Friday, 4 October 2013

Erdős Centennial Conference

Three months ago today, I was in Budapest at a conference celebrating the hundredth anniversary of the birth of Hungarian mathematician Paul Erdős. It was also my first proper conference in a decade since I started my PhD. Erdős was surely the most prolific mathematician in history with over 1600 papers to his name, a great collaborator because the majority of those papers were joint with other people, a great pollinator of ideas because he never held a full-term position at any university but travelled ceaselessly from conference to conference spreading news and ideas and open problems, a great problem-solver without question, but also a great conjecturer with an uncanny knack of asking the right questions and knowing the right people to whom to give them to.

Most strikingly, over half of his mathematical output was in the last twenty years of his life (though admittedly under the influence of amphetamines). This puts him alongside the likes of Kant as a great man who didn’t fizzle out but grew and ripened and even accelerated with age. In the face of the ever-advancing sands of time, it serves as a wonderful inspiration and disproves the myth expounded in G. H. Hardy’s Apology that maths is a young person’s game. It also disproves a second myth that mathematics is a form of competition. For if it were really so, as sport is, then fellow mathematicians would have begrudged Erdős’s use of “performance-enhancing drugs”, instead of which we are grateful for what he did for the advancement of mathematics and his mentoring of young mathematicians all over the world. The pursuit of knowledge is a collective endeavour, and while there is a sense of urgency to solve a problem before another does so, mathematicians would agree with Erdős that while we would dearly like to be the one who makes a beautiful discovery or finds a beautiful proof, we would rather the discovery were made by someone than for our desired prize to be left undisturbed. This is because whatever discoveries we make, these always open up new horizons, new problems, and there is never any sense or fear that our knowledge could ever be complete. The mathematician’s task is never done, and always interesting.

The twentieth century has seen such a fragmentation of new areas of mathematics with underlying profound connections between them that even Erdős himself, whose interests were so broad, was bemused by their complexity and never able to research into them. These are the specialisms of what are sometimes called the theory-builders, who open up new frontiers of abstractness. Erdős by contrast was always alert to what theory was for, what purpose it could be put to, what problems it could solve, and perhaps his crowning achievement was a theory as beautiful as any, incredibly powerful but also incredibly simple in its conception, and certainly fitting Hardy’s criterion of beauty as the measure of all things mathematical. It was the use of probabilistic ideas to solve problems in combinatorics. But despite the wealth of his research in probability, combinatorics, analysis, and logic, at heart Erdős always felt drawn back to number theory: the queen of mathematics as Gauss called it. Indeed, numbers, that is the stuff that mathematics is made of. In the words of Kronecker, God made the natural numbers; all else is the work of man.
Erdős had always been my childhood inspiration, as well as the British cricket-lover G. H. Hardy (pictured right) and Sierpinski (after whom the fractal Sierpinski triangle is named). I would mention Ramanujan also but I am more in awe of Ramanujan than inspired by him because though overshadowed by the achievements of Hardy and Littlewood, mathematicians to this day cannot conceive how his mind worked, and he himself claimed direction from his goddess in dreams, so to my knowledge he is the only genius that mathematics has ever known  (in the true sense of the word - that is to say, unexplainable, as if inspired by a genie). Erdős at least left footsteps one could follow after.

This was my first visit to central Europe. I had never travelled within Europe beyond Graz, where the Journées Arithmétiques was held exactly ten summers ago. Indeed, Graz was the origin of my user-name "okei": the name of a fast-food joint where I had lunch the morning I left. In preparation, I learnt some Hungarian on a wonderful user-created site called I have a sense my mathematical proficiency as a child was symbiotic with my learning of languages. Though almost all of what I learnt of German, Latin or Greek is now forgotten, the quality of mind these languages left on me was a receptiveness to new terminology which is essential to mathematics whose terminology is always adapting and changing through history as theories are laid down and perfected. I hope to use this website more in the future and hopefully learn Chinese, though in the last months I’ve done little to keep up that promise, and even my few words of Hungarian are mostly forgotten. But the sounds of the letters and words remain.

For example, sz = soft s, s = sh, c = ts, j = y, etc. so for example utca (pronounced utsa) means a road, jó napot (pronounced yo napot) means good day, and most important of all, the only expression you really absolutely must learn when going to a foreign country, köszönöm (pronounced kesenem) means thank you. This was the only expression I actually got to use in practice. (I had a great time, so lots to thank!)

