I set off from Haifa just as the first rain since the start of the summer started to fall. On arrival in Montreal the shorts and T-shirt I had set off in became insufficient to the demands of the local climate, so I had to switch into warmer clothes and revive myself with Tim Horton’s hot chocolate.
Two years had passed since I was last in Montreal to defend my thesis — the morning after the 2016 election. It was interesting to see what had changed. Cannabis was about to be legalized. The building work on McGill/Sherbrooke had been completed. The math department was full of unfamiliar faces. Many restaurants had closed (no more SmartBurger). Murals commemorating the late Leonard Cohen had appeared across the city. Poutine was pretty much as I remember it, though.
Montreal is now also home to the world’s largest permanent barbie exhibit. Which is completely free to access.
Canadian Thanksgiving took us all by surprise, so I gave my McGill seminar talk earlier than expected. It was the first outing of the talk I’m touring while I’m out here in North America, presenting my new proof (and generalization) of Leighton’s graph covering theorem. The seminar went well, but I feel like I’m going to be experimenting a little to find the best way to explicate the coset summation argument I use. Piotr appreciated the fact that I was able to give the entire proof within the hour.
I was also able to do quite a bit of math. A fair chunk of Thanksgiving was spent discussing math with Dani and scrawling our ideas all over my notebook.
I also took pictures of new murals I spotted around this city:
In December last year, the Notices of the AMS ran a collection of reminiscences in memory of Marcel Burger (1927-2016), the late French differential geometer. He was also a former director of the Institut des Haute Etudes Scientific and, according to the Wikipedia, played a major role in getting Gromov positions in Paris and at the IHES in the 80s. Gromov contributed to the article, listing Berger’s mathematical achievements, before sharing a more personal anecdote:
Within my own field Gromov has had a profound influence. His essay Hyperbolic Groups led to the term “combinatorial group theory” being more or less abandoned and replaced with “geometric group theory”. As a graduate student I found the monograph frequently cited as the origin for an astounding range of ideas. At some point I had trouble finding a copy of the paper online and for a brief moment wondered if the paper itself were just an urban myth or elaborate hoax.
Gromov’s foray into group theory is just one episode in a long career. His first major breakthrough was in partial differential equations; the “h-principal” which, according to Larry Guth, was analogous to observing that you don’t need to give an explicit description of how to put a wool sweater into a box in order to know that you can actually put it into the box. It is actually a little hard, at least for myself, to get a full grasp on Gromov’s other contributions as they span unfamiliar fields of mathematics, but I recommend this nice What is… article, written by the late Marcel Berger, describing Gromov’s contribution to the understanding of isosystolic inequalities.
There is the perception about great mathematicians that, while they are no doubt very clever, somehow they have lost a little of the common sense that the rest of us possess. I’m naturally inclined to discount such thinking; I am far happier believing that we are all fool enough to take absence of common sense, on certain occasions. However, it is hard to dismiss the idea entirely given the following admission by Gromov, in his personal autobiographical recollections he wrote on receipt of the Abel prize in 2009:
The passage speaks for itself, but I wish to emphasize that Gromov’s discovery of the correct pronunciation of French verb endings came after ten years of living in Paris. You don’t have to have extensive experience learning foreign languages to appreciate how remarkable an oversight this is. It certainly puts his remarks in other interviews about dedicating one’s life to mathematical pursuits in a rather strong light.
If you read the entire autobiographical essay you will find it rather short on biography. The best biographical details I have found came from this La Monde article written on his being awarded the Abel prize. Even then the details seems to be coming second hand. The most interesting parts concern his leaving the Soviet Union:
I wanted to leave the Soviet Union from the age of 14. […] I could not stand the country. The political pressure there was very unpleasant, and it did not come only from the top. […] The professors had to teach in such a way as to show respect for the regime. We felt the pressure of always having to express our submission to the system. One could not do that without deforming one’s personality and each mathematician that I knew ended up, at a certain age, developing a neurosis accompanied by severe disorders. In my opinion, they had become sick. I did not want to reach that point.
As the article goes on to explain, Gromov decided his best chance to escape was to hide his mathematical talent. He quit math, quit his university, and burned all his academic bridges. He stopped producing mathematics. Or at least writing it. He joined some meteorological institute and did research on paper pulp. Eventually, he was granted permission to emigrate to Israel, but on landing in Rome in 1974 he set off for the States instead, where Jim Simons secured him a position at Stony Brook.
(As a side note, this is Jim Simons of Renaissance Technology and Simons foundations fame. Simons, aside from his mathematical contributions, is probably one of the most important mathematicians alive in terms of funding, supporting, and propagandizing for mathematics. He is considered influential enough for the New Yorker to profile. Alongside Gromov, he is one of the names that every mathematicians should know.)
Yom Kippur, or the Day of Atonement, is the tenth day in the Jewish new year. It precedes the start of the new academic year here in Israel. Due to all the High Holidays — Rosh Hashanah, Yom Kippur, and Sukkot — new arrivals at the Technion, eager to start postdoctoral fellowships, find themselves sitting things out for a month until university life commences. For those of us already here, this is usually time spent getting job application material together. So it isn’t the most exciting month of the year for us.
There is a silver lining: witnessing first hand the one day (from sunset to sunset) that the streets of Israel are empty of cars. Because Yom Kippur is more than just a legal holiday. Everything is shut down: TV, radio, airports, shops, and public transport. I’ve even heard a third hand story of someone with a minor injury being told to wait until the next day before going in to hospital.
I was in Israel two years ago for Yom Kippur. I went out for an evening jog and, to my pleasant surprise, found the streets full of children tearing downhill on their push bikes being chased by their parents. While observant Israeli’s fast, a lot of secular Israelis — kids in particular — take the opportunity to do some serious cycling. You need to appreciate how unfriendly Israeli roads are to cyclists every other day of the year to understand how magical a time this must be.
This year we went out for a walk around the Carmel center just after sunset to enjoy the empty streets. We spotted this car sitting in the middle of the street, apparently abandoned as the final seconds of the day had passed by.
You can find plenty of videos on youtube of people out cycling on the empty streets, but here is just one of them:
As you can see from the video, it is inaccurate to say that there are absolutely no cars on the road. In this video, at least, the reason is that their route passes through Daliyat al-Karmel , a Druze town, where few people observe the holiday.
Even within Haifa, however, we were still able to spot a few cars on the streets. One in particular had a gang of skateboarders clinging to it. I was just quick enough to take the following picture:
This year I wanted to see the highway deserted, so in the afternoon we walked down from the mountain to the beach, crossing the main road along the coast on the way.
One way or another, this was my last Yom Kippur in Israel. I think it might be the one facet of Israeli life — a day when even the cars stop — that I will miss the most.