MathOverflow is a remarkable recent platform for research level questions and answers in mathematics. Joe O’Rourke have asked over MO wonderful questions. (Here is a link to the questions) Many of those questions can be the starting point of a research project usually in discrete and computational geometry and sometimes in other areas. Many of the questions remained open, quite a few have led to definite quick solutions, and for many others substantial answers were offered. Usually Joe’s questions (and also his MO answers) contain beautiful and illuminating pictures. Amog the highlights: Joe’s question on Billiard knots; a poetic question about “light reflecting off christmantree balls“; rolling a random walk on a sphere – with a definite answer by S. Carnahan; Pach animals of high genus; Fair irregular dice (with a nice answer by Bill Thurston); Parabolic envalope of fireworks; Coiling rope in a box; A convex polyhedral analog of the pentagram map ; Randompolycubeshapes ; Which convex bodies roll along closed geodesics and many more. The 100th question is The rain hull and the rain ridge.
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Recent Posts
 Hoi Nguyen and Melanie Wood: Remarkable Formulas for the Probability that Projections of Lattices are Surjective
 Petra! Jordan!
 The largest clique in the Paley Graph: unexpected significant progress and surprising connections.
 Thinking about the people of Wuhan and China
 Ringel Conjecture, Solved! Congratulations to Richard Montgomery, Alexey Pokrovskiy, and Benny Sudakov
 Test your intuition 43: Distribution According to Areas in Top Departments.
 Two talks at HUJI: on the “infamous lower tail” and TOMORROW on recent advances in combinatorics
 Amazing: Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen proved that MIP* = RE and thus disproved Connes 1976 Embedding Conjecture, and provided a negative answer to Tsirelson’s problem.
 Do Not Miss: Abel in Jerusalem, Sunday, January 12, 2020
Top Posts & Pages
 Hoi Nguyen and Melanie Wood: Remarkable Formulas for the Probability that Projections of Lattices are Surjective
 Aubrey de Grey: The chromatic number of the plane is at least 5
 Konstantin Tikhomirov: The Probability that a Bernoulli Matrix is Singular
 Elchanan Mossel's Amazing Dice Paradox (your answers to TYI 30)
 Ringel Conjecture, Solved! Congratulations to Richard Montgomery, Alexey Pokrovskiy, and Benny Sudakov
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 Gil's Collegial Quantum Supremacy Skepticism FAQ
 Coloring Problems for Arrangements of Circles (and Pseudocircles)
 Amazing! Keith Frankston, Jeff Kahn, Bhargav Narayanan, Jinyoung Park: Thresholds versus fractional expectationthresholds
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Joe has become quite renowned for his figures :). He also has two new books out (How to Fold It, Discrete and Computational Geometry) that are filled with many such great images, which are produced using Mathematica I believe.
Wow, I am truly honored, Gil (and thanks, Andrew)! Gil, I owe you one. Request refereeing, whatever … 🙂
GK: my pleasure Joe, keep the wonderful question comming
Wonderful post!
Would it be at all possible to tag this post “planetMO” so that it can be found via mathblogging.org/planetmo ?
Sorry about the typo, there’s a ” missing — here’s a working link planetMO
On September 2018 Joe asked his 600th MO question!