It was wonderful also to see the names of the mathematicians I knew take on meanings: Fejér means white, Fekete means black, Katona means soldier, Bárány means sheep. I also discovered that erdő means forest, and eső means rain, while esős means rainy, so by extrapolation perhaps erdős means forested? I never thought to ask if this were in fact so. In Zen, there is a very old tradition of travelling forest monks unlike the monks who meditate alone in mountain caves. The name seems particularly apt, the image of Erdős as a forest monk spreading the mathematical dharma. How I would love to be like him!

It was a two and a half hour flight from London. As always in such moments, one expects the plane to be full of fellow travellers flocking to the same event. And yet always the reality turns out rather different. There was in fact one other who took the same flight from Stansted, but I only met him later. Then there was a blue bus to the end of the metro, and within another hour I was in the centre of Budapest, facing the Cathedral of St. Stephen (Szent István Basilika, or just Basilika for short), and eventually found my room and deposited my rucksack.
I spent the rest of Sunday wandering around town, hoping to find a nice spot to get something to eat, but in the end I just kept wandering. I first passed through the Jewish quarter with its two impressive synagogues. The great (Dohany Street) synagogue is the largest in Europe and built in the 19th century. Jewish architecture was inspired in those days by Islamic architecture from North Africa and Granada. It made me think how the Jews and Muslims were much closer then, both expelled from parts of Europe like Spain, so there was a kind of brotherhood of faith between them. I then passed the famous Renyi Institute where many famous Hungarian mathematicians have research-only jobs, sometimes combined with teaching jobs in America or elsewhere. Finally, still hungry, and tired by all the walking, I went on to the registration and reception being organized for us at the Hungarian Academy of Sciences, and sure enough they provided plenty of cold refreshments. The Hungarian Academy is a very grand building on the banks of the river Danube. There are plenty of grand buildings on the river, but these are mostly expensive hotels! You can tell something of the nature of a place from its finest buildings, and for Budapest it is tourism, but also the Academy. The Academy of Sciences was built in the 19th century, funded entirely by donations from private individuals, not by government as one would expect such projects would be. It was the Victorian age of philanthropism. A wealthy Hungarian politician dedicated his whole income from one calendar year towards this project, and in doing so convinced others to pledge their money also. This beautiful hall was the site of the lectures with a capacity of 400, statues standing along the walls, and a painted ceiling and backdrop. Since there were 700 participants at the lectures, there was a second room where the lectures were broadcast via a tele-link.

My overall first impression of Budapest was how 19th century and grand it felt, like old London, in need of constant renovation which is expensive for Hungary, not being a wealthy nation. There is a sense of hard-working efficiency and pride in great organisation as in Germany, of zebra crossings meaning something for pedestrians unlike in France, of being central European and not wanting to be regarded as eastern European, of entitlement as a people and directness in their manners which could be misinterpreted by some as unfriendliness, and of course heritage and history, but also a feeling of vulnerability to crippling debts and poverty within and to bullying from bigger European neighbours without. They have done a lot of work in recent decades in restoring their heritage, and this is important for tourism, but it also creates resentment among those who feel the money could be better spent on local needs and creating jobs. There is a noticeable nationalistic strain to Hungarian politics, an irrational fear that Hungarians are leaving and others will take their place, the Jew and the Romani bearing the brunt of this racism, one for buying the country up, the other for bringing it down. Why the underlying fear? The other side of fear is a healthy pride. A charming blonde girl with Hungarian origins gushed that her boyfriend was completely Hungarian. What does this even mean? For her, this was a way of expressing that her love was the real thing, and seeing in her boyfriend a quality of transcendence. She was just idealizing her love. But when this takes on a political character among parties and politicians in a nationalistic love, then the imagined ideal of this love is usually something in the past, a particular past, which carries the danger of excluding people in the present. History tells how the magyar (Hungarian) people invaded the land in 896 A.D. (in celebration of which the St. Stephen Basilika is exactly 96m high). It is funny how any nationalism has a point of beginning, a point of conquest in which others were no doubt displaced. In the UK, the nationalist parties talk about white Britain, but the indigenous people of England were in fact the Welsh of darker complexion, driven back by Viking and Norman conquests into what is now Wales. Nationalistic identity is an essentially imagined concept, an imagined beginning that ignores the fluid character of peoples and even boundaries. Ultimately identity comes to rest in language, and Hungarian being notoriously difficult, they should have less to fear in the first place, confident that their language provides an adequate test of commitment.
Budapest is actually a combination of two older cities Buda and Pest, separated by the river. It was only in the 19th century that the first permanent bridges were built uniting them. I spent most of the time in Pest. Buda is named after an old ruler of Hungary of Turkish origin, while Pest means cave, so together Budapest sounds a lot like "Buddha's cave". Most of the caves though seem to be on the Buda side, but I sadly never got the chance to explore them, nor the many grand Turkish baths, a legacy left from 150 years of Turkish rule. The Turks were much disliked then, yet Hungarians are grateful for this positive effect they had on the city. The hot waters are rich in sulfur and supposed to be very healing. Other first impressions were the July heat, like in Spain, and also the really wide roads running through the heart of the city, perhaps a Soviet influence. Hungary was under communist occupation for much of the second half of the last century. They tried to revolt in the 1950s hoping the West would intervene and help them, but the revolt was brutally put down by the Soviets.

