I have changed the appearance of the blog. The main feature of the new appearance that I like is that the comments are with the same size fonts as the posts themselves. This is especially useful for the polymath3 posts. (I will make some tuning to the new appearance once I will learn how to.)
Here we continue the previous post on Summer 2010 events in Reverse chronological order.
Happy birthday Srac
In the first week of August we celebrated Endre Szemeredi’s birthday. This was a very impressive conference. Panni, Endre’s wife, assisted by her four daughters, organized a remarkable exhibition by mathematicians who are also artists. Panni also organized tours and activities for accompanying people which my wife told me were great. A few mathematicians chose to attend the tours rather than the lectures. In Hungary, Endre has a nickname “Srac” which means “kid”, and, to my amazement, people (including young people) really call him Srac.
Szemeredi Kati and Zsuzsa
After-dinner speech. The distinction between surprising and amazing, and the question of do we age when it comes to our emotions and inner soul experiences
Being asked to give the after-dinner speech for Endre in the festive boat dinner ranks second in my life among cases where I was chosen for a job for which so many others were much, much more deserving and qualified. Continue reading
I am starting this post in Jaipur. My three children are watching a movie in our Jaipur hotel room and I watch them while I begin to write this post. Hagai is in the middle of a long-planned three-month trip to India, and when I told my family about the ICM in Hyderabad, my two other children Neta and Lior jumped at the opportunity, and decided to come to India for three weeks, and in the last week give me a taste of India. Hagai started his visit in Leh and experienced the flooding there. By the time we heard about it, already two days after the flooding, the Israeli foreign office’s emergency room had already made contact with the Israelis in Leh, including Hagai. Hagai decided to stay in Leh to help clean houses and (mainly) the local hospital of the huge amounts of mud. He spent almost a month there and took a bus to meet me at Delhi. Neta and Lior were in Hampi, before we all met in Agra.
India is overwhelming and I do not even begin to comprehend her. Perhaps it will be easier to comprehend why so many young Israelis fall in love with India.
In this post (which I split to two parts), I wish to describe some of my Summer 2010 excitements in reverse chronological order.
Before that, here are the slides of my lecture on combinatorial and topological aspects of Helly-type theorems from the Szemeredi birthday conference, and my laudation paper and lecture slides on Dan Spielmen’s work from ICM 2010.
ICM 2010, India
Monday evening was the end of the fourth day in ICM 2010. ICM stands for the International Congress of Mathematicians. This is an event that has taken place once every four years for over a century. This was the second meeting of the Combinatorics session featuring Henry Cohn, Brendan McKay and Benny Sudakov as invited speakers. It was followed by a session of short 15-minute communications in combinatorics. Laci Lovasz, the president of IMU, had a lot on his mind in these four days. Due to his duties he had to miss many important lectures and events, but he nevertheless set aside time to attend this “contributed talks” session and I found it very nice. Continue reading
So I did try mathoverflow a bit and it is a cool site. Over the few days I spent there I gained 593 reputation points, and no less than 9 bronze badges. The first answer I proposed gave me a badge as “teacher”, and the first question I asked gave me a badge as “student”. In fact, if I will only reveil my age I would gain also a badge as “autobiographer”.
Indeed, mathoverflow is ran by an energetic and impressive group of very (very very) young people (more precisely, very very young men). Here is the link to the 35 users with highest reputations.
Update: Well, I got a little addicted and visited quite a bit this nice site. Among other things, I tried to promote my fundamental examples question. Basic examples can give a quick invitation to wide areas of mathematics. (Maybe to most areas, I find it hard to think about a counterexample.) Overall, there are not that many basic examples and I think there will be a consensus about most of them so lists of different mathematicians will not be so different. More examples of important examples are welcome.
In my profile you can find there the six questions that I asked and the 10 answers or so that I offered (to other questions).
Adventures in the
Blogosphere String War
selected and edited by Gil Kalai
Among the highlights: Too good to be true (Ch 17); Dyscalculia and Chomskian linguistics (Ch 19); Baker’s fifteen objections to “The Trouble with Physics” (Ch. 25); Maldacena (Ch. 28); High risks endeavors for the young (Ch 31);How to treat fantastic claims by great people (Ch. 33); Shocking revelations (Ch. 38); How to debate beauty (Ch 41.)
Some little chapters appeared also as posts: Continue reading
I wrote a book. It is a sort of a popular science book and it is also about blogging and debating.
You can download the first part of the book : It is a 94 page pdf file.
Adventures in the
Blogosphere String War
selected and edited by Gil Kalai
Debates portrayed in books, are the worst sort of readings, Jonathan Swift.
In the summer of 2006 two books attacking string theory, a prominent theory in physics, appeared. One by Peter Woit called “Not even wrong” and the other by Lee Smolin called “The trouble with Physics.” A fierce public debate, much of it on weblogs, ensued.
Gina is very curious about science blogs. Can they be useful for learning about, or discussing science? What happens in these blogs and who participates in them? Gina is eager to learn the issues and to form her own opinion about the string theory controversy. She is equipped with some academic background, even in mathematics, and has some familiarity with academic life. Her knowledge of physics is derived mainly from popular accounts. Gina likes to debate and to argue and to be carried by her associations. She is fascinated by questions about rationality and philosophy, and was exposed to various other scientific controversies in the past.
