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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 Polymath 10 post 6: The ErdosRado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
 Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
 Polymath 10 Emergency Post 5: The ErdosSzemeredi Sunflower Conjecture is Now Proven.
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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