The first night, after the registration-reception, I went to the operahaz (haz=house) for my first ever experience of opera (the cheapest tickets were just over a pound (300 forint) and I was hoping to get a 1000 forint ticket on the second floor, but as I was queuing, we were told that the performance was sold out. I was quite disappointed, as were some Chinese girls in the queue in front of me, and I was asking the lady in charge if I could come back in the interval or something. Then a Chinese girl handed her back the ticket she'd already bought because her friends couldn't join her, and she passed the spare ticket on to me, and it was a better ticket too, on the first floor. So I ended up getting a 4000 forint ticket to the opera for free! “Lucky you!” as the woman on the blue bus said on the way back to the airport. I was even luckier than I thought, because I later discovered that this was the very last performance before the traditional summer break in July and August.
Hungary was not the easiest place to be vegetarian, so I started eating chicken again. But I also went off a couple of times to try a raw vegan café near the parliament building, and a really lovely vegetarian place called Napfenyes, hidden away in the basement and on the way towards Hero’s Square. Unfortunately, I couldn't convince others to join me though. As for raw vegan fair, I must admit I didn't like it much and only ate half of it, but I did feel like superman afterwards, plus the black sesame based drink was absolutely delicious. I didn't even feel hungry for breakfast the following day, so my body must have been really satisfied even if my taste buds weren't. Towards the end of the week, I discovered a nice bakery on the walk to the Academy, and enjoying sleep too much to have a proper breakfast, I’d satisfy myself with their delicious custard pastries en route to the 9a.m. lectures.

Monday to Friday we had talks from 09:00 till 18:30 with only a 90 minute break to wander and find lunch somewhere, so not much chance really to explore the city. On the final evening, the conference organized a banquet on the river. I spent most of it with a clever mathematician called Bob H. who had just solved a long-standing unsolved problem of Erdős. On the plane back, I enjoyed the company of Alex P. whose seminar in Cambridge I once attended, and coincidentally the only seminar I blogged about in my aborted attempt at blogging mathematics.
In summary, the lectures were mostly good and the choice of parallel afternoon sessions was overwhelmingly brilliant. It was great to go to talks by people I'd heard of and read, but never got the chance to see or listen to before.
Budapest itself was very beautiful and I wrote soon after returning, "I could almost imagine living here", not quite ready to let it go. If you talk to Hungarians abroad, they sometimes have a very negative view of their own country citing low wages, petty crime and a lack of friendly community, but personally I didn’t experience any of this.
One final thing: the windows in the shared dining or common room where I stayed were always flung open, giving a lovely feeling of cool wind after a warm day. The room was spacious and tall-ceilinged with a chandelier and a couple of posters of London and its red buses on the walls reminding me of home. And then these open windows, as if the wind itself had thrown them open, brought to mind some line of a poem I couldn’t quite remember. I looked it up ­— it is a poem by Shinji Moon, an 18-year old student in New York when she wrote it. She is already really famous on Tumblr (where I first read it), and indeed this is her most famous poem:

Here’s what our parents never taught us
(Shinji Moon) 
You will stay up on your rooftop until sunlight peels away the husk of the moon
chain-smoking cigarettes and reading Baudelaire,
and you will learn that you only ever want to fall in love with someone
who will stay up to watch the sun rise with you.
You will fall in love with train rides, and sooner or later you will
realize that nowhere seems like home anymore.
A woman will kiss you and you’ll think her lips are two petals
rubbing against your mouth.
You will not tell anyone that you liked it.
It’s okay.
It is beautiful to love humans in a world where love is a metaphor for lust.
You can leave if you want, with only your skin as a carry-on.
All you need is a twenty in your pocket and a bus ticket.
All you need is someone on the other end of the map, thinking about the supple curves of your body,
to guide you to a home that stretches out for miles
and miles on end.
You will lie to everyone you love.
They will love you anyways.
One day you’ll wake up and realize that you are too big for your own skin.
Don’t be afraid.
Your body is
a house where the shutters blow in and out
against the windowpane.

You are a hurricane-prone area.
The glass will break through often.
But it’s okay. I promise.
a stranger once told you that the breeze
here is something worth writing poems about.

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