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Results tagged with big-list
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user 9417
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.
3
votes
Never appeared forthcoming papers
"The Aarhus integral of rational homology 3-spheres IV," by Bar-Natan, Garoufalidis, Rozansky and D. Thurston, never appeared. I think developments in the field overtook the need for the paper, which …
5
votes
What are some examples of ingenious, unexpected constructions?
Kontsevich's construction of a universal rational-valued Vassiliev invariant via the Kontsevich integral. It is a truly ingenious construction; it as an integral over a configuration space of an embed …
1
vote
Which book would you like to see "texified"?
"Rational Homotopy Theory and Differential Forms." by Griffiths and Morgan.
6
votes
Examples of great mathematical writing
Lou Kauffman's book "On Knots" inspired me to become a topologist. It conveys the feel of the way topologists think with copious hand-drawn pictures. It also gets into deep waters without losing a pla …
6
votes
Not especially famous, long-open problems which anyone can understand
I like the Montesinos-Nakanishi 3-move conjecture from knot theory. A 3-move on a link is the replacement of two parallel strands by three half twists. The conjecture is that any link can be turned in …
3
votes
Theorems that are 'obvious' but hard to prove
Inspired by ``the trefoil knot is knotted" answer, how about the fact that Reidemeister moves generate isotopy of PL knots? This is pretty obvious but a full proof requires a lot of machinery. Indeed, …
34
votes
Examples of interesting false proofs
I came across this one in a book of false proofs, the name of which I can't remember. It stuck out because it's not the usual hidden division by $0$ or unestablished base case in an induction.
Theore …
4
votes
Favorite popular math book
Title One Two Three . . . Infinity: Facts and Speculations of Science
Author George Gamow
Short description While not limited to mathematics, this is a great book which presents some subtle mathemat …
3
votes
Mathematicians with both “very abstract” and “very applied” achievements
William Tutte. He is well known for his contributions to graph and matroid theory, including pioneering the enumeration of planar graphs, and introducing the so called Tutte polynomial. He is less wel …
39
votes
What makes four dimensions special?
It's the only dimension in which the smooth Poincare conjecture is still open. It's the only dimension in which $\mathbb R^n$ has a nonstandard smooth structure. (In fact uncountably many of them.)
…
48
votes
Are there examples of non-orientable manifolds in nature?
Some industrial conveyor belts are hooked up like a Möbius strip, so I've heard, in order to wear evenly on "both" sides.
Of course nonorientabilty has got to show up in more fundamental physical wa …