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Results tagged with soft-question
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user 934
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.
6
votes
Which mathematical ideas have done most to change history?
My vote goes for calculus and in particular the Fundamental Theorem of Calculus (FTC) and Stirling's approximation for the factorial. Can you imagine doing basic mathematics in any scientific field wi …
4
votes
Accepted
Fourier Series application for dissertation
You can use Fourier series to prove Weyl equidistribution theorems. Take any irrational number $a$ and look at the fractional parts of $a,2a,3a,...$. Then this sequence is equidistributed in $[0,1]$. …
56
votes
What should be offered in undergraduate mathematics that's currently not (or isn't usually)?
I would have loved a class on how to write mathematical papers and what goes into mathematics research. Everything from neat Latex tricks to how to organize and structure ideas, theorems, etc, going o …
8
votes
Accepted
Dynamical Systems for undergraduate students
I would recommend reading through Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering by Steven Strogatz. He does a great job of motivating the applications …
- 4,952
22
votes
Problems where we can't make a canonical choice, solved by looking at all choices at once
It sounds like the probabilistic method fits your description. The following is an old Putnam problem (which has a detailed solution in the book, "The Probabilistic Method" by Alon and Spencer). Consi …
6
votes
6
answers
402
views
Physical Disturbances to Computations [closed]
In this paper, page 7 (160 of the Journal), Fig 3, there is a particularly amusing (not to the authors!) caption:
"... On April 1 of year 2 in the $S_0$ experiment, the computer was hit by a cosmic …
6
votes
Why do so many textbooks have so much technical detail and so little enlightenment?
I agree that sometimes authors present a concept simply because it's a standard example in the subject, but then spend a single page on it and just move on to other things. One example that comes to m …
4
votes
0
answers
787
views
How many projects do you work on concurrently? [closed]
I was wondering how many concurrent research projects a typical math researcher works on at a given time. I ask because I currently have the oppertunity to start a second project on something I'm fair …
5
votes
Accepted
What does log convexity mean?
From the comments, log convexity leads one to conclude that Riemann Hypothesis implies Lindelof hypothesis. The implication of log convexity comes from Hadamard Three Circle Theorem
- 4,952
8
votes
Surprising and Useful Physical Intuition for Mathematical Objects
I remember from Folland's PDE book an anecdote about Green convincing himself of the existence of a Green's Function:
Let $\Omega$ be a vacuum and $S$ a perfectly conducting shell grounded to zero po …
36
votes
Your favorite surprising connections in mathematics
The pair correlation function between Riemann zeta function zeros is the same as the pair correlation function between eigenvalues of random Hermitian matrices.
9
votes
Recent Applications of Mathematics
How about applications of discrete complex analysis to statistical physics? There was a surge of work this past decade on the subject, such as proofs of conformal invariance of 2-D models (Ising, Pott …
4
votes
What are some famous rejections of correct mathematics?
Riemann's work with curved spaces, particularly their applications to physics was at least 40 years ahead of it's time. He pushed forward ideas that space is perhaps curved and that forces such as gra …
9
votes
(Preferably rare) Audio/Video recordings of famous mathematicians?
Here is a long video about Richard Courant. Apparently he was one of the first people to own a video camera so there is some really old footage of some of the fathers of modern mathematics. If you scr …
19
votes
Describe a topic in one sentence.
Analytic Number Theory: log log log log log...
Did I see that quote in Havil's book Gamma?