New York

I've been visiting two former housemates in New York for the last week and the experiences couldn't have been more different. I'm staying with D in Manhattan and he now works as a banker and has the stereotypical young New York banker life. A great apartment in the heart of Manhattan, a few blocks from Central Park and tons of things to do within minutes of his house. Goes to work at 630 in the morning and stays there till 8 or 9 pm. His apartment is pretty bare with an empty fridge but a great TV and stereo system. In his absence, I've made good use of living close to Central Park by going running there and also watching TV in surround sound. The weekend was quite crazy as I ended up going out with his banker friends to a bunch of bars and clubs in the village. All of them have a work hard, party harder lifestyle and I was completely groggy the next day. They were all back at work the same day though. D has dragged me to a lot of places so far - a baseball game, a golf driving range, a comedy club and lots of bars. It's been a lot of fun but a bit draining.



For the last 3 days, I've been in Ithaca in upstate New York staying with another former housemate, C. She's now married to E and they're both postdocs in Cornell and have a life on the other end of the spectrum. A huge apartment (where I had my own room and bathroom) within 10 minutes of the University, relaxed "work" hours and a kitchen better stocked than almost any kitchen I've seen. Cornell has possibly the prettiest campus of any school I've ever been to, with gorges and waterfalls in the middle of the university. Walking around Cornell was nice with all the hills, streams and trails. Ithaca is a really small town though and in 3 days I think I saw all of Ithaca and met half the people. The cliches of small-town laidback lifestyle are so true out here and for people from a quiet/smalltown background and an affinity for the outdoors it's an ideal place. The walk back from the campus to their apt is along a gorge and past a waterfall. Can't imagine a nicer walk back home everyday.

Perelman

I've been reading a lot about Perelman recently and felt prompted to write something about him. In case you're not aware, he was recently awarded the Fields medal which he declined. The Fields medal is the equivalent of the Nobel prize for mathematics and is awarded once in 4 years and to mathematicians under the age of 40. It is the most prestigious award in all of mathematics and because of the strict guidelines an incredibly hard award to win. He's also likely to win the Clay millenium award of a million dollars for solving one of the millenium problems - which he'll probably decline as well.

He proved the Poincare conjecture about 3 years ago and posted his papers on the internet. After people became aware of his results he was invited to lecture at various universitites in the US. I was a student in Boston at the time and went to MIT to listen to his lectures. Having studied in Boston for 5 years encountering math geniuses, freaks and prodigies was not out of the ordinary but this man was something else.

I reached MIT a bit late and sneaked in through the back door with a couple of friends. Very rarely are mathematics lectures packed to the point where people fight for standing room - this was one of those occasions. Perelman was standing in front of 5 blackboards, with every leading geometry/topology expert in the audience waiting to find a mistake in his lecture/proof and expose him. For any normal person presenting such a high profile proof in front of an audience like this would have been daunting. Not for him though.

He was dressed awkwardly. I can imagine a professor telling him to dress slightly decently as it was such a big occasion. He wore a jacket and pair of pants but underneath was a dirty zip-up jersey and a pair of old, beatup sneakers. The look on his face was one of a crazy man - eyes staring out into infinity, long fingernails and unkempt hair. If he'd stood in Harvard Square with a paper cup asking for change he would have looked like any other homeless guy hanging around. He kept staring away from the audience almost as if he was in a trance even while lecturing.

His lecture started with him writing a simple equation of about 6-7 symbols (The Ricci flow equation). That was it for the next 45 minutes. He held a wireless mike close to his lips and started talking math. Not a single slide was used, no notes and no more equations on the board. I understood almost nothing of what was going on but I could see the bigshot mathematicians leaning forward and their phd students scribbling away. Since the mike was close to his lips, one could hear him breathing heavily and he kept making a weird noise from his throat. I managed to imitate it at the back and forced a lot of other clueless people at the back into fits of laughter.

