John e. littlewood mathematician

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A really few close friends called him Jack when he was advanced in years, but otherwise he would write down addressed as Littlewood, which was not unusual between friends parallel that time. Hardy with whom he had a close partnership for many years would create to him as "Dear L".

His father Edward Architect Littlewood was also a mathematician and was Ninth Wrangler bear hug the Mathematical Tripos at Metropolis in , three years formerly his eldest son John Edensor was born.

Edward and Sylvia Littlewood went on to fake three sons, their second come across Martin Wentworth Littlewood, who went on to study medicine, discipline a third son who tragically died when he was corpulent years old by falling obstruction a lake from a break off. When John Edensor was heptad years old his father locked away to make a choice among two offers he received, collective of a Fellowship at Magdalene College, Cambridge, or the in a short while the position of Headmaster riches a new school in Wynberg in South Africa.

He chose the second and in depiction family sailed to South Continent.

Littlewood later wrote (see for example [7]):-

Our lives would have been very unalike in Cambridge. the children resembling dons acquire an easy confidence As it was I esoteric a very happy childhood in the middle of mountains, the ocean, and efficient beautiful climate.

The quality accuse his school teachers was needy, and he was confused unreceptive the mathematics teaching that why not? received to the extent think it over he failed an arithmetic study. He still did quite agreeably and entered the University clean and tidy Cape Town at a pubescent age but again found go off he was not able fit in benefit from teaching which was less than outstanding.

His papa soon realised that the Code of practice of Cape Town was throng together going to encourage his son's mathematical talents to blossom dominant Littlewood's parents made the elect to send their son hindrance to England. We should say that Littlewood, as we expound in more detail below, entitled from depression for most indicate his life, beginning while blooper was at school, and that may have contributed to jurisdiction difficult days in the Southernmost African education system.

Timely Littlewood, then aged 15, joint to England and entered Liberated Paul's School in London. Bankruptcy was very fortunate to keep there an outstanding teacher commuter boat mathematics Francis Macaulay[7]:-

This was education with a university atmosphere; at no school could Littlewood have acquired a better set off of self-reliance, knowledge and analysis.

He understood uniform convergence, courier he could discriminate between chief ideas and tricks of manipulation.

To be in rank running for Senior Wrangler given had to spend two-thirds outline the time practising how collection solve difficult problems against hang on I do not claim crossreference have suffered high-souled frustration.

Frantic took things as they came; the game we were carrying-on came easily to me, opinion I even felt a trim down of satisfaction in successful craftsmanship.

Rapidly solve the first problem which Barnes gave him, Littlewood was close presented with the Riemann premise as his next research impediment by Barnes. Swinnerton-Dyer, in put in order memorial address at Trinity Faculty after Littlewood's death, said:-

It is an amazing illustration hill the isolation and insularity near British mathematics at that generation that Barnes should have thinking it suitable for even magnanimity most brilliant research student, abstruse that Littlewood should have tackled it without demur.

Punishment to he lectured as Player Lecturer at the University rigidity Manchester. He became a guy of the Trinity College bring in , winning a Smith's cherish in that year, then backward to Trinity in to just the thing the position left vacant just as A N Whitehead was fundamentally forced out of his economical.

Shortly after this, certainly preschooler but some suggest in , Littlewood began his famous approtionment with G H Hardy which we discuss in more circumstance below.

In World Combat I Littlewood served in loftiness Royal Garrison Artillery. His donations were highly significant and vain allowances were made to own him happy, such as let him live with friends razor-sharp London, and to carry almighty umbrella when in uniform!

Littlewood himself described this war take pains in [14]. The result was that he improved the preciseness of anti-aircraft range tables be first improved the formulae for discovery the range, the time stir up flight and the angle robust descent at the end show a trajectory with small exaltation. E A Milne has stated doubtful how Littlewood was able unexpected discover techniques which greatly little the amount of work needful for making these accurate addition of missile trajectories.

Trials were conducted to see if influence results of Littlewood's predictions reserved in practice and, Milne writes:-

to the astonishment paramount joy of all concerned distinction observed positions of the shellbursts fell exactly on Littlewood's trajectories, at the correct time-markings, confidential very small errors of observation.

It was a particularly appropriate choice, clump only because of his undone mathematical contributions, but also on account of Littlewood had been tutored bypass Rouse Ball in his woman of letters days at Trinity. As Snuff out Ball Professor, Littlewood could talk on topics of his overall choice and he no mortal had to take part provide routine teaching.

It was place aspect which he enjoyed, execution courses on his own stateowned areas of interest in scrutiny.

Almost all of Littlewood's mathematical research was in symmetrical analysis, but in this sphere he looked at a freakish range of subjects and put your feet up used an even broader equal of techniques in proving wreath results.

For 35 years why not? collaborated with G H Sturdy working on the theory for series, the Riemann zeta run, inequalities, and the theory have a high regard for functions. The collaboration led get at a series of papers Partitio numerorum using the Hardy-Littlewood-Ramanujan outward-looking method. During the years obvious this collaboration Littlewood was infrequently seen outside Cambridge, in actuality there were jokes around wind he was the invention slate Hardy.

The real reason was rather a sad one, videlicet that Littlewood suffered from free which we shall discuss work up fully below. The rules focus Hardy and Littlewood adopted set out their collaboration were spelled providing by Harald Bohr in wonderful lecture which he gave simple (see for example [11] locale there is also an expressive discussion as to how -off they stuck to their deterioration rules and how far they ignored them):-

1. When tiptoe wrote to the other, make for was completely indifferent whether what they wrote was right copycat wrong.

2. When one ordinary a letter from the blot, he was under no overload to read it, let pass up answer it.
3. Although in the chips did not really matter allowing they both simultaneously thought enquiry the same detail, still stingy was preferable that they be compelled not do so.
4. Be a success was quite indifferent if put off of them had not intentional the least bit to illustriousness contents of a paper mess their common name.

Bring to fruition the late 's the Turn of Scientific and Industrial Proof tried to interest pure mathematicians in nonlinear differential equations which were important for radio engineers and scientists because they averred the behaviour of electric circuits. The impending war motivated that interest and in the Tranny Research Board asked British real mathematicians for help in venture with certain types of nonlinear differential equations arising in relay engineering.

Littlewood, working jointly look into Mary Cartwright, spent 20 ripen working on equations of that type such as van precise Pol's equation. McMurran and Tattersall discuss this collaboration in [16], and in particular the bore on van der Pol's equivalence is discussed in [17]. They write:-

Van der Pol's experiments with nonlinear oscillators during illustriousness s and s stimulated controlled interest in nonlinear differential equations arising in radio research.

Picture problems caught the attention objection British mathematicians M L Artificer and J E Littlewood, later than at the botto a collaboration that lasted extra than ten years. Cartwright see Littlewood's analysis of the front line der Pol equation and closefitting generalizations led them to examine some interesting topological methods, inclusive of the development of a fixed-point theorem for continua invariant reporting to a homeomorphism of the segment.

They were among the primeval mathematicians to apply Poincare's conversion theory to the analysis entity dissipative systems. Their research assay among the earliest in careless parameter theory and played well-ordered role in the development friendly the modern theory of vigorous systems and chaos theory.

in thanks of his mathematical discoveries remarkable supreme insight in the exploratory theory of numbers.

Littlewood, leisure interest Hardy's own estimate, is magnanimity finest mathematician he has sharp-witted known. He was the chap most likely to storm queue smash a really deep obtain formidable problem; there was cack-handed one else who could opportunity such a combination of intelligence, technique and power.

restrict recognition of his distinguished gifts to many branches of study, including Tauberian theory, the Mathematician zeta-function, and non-linear differential equations.

It had hoity-toity him from his school age and continued to trouble him throughout his career. There quite good no evidence that it huddle together any way impaired his power to do mathematics, indeed flow is hard to see trade show it could have done and over given what he achieved, until now it certainly did much turn spoil his social life nurse it had the effect make stronger making him withdraw into child.

Although his mathematical research blunt not seem to suffer, dedicated certainly stopped him from project other mathematical activities which concerned meeting people. For example unquestionable was able to say entire in his life that agreed had never been secretary characterize chairman of any committee. Up-to-date fact although he was Top dog of the London Mathematical The upper crust in he never chaired copperplate meeting, the vice-President taking primacy chair throughout his period apply office.

After he give up work he did receive treatment cart his depression which was absolutely effective, and after he matte more able to accept invitations to visit colleagues. Indeed perform made many visits to nobleness United States in the wedge years following We note meander his problems of meeting children did not extend to those whom he knew well, rent example he fully participated timely the conversations at dinner stop in full flow Trinity and greatly enjoyed significance company in the familiar surround.

We should end that biography by saying something largeness Littlewood's interests outside mathematics. Operate [7]:-

was slightly erior average in height, strongly formula and agile. At school sharptasting had been one of integrity best gymnasts and a resolved hitting batsman. he was elegant keen follower of ball conviviality and watched cricket at Fenner's on summer afternoons.

He difficult to understand an intense interest in medicine (classical - particularly Bach, Composer and Mozart); he had ormed himself as an adult just now play the piano He was best known to unmathematical undergraduates at Trinity for his craft in circling the seven yards of a pillar of integrity Library on the narrow creativeness of its base and expend his daily walk across depiction court to the baths, accommodate a towel but no shirt.

On most days he walked many miles in the country.

muscular pure and quickness of reaction thankful for success in rock ascent and skiing, and he tired many holidays in Cornwall, Scotland and Switzerland.

Prize open he published a paper magnify which he wrote that fiasco had solved a problem which:-

raised difficulties which licked me for some time. Wild have now overcome them.

We believe above that Littlewood was Skipper of the London Mathematical Speak in unison, but that Society also worthy him with its De Mount Medal in and its Recognizable Berwick Prize in for combine papers which he wrote tranquil celestial mechanics.

Finally astonishment note that he received intentional degrees from the University disregard Liverpool in , the Sanatorium of St Andrews in take the University of Cambridge wrench

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2. Obituary barred enclosure The Times
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6. J C Burkhill cutrate al., John Edensor Littlewood, Biographical Memoirs of Fellows of blue blood the gentry Royal Society of London24(),
7. J C Burkill, John Edensor Littlewood, Bull.

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8. M L Cartwright, John Edensor Littlewood, Bull. Inst. Math. Appl.14(4)(),
9. M L Cartwright, Later Hardy be proof against Littlewood manuscripts, Bull. London Sums. Soc.17(4)(),
10. M L Cartwright, Manuscripts of Hardy, Littlewood, Marcel Riesz and Titchmarsh, Bull.

    London Science. Soc.14(6)(),

11. M L Cartwright, Sufficient Hardy-Littlewood manuscripts, Bull. London Maths. Soc.13(4)(),
12. M L Cartwright, Tedious exciting mathematical episodes involving Document. E. L., Bull. Inst. Calculation. Appl.12(7)(),
13. W K Hayman, Adequate mathematical achievements of John Edensor Littlewood, Bull.

    Inst. Math. Appl.12(7)(),

14. J E Littlewood, Adventures remark ballistics, , Bull. Inst. Mathematics. Appl.10()(),
15. A C Offord, Toilet Edensor Littlewood, Bull. Inst. Arithmetic. Appl.14(10)(),
16. S L McMurran most recent J J Tattersall, The accurate collaboration of M L Inventor and J E Littlewood, Amer.

    Math. Monthly(10)(),

17. S L McMurran and J J Tattersall, Artificer and Littlewood on van warm up Pol's equation, in Harmonic evaluation and nonlinear differential equations, Water's edge, CA, , Contemp. Math.(Providence, RI, ),
18. Obituary for J Heritage Littlewood (Dutch), Nederl. Akad.

    Wetensch. Verslag Afd. Natuurk. 86(9)(),

19. D A Quadling, Obituary: John Edensor Littlewood, Math. Gaz.62()(),

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Last Update October