Klaus Friedrich Roth (29 October 1925 – 10 November 2015) was a German-born British mathematician who won the Fields Medal for proving Roth's theorem on the Diophantine approximation of algebraic numbers. He was also a winner of the De Morgan Medal and the Sylvester Medal, and a Fellow of the Royal Society. Roth moved to England as a child in 1933 to escape the Nazis, and was educated at the University of Cambridge and University College London, finishing his doctorate in 1950. He taught at University College London until 1966, when he took a chair at Imperial College London. He retired in 1988. Beyond his work on Diophantine approximation, Roth made major contributions to the theory of progression-free sets in arithmetic combinatorics and to the theory of irregularities of distribution. He was also known for his research on sums of powers, on the large sieve, on the Heilbronn triangle problem, and on square packing in a square. He was a coauthor of the book Sequences on integer sequences.
Biography
Early life Roth was born to a Jewish family in Breslau, Prussia, on 29 October 1925. His parents settled with him in London to escape Nazi persecution in 1933, and he was raised and educated in the UK. His father, a solicitor, had been exposed to poison gas during World War I and died while Roth was still young. Roth became a pupil at St Paul's School, London from 1939 to 1943, and with the rest of the school he was evacuated from London to Easthampstead Park during the Blitz. At school, he was known for his ability in both chess and mathematics. He tried to join the Air Training Corps, but was blocked for some years for being German and then after that for lacking the coordination needed for a pilot.
Mathematical education Roth read mathematics at Peterhouse, Cambridge, and played first board for the Cambridge chess team, finishing in 1945. Despite his skill in mathematics, he achieved only third-class honours on the Mathematical Tripos, because of his poor test-taking ability. His Cambridge tutor, John Charles Burkill, was not supportive of Roth continuing in mathematics, recommending instead that he take "some commercial job with a statistical bias". Instead, he briefly became a schoolteacher at Gordonstoun, between finishing at Cambridge and beginning his graduate studies. While in Gordonstoun, he became a regular chess partner of Robert Forbes Combe, who won the British championship the following year. On the recommendation of Harold Davenport, he was accepted in 1946 to a master's program in mathematics at University College London, where he worked under the supervision of Theodor Estermann. He completed a master's degree there in 1948, and a doctorate in 1950. His dissertation was Proof that almost all Positive Integers are Sums of a Square, a Positive Cube and a Fourth Power.
Career On receiving his master's degree in 1948, Roth became an assistant lecturer at University College London, and in 1950 he was promoted to lecturer. His most significant contributions, on Diophantine approximation, progression-free sequences, and discrepancy, were all published in the mid-1950s, and by 1958 he was given the Fields Medal, mathematicians' highest honour. However, it was not until 1961 that he was promoted to full professor. During this period, he continued to work closely with Harold Davenport. He took sabbaticals at the Massachusetts Institute of Technology in the mid-1950s and mid-1960s, and seriously considered migrating to the United States. Walter Hayman and Patrick Linstead countered this possibility, which they saw as a threat to British mathematics, with an offer of a chair in pure mathematics at Imperial College London, and Roth accepted the chair in 1966. He retained this position until official retirement in 1988. He remained at Imperial College as Visiting Professor until 1996. Roth's lectures were usually very clear but could occasionally be erratic. The Mathematics Genealogy Project lists him as having only two doctoral students, but one of them, William Chen, who continued Roth's work in discrepancy theory, became a Fellow of the Australian Mathematical Society and head of the mathematics department at Macquarie University.
Personal life In 1955, Roth married Mélèk Khaïry, who had attracted his attention when she was a student in his first lecture; Khaïry was a daughter of Egyptian senator Khaïry Pacha. She came to work for the psychology department at University College London, where she published research on the effects of toxins on rats. On Roth's retirement, they moved to Inverness; Roth dedicated a room of their house to Latin dancing, a shared interest of theirs. Khaïry died in 2002, and Roth died in Inverness on 10 November 2015 at the age of 90. They had no children, and Roth dedicated the bulk of his estate, over one million pounds, to two health charities "to help elderly and infirm people living in the city of Inverness". He sent the Fields Medal with a smaller bequest to Peterhouse.
Contributions Roth was known as a problem-solver in mathematics, rather than as a theory-builder. Harold Davenport writes that the "moral in Dr Roth's work" is that "the great unsolved problems of mathematics may still yield to direct attack, however difficult and forbidding they appear to be, and however much effort has already been spent on them". His research interests spanned several topics in number theory, discrepancy theory, and the theory of integer sequences.
Diophantine approximation
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