Mary Cartwright
Encyclopedia
Dame Mary Lucy Cartwright DBE FRS (17 December 1900 – 3 April 1998) was a leading 20th-century British
mathematician
. She was born in Aynho
, Northamptonshire
where her father was the vicar
and died in Cambridge
, England. Through her Grandmother Jane Holbech she was descended from the poet John Donne
and William Mompesson the Vicar of Eyam.
She then taught at Alice Ottley School in Worcester
and Wycombe Abbey School in Buckinghamshire
before returning to Oxford in 1928 to read for her D.Phil.
She was supervised by G. H. Hardy
in her doctoral studies. During the academic year 1928–9 Hardy was at Princeton
, so it was E. C. Titchmarsh who took over the duties as a supervisor. Her thesis on zeros of entire function
s was examined by J. E. Littlewood
whom she met for the first time as an external examiner in her oral examination for the D.Phil. She would later become a major collaborator with Littlewood, over many years.
In 1930 Cartwright was awarded a Yarrow Research Fellowship and she went to Girton College, Cambridge
, to continue working on the topic of her doctoral thesis. Attending Littlewood's lectures, she solved one of the open problems which he posed. Her theorem, now known as Cartwright's theorem, gives an estimate for the maximum modulus of an analytic function
that takes the same value no more than p times in the unit disc. To prove the theorem she used a new approach, applying a technique introduced by Lars Ahlfors for conformal mappings
.
In 1936 she became director of studies in mathematics at Girton College, and in 1938 she began work on a new project which had a major impact on the direction of her research. The Radio Research Board of the Department of Scientific and Industrial Research
produced a memorandum regarding certain differential equations which came out of modeling radio and radar work. They asked the London Mathematical Society
if they could help find a mathematician who could work on these problems and Cartwright became interested in this memorandum. The dynamics lying behind the problems were unfamiliar to Cartwright so she approached Littlewood for help with this aspect. They began to collaborate studying the equations. Littlewood wrote:
The fine structure which Littlewood describes here is today seen to be a typical instance of the butterfly effect
. The collaboration led to important results, and these have greatly influenced the direction that the modern theory of dynamical systems has taken.
In 1945 she simplified Hermite
's elementary proof of the irrationality of π. Her version of the proof was published in an appendix to Sir Harold Jeffreys
' book Scientific Inference.
In 1947 she was elected to be a Fellow of the Royal Society and, although she was not the first woman to be elected to that Society, she was the first female mathematician.
Cartwright was appointed Mistress of Girton in 1948 then, in addition, a Reader in the Theory of Functions in Cambridge in 1959, holding this appointment until 1968.
She was the first woman:
She also received the De Morgan Medal
of the Society in 1968. In 1969 she received the distinction of being honoured by the Queen, becoming Dame Mary Cartwright, Dame Commander of the Order of the British Empire.
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....
. She was born in Aynho
Aynho
Aynho is a village and civil parish in South Northamptonshire, England, on the edge of the Cherwell valley about southeast of the north Oxfordshire town of Banbury and southwest of Brackley...
, Northamptonshire
Northamptonshire
Northamptonshire is a landlocked county in the English East Midlands, with a population of 629,676 as at the 2001 census. It has boundaries with the ceremonial counties of Warwickshire to the west, Leicestershire and Rutland to the north, Cambridgeshire to the east, Bedfordshire to the south-east,...
where her father was the vicar
Vicar
In the broadest sense, a vicar is a representative, deputy or substitute; anyone acting "in the person of" or agent for a superior . In this sense, the title is comparable to lieutenant...
and died in Cambridge
Cambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
, England. Through her Grandmother Jane Holbech she was descended from the poet John Donne
John Donne
John Donne 31 March 1631), English poet, satirist, lawyer, and priest, is now considered the preeminent representative of the metaphysical poets. His works are notable for their strong and sensual style and include sonnets, love poetry, religious poems, Latin translations, epigrams, elegies, songs,...
and William Mompesson the Vicar of Eyam.
She then taught at Alice Ottley School in Worcester
Worcester
The City of Worcester, commonly known as Worcester, , is a city and county town of Worcestershire in the West Midlands of England. Worcester is situated some southwest of Birmingham and north of Gloucester, and has an approximate population of 94,000 people. The River Severn runs through the...
and Wycombe Abbey School in Buckinghamshire
Buckinghamshire
Buckinghamshire is a ceremonial and non-metropolitan home county in South East England. The county town is Aylesbury, the largest town in the ceremonial county is Milton Keynes and largest town in the non-metropolitan county is High Wycombe....
before returning to Oxford in 1928 to read for her D.Phil.
She was supervised by 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....
in her doctoral studies. During the academic year 1928–9 Hardy was at Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, so it was E. C. Titchmarsh who took over the duties as a supervisor. Her thesis on zeros of entire function
Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic over the whole complex plane...
s was examined by J. E. Littlewood
John Edensor Littlewood
John Edensor Littlewood was a British mathematician, best known for the results achieved in collaboration with G. H. Hardy.-Life:...
whom she met for the first time as an external examiner in her oral examination for the D.Phil. She would later become a major collaborator with Littlewood, over many years.
In 1930 Cartwright was awarded a Yarrow Research Fellowship and she went to Girton College, 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...
, to continue working on the topic of her doctoral thesis. Attending Littlewood's lectures, she solved one of the open problems which he posed. Her theorem, now known as Cartwright's theorem, gives an estimate for the maximum modulus of an analytic function
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others...
that takes the same value no more than p times in the unit disc. To prove the theorem she used a new approach, applying a technique introduced by Lars Ahlfors for conformal mappings
Conformal geometry
In mathematics, conformal geometry is the study of the set of angle-preserving transformations on a space. In two real dimensions, conformal geometry is precisely the geometry of Riemann surfaces...
.
In 1936 she became director of studies in mathematics at Girton College, and in 1938 she began work on a new project which had a major impact on the direction of her research. The Radio Research Board of the Department of Scientific and Industrial Research
Department of Scientific and Industrial Research
Several countries have organizations called the Department of Scientific and Industrial Research, abbreviated DSIR.-United Kingdom:...
produced a memorandum regarding certain differential equations which came out of modeling radio and radar work. They asked 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:* * *...
if they could help find a mathematician who could work on these problems and Cartwright became interested in this memorandum. The dynamics lying behind the problems were unfamiliar to Cartwright so she approached Littlewood for help with this aspect. They began to collaborate studying the equations. Littlewood wrote:
The fine structure which Littlewood describes here is today seen to be a typical instance of the butterfly effect
Butterfly effect
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions; where a small change at one place in a nonlinear system can result in large differences to a later state...
. The collaboration led to important results, and these have greatly influenced the direction that the modern theory of dynamical systems has taken.
In 1945 she simplified Hermite
Charles Hermite
Charles Hermite was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra....
's elementary proof of the irrationality of π. Her version of the proof was published in an appendix to Sir Harold Jeffreys
Harold Jeffreys
Sir Harold Jeffreys, FRS was a mathematician, statistician, geophysicist, and astronomer. His seminal book Theory of Probability, which first appeared in 1939, played an important role in the revival of the Bayesian view of probability.-Biography:Jeffreys was born in Fatfield, Washington, County...
' book Scientific Inference.
In 1947 she was elected to be a Fellow of the Royal Society and, although she was not the first woman to be elected to that Society, she was the first female mathematician.
Cartwright was appointed Mistress of Girton in 1948 then, in addition, a Reader in the Theory of Functions in Cambridge in 1959, holding this appointment until 1968.
She was the first woman:
- to receive the Sylvester MedalSylvester MedalThe Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize...
- to serve on the Council of the Royal SocietyRoyal SocietyThe Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
- to be President of the London Mathematical SocietyLondon 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:* * *...
(in 1961–62)
She also received 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....
of the Society in 1968. In 1969 she received the distinction of being honoured by the Queen, becoming Dame Mary Cartwright, Dame Commander of the Order of the British Empire.
External links
- CWP
- "Mary Lucy Cartwright", Biographies of Women Mathematicians, Agnes Scott CollegeAgnes Scott CollegeAgnes Scott College is a private undergraduate college in the United States. Agnes Scott's campus lies in downtown Decatur, Georgia, nestled inside the perimeter of the bustling metro-Atlanta area....
- Times Obituary for Mary Cartwright