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Results tagged with big-list
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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
274
votes
What are some examples of colorful language in serious mathematics papers?
From the ground-breaking paper: On the complexity of omega-automata by Muli Safra (DOI: 10.1109/SFCS.1988.21948)
Acknowledgements
The author thanks his advisor, Amir Pnueli, for his encouragement an …
154
votes
Examples of common false beliefs in mathematics
Here are a few more: (Everything between quotation marks is a false belief.)
Basic logic: Among students: "If A implies B then B implies A" (or "if A implies B then not A implies not B").
Even among …
96
votes
Most harmful heuristic?
"Generalization for the sake of generalization is a waste of time"
I think that generalization for the sake of generalization can be rather fruitful.
66
votes
What notions are used but not clearly defined in modern mathematics?
I have three (somewhat related) examples:
The notion of explicit construction. Seeking explicit constructions to replace non-constructive existence proofs is an old endeavor. Computational complexity …
63
votes
Fundamental Examples
The Petersen Graph in graph theory.
58
votes
Magic trick based on deep mathematics
Five unrelated items:
Mobius strip
One of the best mathematical tricks is what happens when you cut a Mobius strip in the middle. (Look here) (And what happens when you cut it again, and when you cut …
55
votes
Fundamental Examples
Brownian motion has a central role in the theory of stochastic processes
46
votes
Fundamental Examples
The Prisoner's Dilemma in Game Theory.
42
votes
Fundamental Examples
In complex dynamics: The Mandelbrot set
41
votes
Tweetable Mathematics
33 = 8866128975287528³ + (-8778405442862239)³ + (-2736111468807040)³. Andrew Booker! link.
Update 2019-09-05: $(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 = 42$, https://people …
37
votes
Most memorable titles
Very late addition (August '13) J. J. Sylvester, Thoughts on inverse orthogonal matrices, simultaneous sign-successions and tesselated pavements in two or more colors, with applications to Newton rule …
36
votes
Fundamental Examples
Russell's paradox
Showing that Frege's set theory leads to contradiction.
The example can be described as the set of all sets $A$ such that $A \notin A$.
It is related in spirit to Cantor's proof …
34
votes
Resources for mathematics advising.
The chapter on advice to a young mathematician from the Princeton companion to Mathematics by Atiyah, Bollobas, Connes, McDuff and Sarnak are advice for young mathematicians but one can infer from the …
32
votes
What are some examples of colorful language in serious mathematics papers?
This is taken from the seminal paper "Quantum error correction via codes over GF(4)" by A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane.
32
votes
Fundamental Examples
1The Fano plane in finite geometry
http://en.wikipedia.org/wiki/Fano_plane