Klaus Friedrich Roth overcame early setbacks to become one of the 20th century’s most influential mathematicians, making breakthroughs at UCL that helped shape modern number theory.

It is not difficult to find the moral of Dr Roth's work. It is that the great unsolved problems may still yield to direct attack however difficult and forbidding they appear to be.

Harold Davenport, presenting Klaus Roth with the Fields Medal

Born to a Jewish family in Breslau (now Wrocław in Poland), Klaus Friedrich Roth (1925 – 2015) fled Nazi persecution with his parents, settling in London in 1933. He studied at St Paul’s School before reading mathematics at Peterhouse, University of Cambridge, where he also played first board for the university chess team. However, his years there were unhappy. He suffered from uncontrollable nerves, hampering his examination results, and he graduated with third class honours. 

Peterhouse declined to support Roth’s return after the war, with his tutor J. C. Burkill advising him to give up mathematics and pursue “some commercial job with a statistical bias.” Harold Davenport, however, recognised his exceptional talent and helped secure funding for him to begin PhD research at UCL. Roth went on to join the academic staff in 1950.  

It turned out to be a good move. In 1958, Roth won the Fields Medal, the ‘Nobel Prize’ of mathematics, for his breakthrough in Diophantine approximation, now called Roth’s Theorem. The theorem concerns the limits on how closely algebraic irrational numbers can be approximated by rational ones. He remained at UCL until 1966, becoming a professor in 1961 and elected a Fellow of the Royal Society in 1960. 

Roth went on to become a leading figure in geometric discrepancy theory, pioneering it as a subject, and, in the mid 1960s, he produced his seminal paper on the large sieve. This was a significant step towards advancing understanding of primes in arithmetic progressions, and the beginning of a major development in analytic number theory. His contributions were recognised with multiple honours, including the prestigious De Morgan Medal in 1983.  

Roth continues to inspire mathematicians around the world to approach big problems with courage and creativity. His Telegraph obituary hailed him as “a consummate problem‑solver,” a fitting characterisation of a man who repeatedly confronted mathematics’ most elusive challenges.

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