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Monthly Archives: December 2008
Fundamental Impossibilities
An Understanding of our fundamental limitations is among the most important contributions of science and of mathematics. There are quite a few cases where things that seemed possible and had been pursued for centuries in fact turned out to be … Continue reading
Debates
Debates are fascinating human activities that are a mixture of logic, strategy, and show. Not everybody shares this fascination. The German author Emil Ludwig considered debates to be the death of conversation. Jonathan Swift regarded debates as the worst … Continue reading
Controversies In and Near Science
Controversies and debates in and around science – between researchers within the same discipline, between competing theories, between competing fields, and between accepted scientific viewpoints and viewpoints rooted outside science – are common. Is there global warming and is it … Continue reading
Lior, Aryeh, and Michael
Three dear friends, colleagues, and teachers Lior Tzafriri, Aryeh Dvoretzky and Michael Maschler passed away last year. I want to tell you a little about their mathematics. Lior Tzafriri ( 19362008 ) Lior Tzafriri worked in functional analysis.
Lovasz’s Two Families Theorem
Laci and Kati This is the first of a few posts which are spinoffs of the extremal combinatorics series, especially of part III. Here we talk about Lovasz’s geometric two families theorem. 1. Lovasz’s two families theorem Here … Continue reading
Posted in Combinatorics, Convexity, Open problems
Tagged exterior algebras, Extremal combinatorics, shellability
5 Comments
Seven Problems Around Tverberg’s Theorem
Imre Barany, Rade Zivaljevic, Helge Tverberg, and Sinisa Vrecica Recall the beautiful theorem of Tverberg: (We devoted two posts (I, II) to its background and proof.) Tverberg Theorem (1965): Let be points in , . Then there is a partition of … Continue reading
Test Your Intuition (2)
Question: Let be the cube in centered at the origin and having dimensional volume equal to one. What is the maximum dimensional volume of when is a hyperplane? Can you guess the behavior of when ? Can you guess the plane which … Continue reading
Test Your Intuition (1)
Question: Suppose that we sequentially place balls into boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability balls in it. Suppose instead that … Continue reading
Posted in Computer Science and Optimization, Probability, Test your intuition
Tagged Test
12 Comments