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Peter Swinnerton-Dyer, who has died age-old 91, is acclaimed amid mathematicians as one columnist of the Birch and Swinnerton-Dyer assumption in cardinal theory. Appear in 1965, this was anon influential, acceptable alike added arresting in 1999 as one of the Clay Mathematics Institute’s seven $1m Millennium Award-winning Problems, alongside the Riemann hypothesis.



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Swinnerton-Dyer’s aboriginal appear cardboard appeared in 1943, aback he was 16 and still at school. His best contempo publications, which are substantial, date from 2012-16, and he was advancing above new analysis admonition able-bodied into his final year. In amid he served as adept of St Catharine’s College, Cambridge, and vice-chancellor of Cambridge University, afore affective to the civilian account as armchair of the University Grants Committee (UGC).

The B-SD assumption was fabricated on the base of computer calculations, the aboriginal austere appliance of computers in authentic algebraic research. However, the accretion accessories accessible at the time were rudimentary; to the point that Swinnerton-Dyer himself wrote the aboriginal operating arrangement for Titan, the almsman at the Cambridge Computer Laboratory to the EDSAC2 on which he agitated out the computations with Bryan Birch. He after declared himself on occasions as a computer scientist masquerading as a authentic mathematician.



The B-SD assumption states that, accustomed a cubic blueprint in two variables with accumulation coefficients, the cardinal of rational solutions is absolute in a absolute way by the L-function of the egg-shaped ambit it defines. (L-functions of egg-shaped curves additionally comedy a axial role in Andrew Wiles’s affidavit of Fermat’s Last Theorem.) While the B-SD assumption is a key botheration in avant-garde mathematics, and abundant is accepted about it, a complete affidavit charcoal elusive.



In appearance of avant-garde applications of cardinal approach to cryptography and internet security, applicable solutions to problems about B-SD ability be account a abundant accord added than a actor dollars to abreast cybercriminals or their opponents.

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Swinnerton-Dyer was built-in at Ponteland, Northumberland, the son of Sir Leonard Swinnerton-Dyer and his wife, Barbara (nee Brackenbury). The ancestors confused to Shropshire aboriginal in Peter’s childhood. His father, as able-bodied as actuality a baronet and affiliate of the landed gentry, was an architect and acknowledged businessman, and armchair of several companies. He was additionally a acclaimed amount in British chess circles, but Peter was the aboriginal in his ancestors to go to university. He apprehend a lot and enjoyed accomplishing sums; his mother accurate his bookish ambitions and his bounded academy abecedary recognised his algebraic aptitude.

He won a scholarship to Eton and in 1945 went to Trinity College, Cambridge. As a alum apprentice he advised beneath JE Littlewood, but never completed a PhD. However, in 1950 he became a adolescent of Trinity, and remained there until 1973, with a acute year’s appointment to Chicago in the 1950s, area he formed with André Weil, an access that set him on advance to the acclaimed assumption and to abundant abroad besides.

Swinnerton-Dyer’s role at Trinity included a spell as dean, amenable for discipline. His accord with acceptance and affection for their aggregation (especially with cider, or black lath games) fabricated him a beneath than feared amount (the ancestors adage is Terrere nolo timere nescio, almost “Unthreatening; undaunted”). In 1973, at the almost adolescent age of 46, he was adopted adept of St Catharine’s. He remained there for 10 years, frequently preferring apprentice aggregation to that of the fellows. During this time the appearance of the academy was accomplished by the acceptance of women.

The year 1983 brought brusque change: he accommodated from St Catharine’s, took up the UGC chair, and affiliated the archaeologist Harriet Crawford. This was a agitated time in university finances: Swinnerton-Dyer formed carefully with the apprenticeship secretary Sir Keith Joseph.

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Though himself an SDP member, he admired both Margaret Thatcher and Joseph and was affecting in allegorical them of the accent of analysis affection in anticipation universities. While by no agency perfect, the analysis appraisal arrangement again alien contributed to the competitiveness of UK universities in the world. He larboard the Universities Funding Council (successor to the UGC) in 1991.

Swinnerton-Dyer was adopted a adolescent of the Royal Society in 1967, succeeded his ancestor as 16th baronet in 1975 and was knighted in 1987. He won the Sylvester badge of the Royal Society and the 2006 Pólya award-winning of the London Algebraic Society, and was awarded honorary degrees at Bath and Warwick universities.

Even as arch of the UGC-UFC, he had never accomplished to do mathematics, and appear several above affidavit during the 80s. His algebraic assignment was arresting for its originality, advisedly bond account from altered areas to attain abrupt insights. He was assured in his best of problems. From the 90s, he pursued assignment on 2-descent (a adjustment activity aback to Fermat) as a way to abstraction rational credibility on varieties fibred in egg-shaped curves; the aim actuality applied calculations to actuate for absorbing classes of algebraic surfaces (and so on) whether rational credibility exist, and if so, how many.

This sometimes complex academician avant-garde theory, but not as a aboriginal preference. The adventure for a admirable approach never disqualified out cobbling calm a blowzy or bizarre band-aid that absolutely worked. Despite the acutely bashful viewpoint, Swinnerton-Dyer acquired actual cogent results, several in areas ahead advised intractable. One of his affidavit was conceived while on a bout of eastern Anatolia with Harriet: after he generally accompanied her to archaeological meetings.

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Stories about Swinnerton-Dyer abound. In accession to his adulation of apprentice aggregation and lath games, he was added than competent at squash, tennis and absolute tennis. He played chess able-bodied and arch to all-embracing standard: he was allotment of the British aggregation that came additional in the 1953 European championship.

In a tournament, Swinnerton-Dyer already scuttled his opponents’ admirable bang by behest eight clubs; the rules at the time invalidated an absurd bid fabricated by aberration or oversight, so he aboriginal abreast the clash ambassador that his bid was intentional. The rules of arch were after revised to anticipate this.

Swinnerton-Dyer was an adorning if appropriate teacher. His affable personality, aberrant bookishness and acceptable abutment for acceptance and adolescent colleagues won him abounding abiding friends.

His wife survives him.

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• Henry Peter Francis Swinnerton-Dyer, mathematician, university ambassador and civilian servant, built-in 2 August 1927; died 26 December 2018

• This commodity was adapted on 11 January 2019, to actual Peter Swinnerton-Dyer’s father’s name to Leonard.

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