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Results tagged with soft-question
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user 5371
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.
17
votes
What is the difference between hard and soft analysis?
A historical note.
Hermann Weyl mentioned in his talk "Felix Kleins Stellung in der mathematischen Gegenwart" that the dichotomy of "hard vs. soft analysis" had been suggested by Hardy. According to …
- 22.3k
2
votes
How can I conclude that I live in a solar system?
An interesting (and very old) argument in favour of heliocentrism is based on estimates of the relative sizes of the Earth and Sun.
Actually, Aristarchus of Samos estimated that the Sun is six to …
- 22.3k
6
votes
Individual mathematical objects whose study amounts to a (sub)discipline?
The Korteweg–de Vries equation. For almost 90 years it was seen as just another non-linear equation stemming from fluid dynamics. Everything has changed after people discovered the world of solitons. …
3
votes
Examples of inequality implied by equality.
Two examples due to Hurwitz.
The AM-GM inequality.
For the function $f=f(x_1,x_2,\dots,x_n)$ let $Pf(x_1,x_2,\dots,x_n)$ denote the sum of $f$ over the $n!$ quantities that result from all possible …
36
votes
Accepted
What does the word "symplectic" mean?
The term "symplectic group" was suggested in The Classical Groups: their invariants and representations (1939, p. 165) by Herman Weyl:
The name "complex group" formerly advocated by me in allusio …
- 22.3k
11
votes
When Have Numerology and Computational Experimentation Been Successful?
Three examples from the theory of dynamical systems (in a broad sense).
Edward Lorenz' almost accidental discovery of the first example of a strange attractor and the butterfly effect.
(s …
14
votes
Accepted
approximately linear functions
Let $E$ and $E'$ be Banach spaces. Mappings $f:E\to E'$, which satisfy the inequality
$$\|f(x + y) − f(x) − f(y)\| \leq\epsilon$$
for all $x, y \in E$, are called $\epsilon$-additive (or approximate …
- 22.3k
22
votes
Nontrivial question about Fibonacci numbers?
Two formulas relating $\pi$ and the Fibonacci sequence.
$$\pi=\lim\limits_{n\to\infty}\sqrt{\frac{6\cdot \ln (F_1\cdot F_2\dots F_n)}{\ln(\mbox{lcm}(F_1,\dots,F_n))}},\qquad\qquad\qquad\qquad(1)$$
wh …