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Professor Robert Vaughan, FRS (1956 - 1963)

Robert (Bob) Charles Vaughan is a Fellow of the Royal Society, elected 15th March, 1990.  On leaving Bishopshalt in 1963 he was an undergraduate and then a postgraduate student at University College London in mathematics, latterly specialising in analytic number theory under the supervision of Theodor Estermann.  Bob had postdoctoral positions at the University of Nottingham (1969 - 1970), where he came under the influence of Heini Halberstam, and the University of Sheffield (1970-72).  In 1972 he took up a permanent position at Imperial College London.  At Imperial there was a vibrant pure mathematical scene which included several leading researchers, Harry Reuter, Klaus Roth and Walter Hayman.  Another leading mathematician to influence Bob’s work was Paul Erdős.

Whilst in Nottingham, Heini Halberstam introduced Bob to a young American, Hugh Montgomery, who was completing a PhD with Harold Davenport in Cambridge.  They immediately started a collaboration which continues to this day.  In 1972 Hugh took up a position at the University of Michigan and this has led to a series of visiting positions at that university, including 1974-5, 1982-3, 1991, 1997-8.  On one of these visits in 1982, Bob met Anita Bosky, who was then studying for a PhD in special education and they were eventually married in 1992.  From 1992 until 1997 Bob held an EPSRC Senior Fellowship which was designed to facilitate his research and during which teaching and administration were expressly forbidden!  This allowed frequent visits to the USA to collaborate with Hugh and Trevor Wooley, one of Bob’s former students who was then also at Michigan.

When the Senior Fellowship came to an end, it became necessary to make an important decision.  The UK or the USA?  Since there was illness in Anita’s family it became clear that it had to be the USA.  Hence in 1999 Bob became a Professor at Penn State University.

Bob has over 130 research publications in refereed journals and two substantial graduate texts, and has contributed to a wide range of famous problems and techniques in number theory, including the Goldbach Conjecture, Waring’s Problem, The Hardy-Littlewood Method, square packing, the Duffin-Schaeffer conjecture, the Erdős–Straus conjecture, and character sums, and he even has an identity named after him.  In 1979 he received the Berwick Prize of the London Mathematical Society and in 1985 shared with Hugh Montgomery an Erdős prize for the solution to Erdős’ conjecture on reduced residues. In October 2018 he co-organised a meeting at the Royal Society to celebrate the centenary of the election of Srinivasa Ramanujan to the Royal Society.

In his youth Bob was also a keen chess player and in 1962 was Middlesex under 18 champion.  He continued to play at university and was captain of the university team in 1967 - 1968.  He was a member of the Middlesex team which won the county championship in 1969.  He also played for some years in the London League, the UK’s strongest league.  In the early 1980s he was on the League’s executive committee and was its President in 1981 – 1982.

Bob has an Erdős number of 1 and a Morphy number of 4.  Only Peter Swinnerton-Dyer has a comparable combined score with 2 and 3 respectively.

Bob is a keen follower of cricket and he has membership of both Middlesex and Surrey.  He gets to Lords and the Oval whenever he can, and usually spends all five days at the Oval test.

Bob continues to be employed full time with teaching and research.  He is continually amazed that he should be paid substantially for something which he thinks is fun and enjoys doing.  He intends to continue as long as he can do so competently.  He believes in Sir Nevill Cardus’s dictum that work is something he would give up if he won the pools.

 Bob Vaughan - May 2019