Monthly Archives: December 2008

Fundamental Impossibilities

Posted on December 31, 2008 by Gil Kalai

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 →

Posted in Philosophy, What is Mathematics | Tagged | 7 Comments

Debates

Posted on December 30, 2008 by Gil Kalai

  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 →

Posted in Controversies and debates, Rationality | Tagged | 3 Comments

Controversies In and Near Science

Posted on December 28, 2008 by Gil Kalai

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 →

Posted in Controversies and debates | Tagged , , , , , , , , | 5 Comments

Lior, Aryeh, and Michael

Posted on December 26, 2008 by Gil Kalai

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 (  1936-2008  )  Lior Tzafriri worked in functional analysis.

Posted in Obituary | Tagged , , | 10 Comments

Lovasz’s Two Families Theorem

Posted on December 25, 2008 by Gil Kalai

Laci and Kati This is the first of a few posts which are spin-offs 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 , , , | 7 Comments

Seven Problems Around Tverberg’s Theorem

Posted on December 23, 2008 by Gil Kalai

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 →

Posted in Combinatorics, Convexity, Open problems | Tagged , , | 23 Comments

Michal Linial: Vive La Technology

Posted on December 11, 2008 by Gil Kalai

  Nebi Samuel   It was a long night after crossing the Atlantic. I got to the airport and indeed the big signs of ‘Welcome’ and “TAAM SHEL BAIT” (taste of home) had a special appeal. It was 3:30 in the … Continue reading →

Posted in Guest blogger, Taxi-and-other-stories | Tagged , , , | 1 Comment

1:0 to Italy: Michal Linial

Posted on December 10, 2008 by Gil Kalai

Coming back from Hinxton, the most exciting genome center in the world and the most boring place after 5pm… At 5:30, a shuttle bus takes all the ‘workers’ to the big city – to Cambridge. The shuttle bus dropped us … Continue reading →

Posted in Guest blogger, Sport, Taxi-and-other-stories | Tagged , , , , , | 2 Comments

Test Your Intuition (2)

Posted on December 9, 2008 by Gil Kalai

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 →

Posted in Convexity, Test your intuition | Tagged | 6 Comments

Test Your Intuition (1)

Posted on December 7, 2008 by Gil Kalai

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 | 12 Comments