**David Rees** was a Welsh mathematician who worked on semigroups and on commutatiive algebra. During World War II he worked on cracking codes.

- His undergraduate studies were supervised by Gordon Welchman (1906-1985), a fellow of Sidney Sussex College, and Rees graduated in 1939 as Second Wrangler.
- Rees continued to study at Cambridge but, on 1 September 1939, German troops invaded Poland and Britain declared war on Germany two days later.
- The outbreak of war caused a complete disruption in Rees's university studies since he was quickly recruited to undertake war work at Bletchley Park, the British codebreaking centre in Buckinghamshire.
- This took place before the outbreak of war while Rees was beginning his research career at Cambridge.
- They contain the concept known today as a Rees matrix semigroup which Rees defines and uses to classify completely 0-simple semigroups.
- This problem was quickly surmounted and Rees put his mathematical research on hold while he worked at Bletchley Park.
- John W Herivel (1918-2011), like Rees, had been an undergraduate at Cambridge.
- Herivel, who worked with Rees in Hut 6, made the suggestion in February 1940 that if the operators were lazy they might not move the rotors far from their position at the end of the last message sent on the previous day.
- This was one of the most significant breakthroughs in cracking the Enigma codes, although Rees later said that, 40 years after the event, he did not remember being the one to make the breakthrough.
- Rees was seconded to the Enigma Research Section in late 1941 to help with the task of decoding the Abwehr Enigma code used by the German secret service.
- Rees joined the "Newmanry" where the Colossus reduced the time taken to decode a message from days to hours.
- Rees, who was a very fine chess player, was a member of the winning team.
- Rees was appointed as an assistant lecturer in mathematics at the University of Manchester at the same time and assisted Newman in the pioneering work that led to the construction of the first mainframe computer.
- Rees was appointed as a lecturer at the University of Cambridge in 1948, becoming a fellow of Downing College.
- This seminar had two major impacts on Rees's life.
- Joan Rees became a Lecturer in Mathematics at the University of Exeter.
- Before moving into the area of commutative ring theory, Rees had published two further papers on semigroups, On the group of a set of partial transformations (1947) and On the ideal structure of a semi-group satisfying a cancellation law (1948).
- The influence of Douglas Northcott on Rees is easily seen since his first two papers on commutative rings are written in collaboration with him, namely Reductions of ideals in local rings (1954) and A note on reductions of ideals with an application to the generalized Hilbert function (1954).
- Over the next years, Rees continued to produce a whole series of important papers on local rings.
- In 1982 Rees lectured at Nagoya University in Japan, giving a course 'The asymptotic theory of ideals' during the winter of 1982-83.
- Rees produced duplicated lecture notes for those attending the course and copies were in circulation for several years.
- Over the last thirty-five years, few people could hope to rival the influence which David Rees has had in commutative ring theory.
- Many concepts are named after Rees which is a good indication of Rees's very significant influence on different areas of algebra.
- For example: the Artin-Rees lemma; Rees quotients; Rees-Sushkevich varieties; Rees algebras; Rees valuations; Rees polynomials; and Rees modules.
- Rees received many honours for his outstanding contributions.
- Conferences were organised to celebrate his 70th birthday and 'Commutative Algebra in Honour of David Rees's 80th Year' was held in Exeter in August 1998.
- David and Joan Rees built up a rather remarkable mathematical library which they kept in their Exeter home.
- However, eventually, both David and Joan moved into a care home in Exeter and they disposed of their mathematical library.
- David Rees died peacefully in hospital in Exeter aged 95.

Born 29 May 1918, Abergavenny, Monmouthshire, Wales. Died 16 August 2013, Exeter, England.

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Origin Wales

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive