Person: Littlewood, John Edensor
Littlewood collaborated with G H Hardy, working on the theory of series, the Riemann zeta function, inequalities and the theory of functions.
Mathematical Profile (Excerpt):
- A very few close friends called him Jack when he was elderly, but otherwise he would be addressed as Littlewood, which was not unusual between friends at that time.
- Hardy with whom he had a close collaboration for many years would write to him as "Dear L".
- If the climate and scenery were superb, certainly the education that the young Littlewood had in South Africa was not.
- The quality of his school teachers was poor, and he was confused by the mathematics teaching that he received to the extent that he failed an arithmetic examination.
- He still did quite well and entered the University of Cape Town at a young age but again found that he was not able to benefit from teaching which was less than outstanding.
- We should mention that Littlewood, as we explain in more detail below, suffered from depression for most of his life, beginning while he was at school, and this may have contributed to his difficult days in the South African education system.
- In 1900 Littlewood, then aged 15, returned to England and entered St Paul's School in London.
- He understood uniform convergence, and he could discriminate between basic ideas and tricks of manipulation.
- While at St Paul's School in December 1902, Littlewood won a scholarship to Cambridge.
- Littlewood entered Trinity College Cambridge in October 1903.
- His tutor at Trinity was Walter Rouse Ball, the author of the famous popular book Mathematical Recreations and Essays.
- Rapidly solving the first problem which Barnes gave him, Littlewood was next presented with the Riemann hypothesis as his next research problem by Barnes.
- Littlewood never regretted having tackled the Riemann hypothesis, remarking that if one attempted a problem that was too difficult then one would always end up proving some interesting related results.
- From 1907 to 1910 he lectured as Richardson Lecturer at the University of Manchester.
- He became a fellow of the Trinity College in 1908, winning a Smith's prize in that year, then returning to Trinity in 1910 to fill the position left vacant when A N Whitehead was essentially forced out of his job.
- Shortly after this, certainly by 1911 but some suggest in 1910, Littlewood began his famous collaboration with G H Hardy which we discuss in more detail below.
- The result was that he improved the accuracy of anti-aircraft range tables and improved the formulae for finding the range, the time of flight and the angle of descent at the end of a trajectory with small elevation.
- E A Milne has described how Littlewood was able to discover techniques which greatly reduced the amount of work needed for making these accurate calculation of missile trajectories.
- To the astonishment and joy of all concerned the observed positions of the shellbursts fell exactly on Littlewood's trajectories, at the correct time-markings, within very small errors of observation.
- Littlewood become Rouse Ball professor of mathematics in Cambridge in 1928.
- This chair had been founded by a benefaction from Walter Rouse Ball after his death in 1925, and Littlewood was its first occupant.
- It was a particularly appropriate choice, not only because of his outstanding mathematical contributions, but also since Littlewood had been tutored by Rouse Ball in his undergraduate days at Trinity.
- As Rouse Ball Professor, Littlewood could lecture on topics of his own choice and he no longer had to take part in routine teaching.
- It was an aspect which he enjoyed, delivering courses on his own wide areas of interest in analysis.
- Almost all of Littlewood's mathematical research was in classical analysis, but in this area he looked at a remarkable range of subjects and he used an even broader range of techniques in proving his results.
- For 35 years he collaborated with G H Hardy working on the theory of series, the Riemann zeta function, inequalities, and the theory of functions.
- The collaboration led to a series of papers Partitio numerorum using the Hardy-Littlewood-Ramanujan analytical method.
- During the years of this collaboration Littlewood was seldom seen outside Cambridge, in fact there were jokes around that he was the invention of Hardy.
- The real reason was rather a sad one, namely that Littlewood suffered from depression which we shall discuss more fully below.
- When one received a letter from the other, he was under no obligation to read it, let alone answer it.
- Although it did not really matter if they both simultaneously thought about the same detail, still it was preferable that they should not do so.
- It was quite indifferent if one of them had not contributed the least bit to the contents of a paper under their common name.