After 45 minutes of talking he proceeded to write a long equation with at least 20 different indices (I tried counting them as that was the only thing I could do to keep busy) which stretched across 3 blackboards. He paused, looked at it again and then changed a couple of symbols and then looked back and said something to the effect - I think that's it. The whole audience burst out into spontaneous applause but he seemed unruffled. He went on to give 3 lectures almost flawlessly and everyone believed he'd proved what he claimed.

He has a reputation of being a bit crazy. He loves to walk and once on his way to a conference met another participant at the airport. The other guy asked him how he was going and Grisha replied he was going to walk. The other guy walked along with him and 8 hours later, they reached the conference venue! He's retired from mathematics now and lives with his mother off the money he saved from his visiting positions in the US about ten years ago.

It's a bit sad to see how a lot of other mathematicians have tried to plagiarise and build on his work for the sake of tenure, prestige or money. But it's reassuring to know that among the math community it's accepted that he's the one who proved it and it's understandable why he's refused to accept an award in such circumstances. The Chinese mathematicians who claim to have proved it (using his ideas) should take a cue from him. He cared only about proving it to his own satisfaction and that was it. The rest can fight for all they want but he's going to sit happily in St Petersburg knowing he proved one of the hardest problems in all of mathematics - even Terrance Tao (one of the other Fields medalists) claims Perelman's work was easily the most important mathematical breakthrough in the last 10 years.

Breakdown

I had a fairly eventful drive down from Berkeley to LA. On the way up from LA, the car had been wobbling a little bit and I knew it was because of the alignment and old tires. Both my brother and I had been lazy about getting it fixed and kept telling the other one to do it and then finally didn't get around to it. I had just finished some stuff in Berkeley I was a bit tense about and also avoided a parking ticket by a few minutes. Hit a lot of traffic on the way out and so when I finally hit the highway to LA I turned up the radio, the AC was humming away and I felt relaxed. LA was about 4 hours away if I drove fast enough and there wasn't much traffic on the road. Suddenly, the car started wobbling even more and I heard a loud bang and the car almost veered out of control. Thankfully, there was nothing behind me and I managed to pull the car over onto the shoulder. It looked pretty bad. One of the front tires was completely gone and had almost come off.



I had no cellphone and was trying to figure out what to do. Looked around and in the distance saw this. Thankfully, till a few years ago there weren't too many cellphones around and in case of emergencies, things like this existed.



Picked up the phone and got through to an operator who first put me through to my brother in LA. His AAA insurance wouldn't work so he suggested I should get it towed to the closest mechanic and get the tires changed. After more than an hour of waiting a tow truck finally showed up. I didn't want to wait inside the car as it was pretty close to the cars and trucks driving by and each time a truck drove by the whole car would shake. Ended up sitting on the side on the grass in the harsh sunlight staring out across Fresno County. The tow truck guy came and said all the mechanics were closed (it was past 7pm) and I would have to wait till the morning to get it fixed. I had a flight to New York the next day and driving the same day would have made it very tight. Also, the idea of spending the night in a cheap motel in the area wasn't too exciting. He put on the spare tire and since it was a replacement I wasn't sure if it would last all the way to LA. Asked him and he said if I drove around 50 throughout it would probably last. Decided it was worth going ahead than sit around and do nothing till the morning.

Left around 730pm and drove at 50-55 throughout. The car was going fine so I relaxed and put on the AC and turned up the radio. The next 5 hours were excrutiatingly boring and driving so slowly meant I didn't overtake a single car on the way. Trucks, buses and even motorcycles zipped past me and I plodded along. The last 2 hours were a bit tense as it started to wobble again and with trucks all around me (I had to drive in the slow lane) I had to drive on red alert. Since I was driving uphill it seemed to be under quite a bit of strain. Turned off the AC and radio and every sound, bump and wobble made me more tense. If the car went out of control in this situtation it wouldn't be good with those gigantic trucks all around me. Finally managed to reach home at 2 am. It took me almost 10 hours from the time I left Berkeley.

