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Results tagged with soft-question
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user 5712
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.
54
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34
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Most intriguing mathematical epigraphs
Good epigraphs may attract more readers. Sometimes it is necessary.
Usually epigraphs are interesting but not intriguing.
To pick up an epigraph is some kind of nearly mathematical problem: it shoul …
- 337
8
votes
Can the theory of elliptic functions developed from purely geometric considerations?
One possible source is the book
Lawden, D. F. Elliptic functions and applications, New York, NY etc.: Springer-Verlag, 1989, doi:10.1007/978-1-4757-3980-0,
(esp. Ch. 4 Geometrical Applications). In …
- 35.5k
17
votes
Examples of unexpected mathematical images
This is unexpected Voronoi diagram (see the full story). By zooming in and out of the following pictures, such a picture can be seen on the screen for a short time (less than 1 second).
It illustrate …
- 12.3k
15
votes
LaTeX tricks that save time in typesetting
Mathpix is a nice tool to convert images to LaTeX: "Take a screenshot of math and paste the LaTeX into your editor, all with a single keyboard shortcut". Formulae can be taken from Internet browser, d …
- 12.3k
3
votes
Widely accepted mathematical results that were later shown to be wrong?
Hilbert's sixteenth problem. In his speech, Hilbert presented the problems as:
The upper bound of closed and separate branches of an algebraic curve of degree n was decided by Harnack (Mathematische …
- 4,713
11
votes
Examples of unexpected mathematical images
The Mandelbulb is a three-dimensional fractal, constructed by Daniel White and Paul Nylander using spherical coordinates in 2009.
- 12.3k
24
votes
1
answer
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"Gauss trick" vs Karatsuba multiplication
This question is inspired by article Alexander Shen "Gauss multiplication trick?" (Russian, "Mathematical Enlightenment", 2019).
Dasgupta, Papadimitriou, Vazirani, Algorithms (2008) Ch. 2:
The ma …
- 12.3k
3
votes
Examples of mathematics motivated by technological considerations
Markov chains have applications in speech recognition (see A tutorial on hidden Markov models and selected applications in speech recognition by Rabiner), analysis of DNA sequences (see Biological Seq …
- 4,713
4
votes
Non-computational software useful to mathematicians
Mathpix is a nice tool to convert images to LaTeX: "Take a screenshot of math and paste the LaTeX into your editor, all with a single keyboard shortcut". Formulae can be taken from Internet browser, d …
- 12.3k
14
votes
LaTeX tricks that save time in typesetting
I'm not sure but new commands can be inconvenient for the editors. So the long plain commands can be better in this case. In order to save time I use macros which replace some simple strings by usual …
- 12.3k
10
votes
Different derivations of the value of $\prod_{0\leq j<k<n}(\eta^k-\eta^j)$
Your are asking about determinant of the Schur Matrix. So you can use original Schur's article or another classical expositions mentioned at Mathworld.
- 12.3k
3
votes
Nontrivial question about Fibonacci numbers?
Parametrization of the equation $x^2-xy-y^2=\pm1$. Next step is a 2-dmensional isolation theorem, see Cassels, J. W. S. An introduction to the geometry of numbers, sec. II. 4. Indefinite quadratic f …
- 12.3k
13
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Mathematical conjectures on which applications depend
Many cryptographic protocols are based on the problem which seem to be hard. Among them Discrete logarithm problem and its variants (Diffie–Hellman problem, Decisional Diffie–Hellman assumption, Ellip …
- 12.3k
10
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Mathematical conjectures on which applications depend
Tonelli–Shanks algorithm needs quadratic nonresidue $n$ modulo prime $p$. If the extended Riemann hypothesis is true, then the first quadratic nonresidue $n_p$ is always less than $3(\log p)^2/2$ (Wed …
- 12.3k
5
votes
Most intriguing mathematical epigraphs
Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. (John von Neumann, 1951)
Knuth, D. E. The art of computer programming. Volume 2.
Ch. 3 Ran …
- 21.3k