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Results tagged with soft-question
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user 21907
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
What is Quantization ?
A very basic answer: think about the classical Hamiltonian,
$$
a(x,\xi)=\vert \xi\vert^2-\frac{\kappa}{\vert x\vert},\quad \text{$\kappa>0$ parameter}.
$$
The classical motion is described by the inte …
- 16.2k
2
votes
Reference request: any 20th century German critiques of Bourbaki?
Another scathing critic of Bourbaki can be found in the article "The Ignorance of Bourbaki" by the Logician A.R.D. Mathias in THE MATHEMATICAL INTELLIGENCER VOL. 14, NO. 3, pp.4-13. So it is not a Ger …
28
votes
Does Physics need non-analytic smooth functions?
A strong argument is given above on the heat equation; let me be more specific. The heat equation, one of the most basic in PDE and mathematical physics, already known to Fourier, is
$$
L=\frac{\parti …
- 16.2k
5
votes
fourier analytic proofs
Let me speak about the "Triumph of Fourier" according to the words of Laurent Schwartz in his autobiography. The Fourier transformation is a handy tool to characterize regularity of functions.
Let $ …
2
votes
Concrete example of BV function $u:\mathbb{R}^2 \to \mathbb{R}$ with singular derivative
The absolutely continuous part and the jump part of the derivative are easy to understand: taking $\mathbf 1_{\mathbf R_+}(x_1)$ provides a $BV$ function with jump at $x_1=0$. As far as the Cantor par …
- 16.2k
2
votes
Revisiting the unreasonable effectiveness of mathematics
As a rather recent revisitation of Wigner's article, one may also quote James Glimm, who wrote in the article "Mathematical perspectives" (Bull. Amer. Math. Soc. (N.S.) 47 (2009), no. 1, 127–136),
In …