John Edensor Littlewood
Encyclopedia
John Edensor Littlewood (9 June 1885 – 6 September 1977) was a British
mathematician
, best known for the results achieved in collaboration with G. H. Hardy
.
. He lived in Wynberg in Cape Town
from 1892 to 1900 where his father (a 9th wrangler) was a headmaster. He then attended St Paul's School in London
for three years, where he was taught by F. S. Macaulay, now known for his contributions to ideal theory
. He studied at Trinity College, Cambridge
and was the Senior Wrangler in the Mathematical Tripos of 1905. He was elected a Fellow of Trinity College in 1908 and, apart from three years as Richardson Lecturer
in the University of Manchester
, his entire career was spent in the University of Cambridge
. He was appointed Rouse Ball Professor of Mathematics in 1928, retiring in 1950. He was elected a Fellow of the Royal Society in 1916, awarded the Royal Medal
in 1929, the Sylvester Medal
in 1943 and the Copley Medal
in 1958. He was president of the London Mathematical Society
from 1941 to 1943, and was awarded the De Morgan Medal
in 1938 and the Senior Berwick Prize
in 1960.
John Edensor Littlewood was born in 1885, the son of Edward Thornton Littlewood and Sylvia Ackland. His unusual middle name came was the maiden name of his Great-great Grandmother Sarah Edensor who married Thomas Littlewood.
. He began research under the supervision of Ernest William Barnes
, who suggested that he attempt to prove the Riemann hypothesis
: Littlewood showed that if the Riemann hypothesis is true then the Prime Number Theorem
follows and obtained the error term. This work won him his Trinity fellowship.
He coined Littlewood's law
, which states that individuals can expect miracles to happen to them, at the rate of about one per month.
He continued to write papers into his eighties, particularly in analytical areas of what would become the theory of dynamical systems.
He is also remembered for his book of reminiscences, A Mathematician's Miscellany
(new edition published in 1986).
Among his own Ph. D. students were Sarvadaman Chowla, Harold Davenport
and Donald C. Spencer
. Spencer reported that in 1941 when he (Spencer) was about to get on the boat that would take him home to the United States
, Littlewood reminded him: "n, n alpha, n beta!" (referring to Littlewood's conjecture).
His collaborative work, carried out by correspondence, covered fields in Diophantine approximation
and Waring's problem
, in particular. In his other work Littlewood collaborated with Raymond Paley
on Littlewood–Paley theory
in Fourier theory
, and with Cyril Offord
in combinatorial work on random sums, in developments that opened up fields still intensively studied.
He worked with Mary Cartwright
on problems in differential equations arising out of early research on radar
: their work foreshadowed the modern theory of dynamical systems. Littlewood's inequality on bilinear forms was a forerunner of the later Grothendieck tensor norm theory.
. Together they devised the first Hardy–Littlewood conjecture, a strong form of the twin prime conjecture, and the second Hardy–Littlewood conjecture.
In a 1947 lecture, the Danish mathematician Harald Bohr
said, "To illustrate to what extent Hardy and Littlewood in the course of the years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: 'Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy–Littlewood.'"
There is a story (related in the Miscellany) that at a conference Littlewood met a German mathematician who said he was most interested to discover that Littlewood really existed, as he had always assumed that Littlewood was a name used by Hardy for lesser work which he did not want to put out under his own name; Littlewood apparently roared with laughter. There are versions of this story involving both Norbert Wiener
and Edmund Landau
, who, it is claimed, "so doubted the existence of Littlewood that he made a special trip to Great Britain to see the man with his own eyes".
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, best known for the results achieved in collaboration with G. H. Hardy
G. H. Hardy
Godfrey Harold “G. H.” Hardy FRS was a prominent English mathematician, known for his achievements in number theory and mathematical analysis....
.
Life
Littlewood was born in Rochester in KentKent
Kent is a county in southeast England, and is one of the home counties. It borders East Sussex, Surrey and Greater London and has a defined boundary with Essex in the middle of the Thames Estuary. The ceremonial county boundaries of Kent include the shire county of Kent and the unitary borough of...