Anyway, I'm in New York right now, sitting comfortably in Deniz's apartment enjoying his fancy home theatre system. Felt completely disoriented this morning so will just spend the day lying around here.

Point Reyes

Just spent the last two days at Point Reyes park. It's about an hour north of San Francisco and since I had a car and a couple of days to kill (I'm back in the bay area) I decided to head out there. I was carrying my tent and sleeping bag so that I could camp out there for one night. Since it was a sunday afternoon, it wasn't too busy and the ranger at the visitor centre told me I could camp almost anywhere. Parked my car, packed my stuff into my smaller backpack and headed out with a map following a trail and encountered this pretty soon.



Walked on and found the first campsite (the one I had a permit for) after a decent 2-3 hour walk. Decided it was a bit boring and hiked up another trail towards the beach. It was a pleasant walk and since it was overcast I didn't sweat much either. After another hour or so of walking came up to the edge of some cliffs over the water and found another campsite and decided this was it - even though I didn't have a permit for that site. It was right next to the ocean and apart from one other tent it seemed very quiet and not busy at all. Pitched my tent with a great view of the ocean and walked down to the beach.





Crashed around 9 as it was pretty dark and went off to sleep with the sound of the ocean waves crashing furiously against the rocky cliffs. Woke up early to catch the sunrise. It was too overcast to see anything so I went back to sleep and then woke up hearing noises next to my tent. Poked my head out and saw my old friend.



He didn't seem to bothered by my presence but after I came back from my morning routine he was gone. Walked up along the coastal route and since it was a monday morning it was absolutely empty. Found a huge rock in the middle and had lunch consisting of two energy bars and a bottle of water. After another 2-3 hours of walking I reached my car and then drove out towards the lighthouse on the southern side of the park. It's not in service anymore but is very pretty especially as it juts out into the ocean.



It was almost 4 so I decided to head back to Berkeley. On the way back I missed the Bay bridge towards Berkeley and ended up on the highway towards the Golden Gate bridge. Driving over the Golden Gate bridge was a nice experience with the huge red columns and the SF skyline on the left. At the toll booth, I asked the attendant about getting towards Berkeley and she gave me some directions. Since I'd spent 3 days in San Francisco and walked all over I was familiar with the city so I had no problem following her directions though I hit some really bad traffic and was also running out of gas as I didn't think I'd need to refuel before reaching Berkeley. The freeway was bumper to bumper traffic and I also didn't have a cellphone so I had to make some very bold moves across three lanes to take the right exit for Berkeley. Am back in A & L's apt and ready to pass out. Heading back to LA tomorrow and then flying out to New York the next day.

LALA land

This is my umpteenth trip to LA and the first time I've felt independent enough to drive around and do stuff on my own. The last time I was here I drove quite a bit but I wasn't too familiar with the streets or comfortable enough to drive around. To take a break from sitting at home most of the day struggling to get some work done I managed to go down to Venice beach a few times to go for a run. Around 630 in the evening, the sun isn't too strong and the breeze is invigorating. Running along the beach front, watching the sun set, seeing beach volleyball games and listening to the drummers in the distance is great fun. What makes it even more worthwhile is all the amazingly beautiful people with their perfectly tanned and athletic figures. Sadly, with my receding hairline and beer belly I don't quite fit in with the super athletic bikers and runners. It's even worse if one goes to the some of the cafes or bars in the area but a great place to people watch.

Also went for a free jazz concert at the Hammer art museum. The atmosphere and ambience was great but the music was a bit too much for an untrained or tone deaf person like me. Sounded more like the soundtrack of a bad horror film with all the screechy sounds.

