| A Day in the Life of... A Cambridge Mathematics Professor |
| Wednesday, 26 April 2006 | |
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Anne Hinton strolls with Tom Körner along the Champs Elysées of Mathematics The Centre for Mathematical Sciences is rich in personalities. One
of them is Tom Körner, Professor in the Department of Pure Mathematics,
Teaching Fellow at Trinity Hall and author of several books—“some
popular, some less so”—which convey his enthusiasm for mathematics,
history and life in general.“The odd interests me. I can remember jokes
and very little else!”  Credit: DPMMS How did you become a mathematician? At school, I was a rather erratic student of mathematics. Sometimes I did really well, sometimes really badly. My friends went into science at A-level, so I chose mathematics over history and have never regretted my choice. The famous Russian mathematician Kolmogorov did historical research in his youth. He analysed tax records and by checking whether the sums involved were whole numbers or fractions was able to discover which taxes were paid by individuals and which by communities. When he presented his work in Moscow a senior historian stood up and said ‘Young man, in mathematics one proof suffices, but in history we require five!’ The truths of mathematics may not be as important as other truths, but they are as close to absolute truths as human beings can get. They can be firmly established. In mathematics someone can be instantly convinced that they are mistaken!
And how did you become an academic mathematician at Cambridge? Having got onto the academic escalator, mathematics was the natural thing to do at university. I enjoyed all parts of mathematics. I started Part III (the final year before research) thinking that I was an algebraist but after a couple of weeks I realised that I wanted to do analysis. Algebraists deal with rigid structures but in analysis you have much more freedom to tinker with the objects of study. My Director of Studies felt that it was more important for a research student to have the right supervisor than the right subject. He phoned me at home at Christmas to say that a mathematician called Varopoulos was in Cambridge for 24 hours and I should come at once. England was blanketed in snow so travelling conditions were chaotic, but I managed to make it to Cambridge and Varopoulos agreed to take me on. It was a great stroke of luck because he was a marvellous supervisor, bubbling with mathematical problems of all sorts. In my second year of research, I followed him to Sweden and then in my third year to the University of Orsay in Paris.Trinity Hall gave me a research fellowship that they then extended for a year in the hope that I would get a university post, which I did. In those days of university expansion it was almost true that everyone who got a PhD could expect to get an academic job.
What skills are needed to become a mathematical researcher? It is useful to be very hard working, but not necessary. It is useful to be very clever, but not necessary. Mathematicians can be very stupid! Some mathematicians are very good at spotting patterns, some have a very good intuition about randomness, some are good at solving concrete problems by placing them in an abstract setting and some at solving abstract problems by using concrete instances. Each mathematician has a different mixture of skills and abilities.What is needed is lots of determination!
Is the approach to mathematical research different from that of other scientific subjects? Yes. If a mathematician has a problem all he or she can do is think about it.When Newton was asked how he solved such difficult problems he replied “by constantly thinking about them”. Although there have been exceptions (both up and down) most mathematical researchers in the past have only published 50–100 papers in their lifetime. It takes a lot of effort to write a mathematical paper and almost as much to read one. Many papers are single author ones, including most of mine. There is an increasing trend towards collaboration (email helps with this) but never 40 authors to a paper.
How much time do you spend on your own research? I generally do research outside term time. It can take a week to get up to speed on a problem, so I like to keep long intervals of time completely clear. I try to push my administration and teaching into term time but sometimes things leak. You can get ideas at any time.Very often these sudden illuminations turn out to be false. Checking ideas requires concentrated work, sitting at a desk for a long time examining each step of the reasoning.
Are you working on any particularly interesting or exciting topics? Whatever one is thinking about seems to be important. At present I am working on a new proof of a result first proved about 40 years ago. The result states that something can happen in spite of certain constraints. I think I can show that it can happen ‘as fast as the constraints allow’ and I think that the new proof is easier than the old. You will need to read A Quantitative Version of a Theorem of Rudin when (and if) it appears to see if you agree.
What happens on a typical day? To the outside observer it must look like an Andy Warhol movie. Nothing much happens. One may read, think, calculate or have coffee with colleagues and gossip. Sometimes I just sits and thinks and sometimes I just sits. By inclination I am a night worker; it is hard to get long uninterrupted periods of work during the day.
When did you start writing books? I wrote my first book, Fourier Analysis, in my early thirties. It was a very happy time for me. I spent four winter months in Ann Arbor whilst writing the first few chapters and composed most of the rest whilst I was courting my wife Wendy. I think the happiness comes through in the writing. I included a lot of historical and physical background beside the hard technical mathematics. Some years later I attended a lecture on the future of mathematics in British schools that angered and dismayed me. I decided that it was better to light a candle than to curse the darkness and wrote The Pleasures of Counting to show the beauty and utility of relatively simple mathematics and its involvement in history and everyday life. Just as you cannot choose your children’s friends so you cannot choose those of your books.The book did not reach as many of its intended audience of schoolchildren as I had hoped but proved very popular with people like engineers who use mathematics and enjoy extending their horizons. Recently, A Companion to Analysis: A Second First and a First Second Course in Analysis appeared. This is addressed to advanced second and third year undergraduates. The foundations of analysis are difficult to learn; they are both technical and philosophically profound. The usual approach to the subject is to make light of the difficulties but I show that although there are difficulties one can get around them. The second half of the book addresses more advanced topics.
What is the satisfaction element for you in writing books? Mathematicians, I think correctly, value the production of new mathematics above all else. However, there is great pleasure in writing out and contemplating other people’s clever ideas. Mathematicians value the composer above the player, but the player derives great pleasure from performing the work of the composer. The business of getting a book published— which seems to take as long as the writing—is not as pleasurable: think of the endless proof-reading.
What does your college work at Trinity Hall involve? I have been Director of Studies for 30 years. The largest and best part of my duties involves taking pairs of students through their week’s work. It is a marvellous occasion for them and for me when they realise that what was impossible at the beginning of a year is now obvious and routine. I am also Vice-Master for the next four years. This is an important position if things go wrong, but the college is working well and I hope to remain a gaily painted fifth wheel during my entire period of office.
What are the best aspects of your job? It is like working in a chocolate factory. I am paid to do what I enjoy doing. Teaching is fun when syllabus and students match as they do in Cambridge. It is a thrill to realise that your first year audience may contain a future Fields medallist. Professionally, Cambridge University is like the Champs Elysées: eventually everyone who is anybody in mathematics strolls by. It is nice to be surrounded by people who are cleverer than oneself—really, really good at their subject.The principle is: you should always play chess with someone who is better than yourself.
What are the worst aspects of your job? Very few. As a university teacher I have lived through a golden age and I suspect my successors will not be quite so fortunate. Compared with when I started, I think that university administrations are very much more eager to offer help and advice when you do not need it and very much less able to give it when you do. There is one intrinsic drawback that I suppose is common to all creative endeavours. After the completion of a piece of research, you always wonder if you will ever produce anything again. But it is better to have enjoyed the thrill of discovery and regret that it lies in the past than never to have enjoyed it at all.And you always have the pleasure of learning and teaching the discoveries of others. Luck plays a great equalizing role in mathematics. Although great mathematics is done by great mathematicians, anyone may suddenly come across a seam of pure gold.We cannot teach students how to have a good idea; we can only teach them how to exploit it. Anne Hinton is an Affiliated Lecturer in the Department of Geography |
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