. He lived in Wynberg in Cape Town
Cape Town
Cape Town is the second-most populous city in South Africa, and the provincial capital and primate city of the Western Cape. As the seat of the National Parliament, it is also the legislative capital of the country. It forms part of the City of Cape Town metropolitan municipality...
from 1892 to 1900 where his father (a 9th wrangler) was a headmaster. He then attended St Paul's School in London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
for three years, where he was taught by F. S. Macaulay, now known for his contributions to ideal theory
Ideal theory
In mathematics, ideal theory is the theory of ideals in commutative rings; and is the precursor name for the contemporary subject of commutative algebra...
. He studied at Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
and was the Senior Wrangler in the Mathematical Tripos of 1905. He was elected a Fellow of Trinity College in 1908 and, apart from three years as Richardson Lecturer
Richardson Chair of Applied Mathematics
The Richardson Chair of Applied Mathematics is an endowed professorial position in the School of Mathematics, University of Manchester, England. The chair was founded by an endowment of £3,600 from one John Richardson, in 1890. The endowment was originally used to support the Richardson...
in the University of Manchester
School of Mathematics, University of Manchester
The School of Mathematics at the University of Manchester is one of the largest mathematics departments in the United Kingdom, with around 80 academic staff and an undergraduate intake of roughly 400 a year and another 200 postgraduate students...
, his entire career was spent in the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
. He was appointed Rouse Ball Professor of Mathematics in 1928, retiring in 1950. He was elected a Fellow of the Royal Society in 1916, awarded the Royal Medal
Royal Medal
The Royal Medal, also known as The Queen's Medal, is a silver-gilt medal awarded each year by the Royal Society, two for "the most important contributions to the advancement of natural knowledge" and one for "distinguished contributions in the applied sciences" made within the Commonwealth of...
in 1929, the Sylvester Medal
Sylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize...
in 1943 and the Copley Medal
Copley Medal
The Copley Medal is an award given by the Royal Society of London for "outstanding achievements in research in any branch of science, and alternates between the physical sciences and the biological sciences"...
in 1958. He was president of the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
from 1941 to 1943, and was awarded the De Morgan Medal
De Morgan Medal
The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the society....
in 1938 and the Senior Berwick Prize
Berwick Prizes
The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the society to establish two prizes...
in 1960.
John Edensor Littlewood was born in 1885, the son of Edward Thornton Littlewood and Sylvia Ackland. His unusual middle name came was the maiden name of his Great-great Grandmother Sarah Edensor who married Thomas Littlewood.
Work
Most of his work was in the field of mathematical analysisMathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
. He began research under the supervision of Ernest William Barnes
Ernest William Barnes
Ernest William Barnes FRS was an English mathematician and scientist who later became a theologian and bishop....
, who suggested that he attempt to prove the Riemann hypothesis
Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by , is a conjecture about the location of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2...
: Littlewood showed that if the Riemann hypothesis is true then the Prime Number Theorem
Prime number theorem
In number theory, the prime number theorem describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are distributed amongst the positive integers....
follows and obtained the error term. This work won him his Trinity fellowship.
He coined Littlewood's law
Littlewood's law
Littlewood's Law states that individuals can expect a "miracle" to happen to them at the rate of about one per month.-History:The law was framed by Cambridge University Professor J. E...
, which states that individuals can expect miracles to happen to them, at the rate of about one per month.
He continued to write papers into his eighties, particularly in analytical areas of what would become the theory of dynamical systems.
He is also remembered for his book of reminiscences, A Mathematician's Miscellany
A Mathematician's Miscellany
A Mathematician's Miscellany is now out of print but Littlewood's Miscellany is its successor, published by Cambridge University Press....
(new edition published in 1986).
Among his own Ph. D. students were Sarvadaman Chowla, Harold Davenport
Harold Davenport
Harold Davenport FRS was an English mathematician, known for his extensive work in number theory.-Early life:...
and Donald C. Spencer
Donald C. Spencer
Donald Clayton Spencer was an American mathematician, known for major work on deformation theory of structures arising in differential geometry, and on several complex variables from the point of view of partial differential equations. He was born in Boulder, Colorado, and educated at the...
. Spencer reported that in 1941 when he (Spencer) was about to get on the boat that would take him home to the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, Littlewood reminded him: "n, n alpha, n beta!" (referring to Littlewood's conjecture).
His collaborative work, carried out by correspondence, covered fields in Diophantine approximation
Diophantine approximation
In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers....
and Waring's problem
Waring's problem
In number theory, Waring's problem, proposed in 1770 by Edward Waring, asks whether for every natural number k there exists an associated positive integer s such that every natural number is the sum of at most s kth powers of natural numbers...
, in particular. In his other work Littlewood collaborated with Raymond Paley
Raymond Paley
Raymond Edward Alan Christopher Paley was an English mathematician. Paley was born in Bournemouth, England. He was educated at Eton. From there he entered Trinity College, Cambridge where he showed himself the most brilliant student among a remarkable collection of fellow undergraduates...
on Littlewood–Paley theory
Littlewood–Paley theory
In harmonic analysis, Littlewood–Paley theory is a term used to describe a theoretical framework used to extend certain results about L2 functions to Lp functions for 11, then the sequence Snj converges almost everywhere...
in Fourier theory
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
, and with Cyril Offord
Cyril Offord
Albert Cyril Offord FRS was a British mathematician. He received two Ph.D.s in mathematics: from the University of London in 1932, and from Oxford in 1936....
in combinatorial work on random sums, in developments that opened up fields still intensively studied.
He worked with Mary Cartwright
Mary Cartwright
Dame Mary Lucy Cartwright DBE FRS was a leading 20th-century British mathematician. She was born in Aynho, Northamptonshire where her father was the vicar and died in Cambridge, England...
on problems in differential equations arising out of early research on radar
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
: their work foreshadowed the modern theory of dynamical systems. Littlewood's inequality on bilinear forms was a forerunner of the later Grothendieck tensor norm theory.
With Hardy
He collaborated for many years with G. H. HardyG. H. Hardy
Godfrey Harold “G. H.” Hardy FRS was a prominent English mathematician, known for his achievements in number theory and mathematical analysis....
. Together they devised the first Hardy–Littlewood conjecture, a strong form of the twin prime conjecture, and the second Hardy–Littlewood conjecture.
In a 1947 lecture, the Danish mathematician Harald Bohr
Harald Bohr
Harald August Bohr was a Danish mathematician and football player. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr...
said, "To illustrate to what extent Hardy and Littlewood in the course of the years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: 'Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy–Littlewood.'"
There is a story (related in the Miscellany) that at a conference Littlewood met a German mathematician who said he was most interested to discover that Littlewood really existed, as he had always assumed that Littlewood was a name used by Hardy for lesser work which he did not want to put out under his own name; Littlewood apparently roared with laughter. There are versions of this story involving both Norbert Wiener
Norbert Wiener
Norbert Wiener was an American mathematician.A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is regarded as the originator of cybernetics, a...
and Edmund Landau
Edmund Landau
Edmund Georg Hermann Landau was a German Jewish mathematician who worked in the fields of number theory and complex analysis.-Biography:...
, who, it is claimed, "so doubted the existence of Littlewood that he made a special trip to Great Britain to see the man with his own eyes".
See also
- Critical line theorem
- Hardy–Littlewood circle method
- Hardy–Littlewood zeta-function conjecturesHardy–Littlewood zeta-function conjecturesIn mathematics, the Hardy–Littlewood zeta-function conjectures, named after Godfrey Harold Hardy and John Edensor Littlewood, are two conjectures concerning the distances between zeros and the density of zeros of the Riemann zeta function....
- Littlewood's conjecture
- Littlewood polynomialLittlewood polynomialIn mathematics, a Littlewood polynomial is a polynomial all of whose coefficients are +1 or −1.Littlewood's problem asks how large the values of such a polynomial must be on the unit circle in the complex plane. The answer to this would yield information about the autocorrelation of binary...
- Littlewood's three principles of real analysisLittlewood's three principles of real analysisLittlewood's three principles of real analysis are heuristics of J. E. Littlewood to help teach the essentials of measure theory in mathematical analysis.-The principles:Littlewood stated the principles in his 1944 Lectures on the Theory of Functions...
- Littlewood–Offord problem
- Hardy–Littlewood tauberian theoremHardy–Littlewood tauberian theoremIn mathematical analysis, the Hardy–Littlewood tauberian theorem is a tauberian theorem relating the asymptotics of the partial sums of a series with the asymptotics of its Abel summation...
- Hardy–Littlewood maximal function
Further reading
- Littlewood's Miscellany, edited by B. Bollobás, Cambridge University PressCambridge University PressCambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...
; 1986. ISBN 0-521-33702-X (alternative title for A Mathematician's MiscellanyA Mathematician's MiscellanyA Mathematician's Miscellany is now out of print but Littlewood's Miscellany is its successor, published by Cambridge University Press....
)