- We should also comment that if it seems strange that such a prolific mathematician as Littlewood has his collected papers published in only two volumes, this is because the large Hardy-Littlewood collection of papers appears in Hardy's collected works.
- In the late 1930's the Department of Scientific and Industrial Research tried to interest pure mathematicians in nonlinear differential equations which were important for radio engineers and scientists because they described the behaviour of electric circuits.
- The impending war motivated this interest and in 1938 the Radio Research Board asked British pure mathematicians for help in dealing with certain types of nonlinear differential equations arising in radio engineering.
- Littlewood, working jointly with Mary Cartwright, spent 20 years working on equations of this type such as van der Pol's equation.
- The problems caught the attention of British mathematicians M L Cartwright and J E Littlewood, initiating a collaboration that lasted more than ten years.
- Cartwright and Littlewood's analysis of the van der Pol equation and its generalizations led them to explore some interesting topological methods, including the development of a fixed-point theorem for continua invariant under a homeomorphism of the plane.
- They were among the earliest mathematicians to apply Poincare's transformation theory to the analysis of dissipative systems.
- Their research is among the earliest in large parameter theory and played a role in the development of the modern theory of dynamical systems and chaos theory.
- Littlewood was elected a Fellow of the Royal Society in 1915,
- He made mathematical discoveries and supreme insight in the analytic theory of numbers.
- Littlewood, on Hardy's own estimate, is the finest mathematician he has ever known.
- He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power.
- He contributed to many branches of analysis, including Tauberian theory, the Riemann zeta-function, and non-linear differential equations.
- As we mentioned on a couple of occasions above, one problem which Littlewood had to cope with throughout his life was depression.
- It had affected him from his school days and continued to trouble him throughout his career.
- There is no evidence that it in any way impaired his ability to do mathematics, indeed it is hard to see how it could have done so given what he achieved, yet it certainly did much to spoil his social life for it had the effect of making him withdraw into himself.
- Although his mathematical research did not seem to suffer, it certainly stopped him from undertaking other mathematical activities which involved meeting people.
- Although he was President of the London Mathematical Society in 1941-43 he never chaired a meeting, the vice-President taking the chair throughout his period of office.
- After he retired he did receive treatment for his depression which was quite effective, and after 1957 he felt more able to accept invitations to visit colleagues.
- Indeed he made many visits to the United States in the ten years following 1957.
- We should end this biography by saying something about Littlewood's interests outside mathematics.
- was slightly below average in height, strongly built and agile.
- At school he had been one of the best gymnasts and a hard hitting batsman.
- he was a keen follower of ball games and watched cricket at Fenner's on summer afternoons.
- He had an intense interest in music (classical - particularly Bach, Beethoven and Mozart); he had taught himself as an adult to play the piano ...
- He was best known to unmathematical undergraduates at Trinity for his skill in circling the seven yards of a pillar of the Library on the narrow ledge of its base and for his daily walk across the court to the baths, with a towel but no shirt.
- On most days he walked many miles in the country.
- muscular strength and quickness of reaction made for success in rock climbing and skiing, and he spent many holidays in Cornwall, Scotland and Switzerland.
- He continued to produce excellent mathematical results for many years after he retired and even when ninety years old he was still sharp and able to come up with new deep ideas.
- raised difficulties which defeated me for some time.
- In addition to the honours which we have mentioned above, Littlewood was honoured with election to the Akademie der Wissenschaften in Göttingen in 1925, the Swedish Academy in 1948, the Royal Danish Academy also in 1948, and the Dutch Academy in 1950.
- In 1957 he was elected to the Paris Académie des Sciences to replace Fréchet.
- We mentioned above that Littlewood was President of the London Mathematical Society, but that Society also honoured him with its De Morgan Medal in 1938 and its Senior Berwick Prize in 1960 for two papers which he wrote on celestial mechanics.
- Finally we note that he received honorary degrees from the University of Liverpool in 1928, the University of St Andrews in 1936 and the University of Cambridge in 1965.
Born 9 June 1885, Rochester, Kent, England. Died 6 September 1977, Cambridge, England.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive