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. These were four intense and exciting days.
Tim Gowers blogged extensively from the Congress. His posts give a very nice picture of the atmosphere, the mathematics, and his state of mind. My overall impression was that the lectures were good and some were excellent. They posed an impossible task for the lecturers. An invited lecture is usually a condensed graduate course on a cutting-edge topic ending with recent deep and difficult advances. Speakers put much thought into their presentations and did a good job, but this is nevertheless an impossible task. It is an even more impossible task to listen to five or more condensed graduate courses every day. So overall the mathematical experience was fruitful, while a bit frustrating.
I like the snapshot meetings of old and new friends (and also virtual friends – people I met in committees that were run by emails, or in blogs, or at mathoverflow.) Here I find myself with Scott Sheffield and Oliver Riordan in a line at the dinner banquet; Scott computes the critical place on the line where the progress changes sign from negative to positive, and realizes that we are behind this point; here I meet for 20 seconds some long-time friends from Barcelona, and here is a snapshot meeting with an old friend from Poland where I learn that he just returned to Poland after many years in Columbus, Ohio. Of course, I’d like to spend an hour or a day with many of the people I meet for half a minute, but still I find these snapshot encounters enjoyable rather than frustrating.
Congratulations Cedric, Chew, Elon, Stas, Dan, Eve and Louis!
Elon Lindenstrauss’ winning the Fields medal was especially exciting for me and for the entire Israeli mathematical and academic community. I have known Elon’s parents Joram and Naomi Lindenstrauss since I was a young student, and I first met Elon when he was a high school student. Elon has fantastic results: His proof of the unique ergodicity conjecture for arithmetic groups, his proof with Einsiedler (whom I also briefly saw at the ICM) and Katok, of a weak form of Littlewood’s conjecture, and many others. I am very proud of and happy for Elon. This is great news (of the right type) for Israel.
Usually, I like to be surprised about the identity of the winner and to brag about not knowing it in advance. But this time I was not taken by surprise by Dan Spielman’s winning the Nevanlinna price since I was asked a few months earlier (under complete secrecy) to give the laudation. I was familiar with Dan’s earlier work on linear programming, and preparing the paper and presentation describing his results was a nice opportunity to learn about his other work and to dream another person’s dreams. So I really enjoyed it. Giving a lecture in front of more than three thousand people was also quite an experience. (Very exciting, a great honor…but not that much different from giving a talk to a smaller audience.
Of the others laureates, I knew personally only Stas Smirnov, and I was very happy to see him getting the medal. I remembered his shocking and beautiful (and rather short) proof for the conformal invariance conjecture of planar percolation on the hexagonal lattices, and at the school we organized he very recently presented another surprising success regarding self-avoiding random walks. And, in between the deep and difficult works on the Ising model.
And I felt happy for the other laureates whom I knew only by name. Aside from the excellent laudations for their works along with informal descriptions that you can find on this page, you can also look at Terry Tao’s blog and at Gowers’ blog. The ICM lectures of the prize winners can be found on this page and they are very good
When we landed in Mumbai after a flight from Jaipur’s new international airport we ran into many people who came from Hyderabad. We met Laci and Kati, who were, together with Cecilia Culcsar, flying back to Budapest. Laci seemed relieved that the ICM task was over. And Kati was amused by an article that claimed to find four mistakes in Cantor’s proof that there are more real numbers than rational numbers. I tried to say to Laci “kol hakavod” which is a Hebrew saying which roughly says “congratulations for a job excellently done” or something like that, but my translation was quite awkward. Anyway, Laci Lovasz, Martin Grotschel (the ICM secretary), and Madabusi Ragunathan (who was the head of the local organizing committee and later the Congress’ president), along with many more, deserve much thanks for the huge work.
Then at the El Al counter we met quite a few Israelis heading home. Elon was tired and was eager to go home. Of all the recipients I think that Elon felt the least comfortable with all the media attention and wanted to see it over.
The distinction between threats and dangers
On the flight I slept and dreamed about traveling in India with my children. While going to sleep (in the dream) I saw my daughter Neta putting her head on a tiger’s nose. “Don’t worry, it’s India”, she said when I, terrified, asked her what she was doing, and indeed the tiger did not mind and just moved his head to the other side. (Disclaimer: I do not recommend approaching tigers or jumping over sleeping dogs anywhere in the world including India.) So I woke up equipped with an important insight about India. One does not feel threatened there. There are risks and dangers but not threats.
Later I tried my newly discovered distinction between threats and dangers on a philosopher friend: “I think you once told me that distinctions are important in philosophy,” I started. “Yes indeed”, came the reply, “Distinctions are the most important thing; we do not have experiments and laboratories, distinctions are our working tool.” I mentioned my distinction between threats and dangers, but my philosopher friend, while complimenting me for thinking philosophically, was not convinced, neither regarding this abstract distinction nor about the insight about India. Later, I tried to discuss this distinction with the shuttle driver from JFK to New Haven, and he was not convinced either.
NP=?P, the neutral group element and electrons
In the week between India and Hungary we were amazed to hear about a paper claiming a proof that NP is not P. This had led to a whole week of excitement and a little controversy. (I still feel bad though about criticizing Scott Aaronson and John Sidles during the excitement.)
I was even mentioned as a member of a group of people determined to check the proof! This is probably the closest I will ever get to being a neutral element in a group. This reminds me of an occasion when I and my friend Alex Lubotzky came as close as we ever will to being electrons: Here is a trivia question with $25 prize for the first correct posted answer. (The prize will be delivered to the answerer in our next meeting; other conditions may apply.) On which occasion were Alex Lubotzky and I (more or less) electrons?
You can read a nice summary of the P=?NP event in an article by Julie Rehmeyer .