LA

Reached LA yesterday after a very boring drive. There are 2 ways to drive from San Francisco to LA - either the Pacific coast highway which is a beautiful, scenic drive along the Pacific but about 12 hrs long or the Interstate 5 which is a flat, boring highway like any other interstate in the country but takes about 6 hours. I've been up and down from LA to SF 2-3 times and each time it's been the flat, fast route. Unfortunately, even this time it was the flat boring route and we covered it in less than 6 hours. The car didn't have any airconditioning and within 20 minutes of heading out of Berkeley, it was quite an energy sapping drive because of the heat. I got a ride from one of the conference participants who was driving down to Caltech and it was hard to talk about anything except number theory and math rumours and gossip.

Since Pasadena and LA (where my brother lives) aren't too close it seemed like a nice idea to get dropped off at the Pasadena metro station and ask my brother to pick me up from the station closest to his house. In hindsight, it was a stupid idea. I've taken the LA-Pasadena metro once and had forgotten how long it can take. The LA metro is possibly the most underused, slow and forgotten subway system in the world. In a city where distances are huge (a 20 min drive = close by) the metro is quite useless. At the Pasadena station there were 4 other people waiting with me - a slightly scared looking elderly couple and 2 black kids talking loudly. With my huge backpack it was hard to fit on the only remaining space on the bench so I just kept standing. It took almost 20 mins for the next train to arrive and I couldn't see a single white person on the train. The crowd seemed like a mix of fairly down-and-out tired looking people and a few young kids talking loudly. Halfway through, a completely drunk, white guy walked in with an 80s style mullet and a bottle of vodka in one hand. He sat right opposite me and kept dozing off and waking up, shouting "nigger" and "bitch" to himself. The stench of cheap vodka almost filled the whole coach. Finally reached Union station after about 30 mins and then had to wait another 20 mins for the next line which I had to take.

Not having a cellphone meant I couldn't call up my brother and tell him to not be at the station for another 20 mins. By the time I reached the station, he'd been waiting for almost an hour and finding parking on a Saturday night near Koreatown wasn't easy. Keeping busy for an hour after parking couldn't have been too much fun with no cafes or bookshops closeby. Reached home around 1030 at night and realised it would have been easier and faster for him to drive to Pasadena and pick me up. Anyway, after more than 2 weeks of shared accomodation and dorm-type food, having homecooked food and my own room and bathroom feels great.

Compute, compute, compute

The workshop gets over tomorrow and then a day later I'm going down to LA to spend about a week with my brother and his wife. It's been an interesting workshop. Of all the conference/workshops that I've gone for this was easily the most useful and productive one. What was different was the style and pace of the workshop. Most math conferences consist of a bunch of lectures, a few question-answer sessions and informal discussions with other mathematicians. Some of the discussions can lead to future work but it's mostly about networking and letting other people know about your work or existence.

This one was a very intense workshop with lectures in the morning on the computational aspects of number theory followed by coding sessions through the day. Different problems had been posed before the workshop and people worked in groups on the problem they were interested in. It was my first experience (since a couple of farcical undergraduate projects) of working in a group and trying to make presentations of everything that had been done in a short period of time. Over the last 10 years, as computers have become faster, a number of programs have been written which make computations of fairly sophisticated and abstract concepts much easier. The main purpose of this workshop is to integrate a lot of the existing programs into a free, open source language called SAGE. This will hopefully become the main resource for programming and building databases of examples and computations. As it's free and open source, changes and developments can be made by anyone using it. It's an ambitious project and it looks like it's gathering a lot of momentum.

For the past few years, I've worked in a very abstract and theoretical aspect of math (number theory - though it has nothing to do with numbers) and become used to working alone using simply pen and paper or a blackboard. Occasionally, about once a week or two, I used to meet my advisor for less than an hour to ask questions or show him what I'd done but that was about it. It takes months or close to a year to work out a reasonably advanced problem so one gets used to plodding away for weeks with nothing to show. There are no experiments to run, events to understand, societies or people to study or laws of nature to follow. Then, there's suddenly a flash of insight and a few lines of abstract nonsense can explain something very clearly. Sometimes subtle mistakes can be passed over since only a few people actually cared about the problem. What is daunting is coming across other mathematicians who are far more comfortable with the concepts one struggles with, and who seem to say things which can seem incredibly vague. When things make sense, it's a very enlightening moment.