This book uses the blog string theory debate to tell about blogs, science, and mathematics. Meandering over various topics Continue reading
There are new exciting blogs and all sort of nice things on old blogs. In Avzel’s journal you can find a post with the words and a link to the performence of a beautiful Leonard Cohen’s song “everybody knows”; and you can find there as well as on Computational Complexity links to some great songs of Tom Lehrer. Noam Nisan (who encouraged me to start this blog) has now a blog of his own called “Algorithmic game theory” of with interesting posts on the econ-CS interface. One post is about Fourier theoretic proof of Arrow’s theorem and the recent paper by Noam, Ehud Friedgut and me on Quantitative Gibbard Satterthwhaite theorem. (BTW, are you aware of blogs devoted to learning?, or to mathematical programming/optimization?) Dick Lipton has a new blog called “Godel’s lost letter and P=NP,” where he covers in a very very nice style, the major developements that occured in theoretical computer science, (and from time to time outside it,) and the people that were involved in these developements. There is a spirit of light skepticism regarding the common wisdom about some of the central problems in some of the posts. This reminds me that scientific skepticism and how it should be practiced (if at all) is a great topic for discussion. Economist Al Roth has an extremely prolofic blog called “Market design.” Roth have created (with the help of Aaron his son,) very eraly on (in 1995,) a scientifically useful home page. And finally Terry Tao had a beautiful post on sailing into the wind in higher speed than the wind. And post-finally Scott Aaronson, breaks yet again new grounds, and asks four questions for Passover about corn, rice, and wheat.
And Frank Morgan (whom both me and Noga TA’d in Calculus 18.001 18.011 in 1983) has a lovely post on optimal paths in Baseball based on work with Davide Carozza and Stewart Johnson, and Jeff Elly has an econ blog with the good name “cheap talk”. And here is an excellent post on the 15 greatest statisticians by Yosi Levy (in Hebrew).
And Terry Tao illuminatingly rescaled the US budget to match incomes and expenses of a single family.
“polymath” based on internet image search
And here is a link to the current draft of the paper.
Update: March 26, the name of the post originally entitled “Polymath1: Probable Success!” was now updated to “Polymath1: Success!” It is now becoming clear that there are three (perhaps four) new emerging proofs of DHJ. (April 2: See this post by Terry Tao. As this update was also based on briefly talking with Terry, Terry’s new post gives a better description on the state of affairs and relations between the different proofs.)
The proof directly emerged from the project indeed looks conceptually different and simpler than all other proofs, and may indeed lead to the simplest known proof for Szemeredi’s theorem. (But for this we will have to wait for the details.) In addition, there is a new Ergodic proof by Tim Austin, which was partially inspired by and which used (among several other ingredients developed by Austin) some ideas and results discovered in the polymath project. Both the original ergodic proof and Austin’s proof were (at least roughly) “combinatorialized”.
In what sense was it a massive open collaboration? It is true that in the crucial phases of polymath, the phases where two concrete strategies for proofs were considered, the number of pivotal participants was not large. But there was an initial phase were probably more than a hundred mathematicians took part as observers and as commentators. The comments in this early phase played some role in the later developments but what is more important is that this stage have led to the (emerging) selection of the team that developed the proof. Among the hundreds, those who felt they have ideas that can be crucial, or methods that could be helpful, and were smart or lucky to be correct, and had the persistence to follow these ideas and how these ideas can be combined with other ideas, became the pivotal players. The team that played the game was not so large, but the main massive ingredient of the project which accounts for its accessive mathematical power was in the “draft”. The team emerged from a massive number of participants. (So if you believe there were 10 pivotal players out of a hundred, think about the emergence of the team among possible (but, of course, not equally plausible) teams, as a point were polymath had extra power.)
Two related posts: Tim Gowers raised inthis post interesting questions regarding the possibility of projects were the actual number of provers will be massive. Here on my blog we have a post with an “open discussion” on what are the correct bounds for Roth type problems. The emphasis is on “small-talk discussion” and not on actual “hard-nose researching”.
We took the opportunity to spend three days of “Purim” visiting northern Israel. Coming back I saw two new posts on Tim Gowers’s blog entitled “Problem solved probably” and “polymath1 and open collaborative mathematics.” It appears that “polymath1” has led to a new proof for the density version of Hales-Jewett’s theorem for k=3 which was the original central goal! Also it looks like the open collaboration mode (while not being a massive collaboration) was indeed useful.
Perhaps the most important thing is to make sure that a complete proof for the k=3 case is indeed in place (as these famous problems sometimes “fight back,” as Erdos used to say). The outline is described here. If everything is OK as Tim and other participants expect, there are already some discussions or even plans about an extension to the general k case. This seems to be the next major step in the project. There are also other fruits from the various threads of the polymath1 project. Overall, this looks very exciting! The mathematical result is a first-rate achievement, and the mode of cooperation is novel, interesting and appears genuinely useful.
Let me quote what Tim writes about it: “Better still, it looks very much as though the argument here will generalize straightforwardly to give the full density Hales-Jewett theorem. We are actively working on this and I expect it to be done within a week or so. (Work in progress can be found on the polymath1 wiki.) Better even than that, it seems that the resulting proof will be the simplest known proof of Szemerédi’s theorem.” sababa!