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Results tagged with big-list
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user 4558
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.
1
vote
Undergraduate Probability Topics
The Bayer and Diaconis paper, "Trailing the Dovetail Shuffle to its Lair" is a classic and Brad Mann gave a very readable exposition of it.
Many people have heard, "seven shuffles are necessary to mi …
11
votes
What are some examples of colorful language in serious mathematics papers?
According to the book "King of Infinite Space" Coxeter, "tickled his readers with unexpected turns of phrase such as":
... dividing the product of the first
three expressions by the product of
the la …
15
votes
What are some mathematical sculptures?
Adding to the list two of my favorite mathematical sculptors:
George Hart:
http://www.georgehart.com/sculpture/sculpture.html
Bathsheba:
http://www.bathsheba.com/
Finally, there are a lot of nice …
43
votes
Most intricate and most beautiful structures in mathematics
The (stable or unstable) homotopy groups of spheres are certainly considered intricate and beautiful by topologists.
Here is an interesting (obvious) fact about the stable homotopy groups of spheres …
47
votes
Which math paper maximizes the ratio (importance)/(length)?
Kahn and Kalai's, "A counterexample to Borsuk's conjecture" is a 3-page paper which settles a sixty-year-old conjecture with an explicit counterexample in $\mathbb{R}^{1325}$ (and in all sufficiently …
3
votes
Applications of the notion of of Gromov-Hausdorff distance
Facundo Memoli applied Gromov-Hausdorff distance to shape matching in his Ph.D. thesis.
http://math.stanford.edu/~memoli/research.html (Wayback Machine, new website)
33
votes
Open problems in Euclidean geometry?
The Unit Distance Problem asks:
For a set of $n$ points in the plane,
what is the maximal number $g(n)$ of
unit distances realized among the
${n \choose 2}$ pairs?
A properly scaled squar …