Working on a computer with a group was completely different. There are instant results popping out all the time. This leads to a lot of quick thrills, high fiving and instant elation. Also, a lot of frustration, when there are errors or bugs in a program. Four of us sat around a computer and kept bouncing ideas off each other and writing down code. Since it was my first experience at programming there were more bugs and errors throughout but getting a program to work is pretty satisfying. A lot of the programming skills and structures that I saw and learnt are definitely useful. Writing a code to compute a series of examples of various cases actually helped to understand a lot of things compared to reading a paper or a book on the same topic. Especially as a slight error or bug is evident immediately. It also involves a completely different way of thinking compared to what I've done in the last few years and it's been an enjoyable experience.

Though the larger question did loom - was it really so useful and important? The main idea of the problem was to compute some very specific examples, so specific that it's hard to come up with a conjecture or construct a general theory around them. What surprised me was the large number of people who seem to do just this - compute, compute and compute. Words like interesting, cool and exciting were used a lot. A few conjectures kept floating around and since it's a high-speed game people tend to claim things too soon. I've always had a fairly low opinion of my own mathematical and research skills and in an objective discipline like mathematics it's easy to see how good/useful someone's paper is. My thesis was pretty average and at most reasonable. Seeing the way people were getting excited over small computations was puzzling. The prospect of publishing a paper out of all this is what seems to excite everyone, not the prospect of coming up with a useful idea. I'm pretty sure it's the same in other disciplines as well.

I have a long rant on how 80-90% of academic/research papers are complete nonsense (including my own thesis). Forget about them being useful to our daily life, they're not even useful in the narrow academic discipline they fall under. But that's something I'll touch on later when I have a lot more time to waste.

math and baseball

Went out with the geeks for a group outing yesterday. After a week of hanging out in the same institute and dorm, 4 of us discovered we were all big baseball fans and decided to go and watch a game in San Francisco on Saturday. Asked around if others were interested and about 10 other people came along. They weren't interested in the baseball but more keen on sightseeing in San Francisco.

Organizing a trip with almost 15 people wasn't fun especially as a lot of them had no clue of how to go into San Francisco and what to do. One of the baseball fans decided to be the tour guide and he took everyone on a walking tour of San Francisco's touristy sights. Cameras were whipped out all the time and it was a bit awkward travelling in a big group, doing headcounts, asking what to do next, etc. Since a bunch of us were going to the baseball game later in the evening and I don't have a cellphone anymore I had to stick with them. Managed to sneak away for a while to City Lights and bumped into Darius and David, 2 physicists from MIT who I knew while in Boston. It was quite bizarre running into them in San Francisco, having not met in Boston for almost a year.

Ended up walking all the way up to the Ghirardelli chocolate factory where I had a sinful sundae. One of the baseball fans, Nathan, told me how he had finished 2 vermonsters. At Ben and Jerry's icecream a vermonster consists of all 42 scoops of icecream and all possible toppings in one huge bucket. It costs 42$ and if any one person can finish it, he doesn't have to pay for it. Nathan used to play semi-professional rugby for a few years and after a 6 hour session, went with his entire team to the store and finished off a vermonster. Apparently, he didn't struggle while finishing it.

The game was pretty ordinary but the baseball park is beautiful. It's on the south side of the city and overlooks the Berkeley and Oakland hills over the bay. Watching the sunset and the hills light up with a game in front was pretty enchanting. Spent most of the time yakking about math gossip and cheering the occasional hit and trying to boo Barry Bonds. The baseball world might boo him for his steroids but San Francisco still loves him. He didn't hit a home run over into the bay but pulled a foul ball over. The lone kayaker in the waters promptly jumped in to fetch it.