The proof is in the prize
Two scholars who are sharing a top maths award this year have more in common, they say, than top-flight grey matter.
A key to their success is that both are loners who are willing to swim against the tide and explore new frontiers, they said on a recent trip to Hong Kong.
Dr Demetrios Christodoulou, a Greek, and Dr Richard Hamilton, an American, are the joint winners of this year's US$1 million Shaw Prize, dubbed Asia's Nobel Prize, in mathematical sciences.
They spoke to the Sunday Morning Post last week, during a five-day visit to Hong Kong for the prize presentation ceremony on Wednesday. The Shaw's winners were announced in the summer.
Christodoulou said: 'The one thing where we both are similar is that we are loners. We don't depend much on collaboration. Among mathematicians, we are the loneliest ones.'
Christodoulou works out of the Swiss Federal Institute of Technology in Zurich, specialising in black hole physics and general relativity.
Hamilton, the Davies professor of mathematics at Columbia University, agreed with Christodoulou, saying, 'there are people who like to be at big institutes, like Harvard, and get all the latest exciting news and try to put a whole bunch of ideas together. They are like the businessmen in the city organising everything with different people.
'And then there are the mountain-man types - the Davy Crocketts of the Americas - who just go off into the wilderness and go exploring something totally new and exciting, and come back and tell strange stories. And then people come and follow after,' he said. 'I like to work with people but I tend to work on my own because I tend to work faster. Working with other people, unless they are really smart, really quick, tends to slow you down.'
The two have known each other for 25 years, since meeting at an academic event. At the time, they were only starting out on the research that has now earned them worldwide recognition, including the Shaw prize.
'We're old friends and I very much admire Demetrios' work, and I am honoured to have my work compared to his,' Hamilton said.
'A lot of the value of the prize, apart from the money, of course, is the honour of who you share it with, and who has had the prize before. And this prize has had a very good track record.'
Recent winners of the prize include Jean Bourgain of Princeton University's Institute for Advanced Study, Simon Donaldson, a professor at Imperial College, London, and Harvard's Professor Clifford Taubes.
Hamilton said about his work: 'I remember one student came up in class and complained 'that homework took me five hours'. I said 'I've been working on the problem, same problem, for 25 years and I still haven't got it.'
But he may accept now that he has 'got' it: the Shaw committee noted that his Ricci Flow is one of the most powerful tools in modern geometry.
Both claim, however, that there is a 'large element of luck' in their success. The key, they agreed, was to develop a 'certain nose' for finding the right things to do.
'In mathematics, you do have to pick the right problems,' Christodoulou said. 'There are people who have the right taste, and are technically capable, but who simply work on certain problems that don't seem to bear fruit.'
Hamilton finds it important to foster mental peace. Contrary to the popular belief that mathematicians are introverted to the point of verging on the autistic, he said: 'I couldn't do very good maths by locking myself in a room. I need to go out for fresh air and exercise and maintain the oxygen flow, because it makes my mind feel good.
'There's a saying: 'You should never trust an idea that comes to you when you're in a library',' he said.
Neither of Christodoulou's parents had a higher education, but his father ignited his passion for mathematics and theoretical physics with stories about ancient Greece's outstanding contributions to human civilisation. Christodoulou said he used to venture out by himself to climb the high mountains of Greece and other parts of Europe. He would gaze at the stars all night to keep his mind peaceful and relaxed.
Differential geometry is not exactly a household phrase. So how would a mathematician describe his work to somebody at a party?
'At most parties I could think of I would try to hide what I do,' Hamilton said. 'There is a certain tendency if you tell people you're a mathematician, and especially pretty young girls, they run away screaming.
'Wonderful new vistas are opening up, partly thanks to the technology. When I began doing something like the Ricci Flow, I thought the success rate would be about one in a million. Then I thought it would be fun to work on. The computer allows you to do a couple of very useful things. For instance I make little movies to show how the geometry moves. They're very, very good at these algebra computations, and get answers very quickly.
'The best thing about it is that the computer never does anything wrong. It only does something wrong when I give it something wrong.'
Christodoulou has made fundamental contributions to mathematical physics. The Shaw committee said his work is characterised by a profound understanding of the physics connected with Einstein's equations and brilliant mathematical technique.
Hamilton introduced the process known as the Ricci Flow - essentially a proposal about how to stretch a surface depending on the way it curves. He used it to establish striking results related to the shape of curved three- and four-dimensional spaces.
When the maths award was announced in June, Kenneth Young, a vice-chairman of the board of adjudicators, said: 'In mathematics, the trick is that certain apparently obvious - and to lay people trivial - statements, if you want to prove them precisely, are a great challenge.
'You don't know if they are generally true until you have given precise proof.'
The Shaw Prize was established by media magnate and philanthropist Run Run Shaw and first awarded in 2004.