducti …
7
votes
Essays and thoughts on mathematics
The Psychology of Invention in the Mathematical Field (Jacques Hadamard's 1945 essay)
5
votes
Physicist trying to understand modern mathematics
On this website http://www.theorie.physik.uni-muenchen.de/activities/schools/archiv/2011_asc_school/index.html there are videos of the lectures given at the 2011 Arnold Sommerfeld PhD School ''Algebra …
4
votes
Book on symplectic geometry
A classic, physically inclined introduction is http://www.springer.com/us/book/9780817636951 (Structure of Dynamical Systems: A Symplectic View of Physics, by J.M. Souriau).
3
votes
Uninteresting questions with interesting answers
Watson's integral. Seemingly uninteresting question: calculate
$$W_S=\frac{1}{\pi^3}\int\limits_0^\pi\int\limits_0^\pi\int\limits_0^\pi
\frac{dx\,dy\,dz}{3-\cos{x}-\cos{y}-\cos{z}},$$
produces truly a …
3
votes
Demystifying complex numbers
An interesting example of usage of complex numbers can be found in
http://arxiv.org/abs/math/0001097 (Michael Eastwood, Roger Penrose, Drawing with Complex Numbers).
2
votes
Accepted
Reference for exercises with solutions for affine Lie algebras
You can find some exercises in the following lecture courses: http://www.maths.ed.ac.uk/~igordon/LA1.pdf (Infinite-dimensional Lie algebras, by Iain Gordon - no solutions are provided, though)
http:// …
2
votes
Interesting Calculus Questions/Exercises
A very good calculus problem book is "Problems in Mathematical Analysis" by Boris Demidovich: http://www.mat.uniroma3.it/users/chierchia/VARIE/bdfc.pdf
1
vote
Accepted
Reference request: a guide through quantum probability
If you are interested in quantum probability from mathematical perspective, these two books will be helpful:
http://www.springer.com/mathematics/probability/book/978-3-540-60270-5 (Quantum Probabilit …
1
vote
Accepted
Reference to complete derivation of Kossakowski–Lindblad equation and its steady solutions
It seems the following two articles http://arxiv.org/abs/1110.2122 (A simple derivation of the Lindblad equation, by Carlos Alexandre Brasil, Felipe Fernandes Fanchini, Reginaldo de Jesus Napolitano) …
1
vote
References on thin film equation: derivation and properties
Earlier references on derivation of this equation can be found in
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/on-the-motion-of-a-small-viscous-droplet-that-wets-a-surfa …
0
votes
Reference request for Stieltjes Transform
Maybe the following reference will be useful https://arxiv.org/abs/1105.0060 (Signal Processing in Large Systems: a New Paradigm, by R. Couillet, M. Debbah). See also chapter 3 in the book "Random Mat …