Professor A. S. Besicovitch

BY M. F. A.

IF, at some time during the last war, you had been wandering through the Great Court of Trinity on a summer afternoon, you might have been privileged to see a distinguished-looking man mowing the lawns in his shirt sleeves. That would have been Abram Samoilovitch Besicovitch, F.R.S.

To the world at large Besicovitch passes for a Russian, but in actual fact he comes from a small and little-known people called the Karaites, a Jewish sect of Turkish origin who are to be found in scattered communities as far apart as Egypt in the south and Finland in the north. Most of them, however, inhabit the area round the Black Sea, and it was there that Besicovitch spent the early years of his life. He himself tells the story of how as a young boy he used to go down to the docks at a small town on the Sea of Azov and ask the English sailors to help him read his English books. On one such occasion he attracted the attention of the captain himself and spent the rest of the time on board as the captain's guest, with a corresponding improvement in the standard of English.

Along with one of his brothers he read mathematics at the University of St. Petersburg, and it was there that he started his academic career, working under the famous mathematician A. A. Markoff on Probability Theory and lecturing, some may be surprised to hear, in Applied Mathematics. With the advent of the revolution life became increasingly difficult in St. Petersburg, and in 1917 he moved to the new University of Perm, in the Urals, where conditions were better but still not really conducive to mathematical research. The rigours of the climate necessitated sitting in a large sack as the only means of keeping warm, and the isolation from the mathematical world was an even more serious obstacle as most of the books in the University were of 1850 vintage and periodicals were an extreme rarity. Despite all these difficulties Besicovitch, during this period, did some work on Real Functions and solved the famous problem of Kakeye. In non-technical language his solution might be described by saying that in order to reverse your car (assumed infinitely thin) you require no room at all, though unfortunately you will have to go off to infinity in an infinite number of directions.

In 1920 he returned to his old University and stayed there until, five years later, he finally left Russia on a Rockefeller research grant and went to Copenhagen. Oxford then claimed him for a year, but fortunately he found his way to Cambridge shortly after, and has remained here ever since.

An analyst throughout his life, he has worked on such topics as Sets of Points, Measure, Real Functions and Parametric Surfaces, not forgetting occasional incursions into other fields such as Number Theory. Perhaps typical of the sort of work he has done is the pathological surface he produced which showed that the definition of area current at the time was completely inadequate. It was the diagram of this surface with its striking similarity to a system of pipes which gave rise to the rumour that he started life as a plumber. Another of his results (though here he was anticipated by Brouwer) was to show that there was no proper equivalent of the four-colour problem in three dimensions, for, even with the obvious restriction to convex polyhedra, the number of colours required turned out to be infinite. With these examples in mind it is not difficult to see why the numbers 0 and \infty were once described as typical Besicovitch numbers.

Original in other fields as well as mathematics, his leisure hours are spent, not in the orthodox academic pursuit of mountain peaks, but in the quiter joys of long-distance swimming, and the Channel rather than Everest is his goal. Recently he caused a minor sensation at the Canadian Mathematical Seminar by swimming a mile between lectures. It was there also that he produced his famous card game which has rules so simple that it is played by Russian peasants, but yet resembles Chess in the skill and subtlety of its play. He offered two dollars to anyone who could defeat him, and though some of the younger mathematicians tried hard for a whole month, he returned unbeaten, to the great satisfaction, no doubt, of the Chancellor of the Exchequer.

Since his election to the Rouse Ball chair in 1950 he has, of course, given up supervising undergraduates, and those who were fortunate enough to work for him in earlier days will realise what a loss this is to succeeding years of Trinity freshmen. His supervisions were definitely an experience in themselves; one climbed his stairs in a state of trepidation, contemplating sadly the fate that awaited one's efforts on last week's paper, and wondering what deceptive little problems he would produce this week, problems that charmed by their simplicity yet obstinately refused to be solved. But the rigours of the mathematical instruction were always mitigated by his essential kindness. On one occasion, in order to cheer the despondent pupil, he went so far as to confess that he had never really understood the whole question of pole and polar in elementary geometry.

It certainly cannot be said of many professors that they take such a friendly interest in the undergraduate world as Besicovitch. One of his favourite past-times, he says, is going for walks with undergraduates; indeed, so keen is he on these walks that he once assured his young companions that the portending blizzard was, in Russian eyes, a sign of mild weather and need not deter them from their walk. On the occasion of the Commemoration dinner with the subsequent intermingling of High and Low Tables, he is always to be seen in the centre of an animated group, relating some of his popular anecdotes and signing menus for the young autograph hunters. In fact, despite all the minor eccentricities and characteristics which are almost de rigueur in a professor of mathematics, the more lasting impressions one carries away are of his extreme amiability and his keen sense of humour.

Eureka, 15.


Reproduced from Eureka 27 pages 26-28.
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Additional notes to the online version

Errata: "Kakeye" should read "Kakeya", "quiter" should read "quieter", "past-times" should read "pass-times".


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