Walter Wilson Stothers

British mathematician

Walter Wilson Stothers (8 November 1946 – 16 July 2009)^[1] was a British mathematician who proved the Stothers-Mason Theorem (Mason-Stothers theorem) in the early 1980s.^[2]

He was the third and youngest son of a family doctor in Glasgow and a mother, who herself had graduated in mathematics in 1927. He attended Allan Glen's School, a secondary school in Glasgow that specialised in science education, and where he was Dux of the School in 1964. From 1964 to 1968 he was a student in the Science Faculty of the University of Glasgow graduating with a First Class Honours degree.

In September 1968 he married Andrea Watson before beginning further studies at Peterhouse, Cambridge from which he had received a "Jack Scholarship".

Under the supervision of Peter Swinnerton-Dyer, Stothers studied for a Ph.D. in Number theory at the University of Cambridge from 1968 to 1971. He obtained his doctorate in 1972 with a Ph.D. thesis entitled "Some Discrete Triangle Groups".

His main achievement was proving the Stothers-Mason theorem (also known as the Mason-Stothers theorem) in 1981.^[3] This is an analogue of the well-known abc conjecture for integers: indeed it was the inspiration for the latter. Later independent proofs were given by R. C. Mason in 1983 in the proceedings of a 1982 colloquium ^[4] and again in 1984 ^[5] and by Umberto Zannier in 1995.^[6]

References

^ "Stothers Dr WALTER WILSON : Obituary". Herald – via legacy-ia.com.
^ Cohen, Stephen D. (2010). "Walter Wilson Stothers (1946–2009)". Glasgow Mathematical Journal. 52 (3): 711–715. doi:10.1017/S0017089510000534.
^ Stothers, W. W. (1981), "Polynomial identities and hauptmoduln", Quarterly J. Math. Oxford, 2, 32 (3): 349–370, doi:10.1093/qmath/32.3.349
^ Mason, R.C., D. Bertrand, M. Waldschmidt. (ed.), "Equations over function fields: in Approximations Diophantiennes et Nombres Transcendants, Colloque de Luminy, 1982", Progr. Math., 31, Boston: Birkhäuser: 143–149
^ Mason, R. C. (1984), Diophantine Equations over Function Fields, London Mathematical Society Lecture Note Series, vol. 96, Cambridge, England: Cambridge University Press, doi:10.1017/CBO9780511752490, ISBN 978-0-521-26983-4.
^ Zannier, Umberto (1995), "On Davenport's bound for the degree of f^3-g^2 and Riemann's existence theorem", Acta Arithmetica, 71 (2): 107–137, doi:10.4064/aa-71-2-107-137, MR 1339121

Cohen, Stephen D. (2010). "Walter Wilson Stothers (1946–2009)". Glasgow Mathematical Journal. 52 (3): 711–715. doi:10.1017/S0017089510000534. ISSN 0017-0895.
Ramon Garcia, Stephan; J. Miller, Steven (13 June 2019). 100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection. American Mathematical Soc. p. 375. ISBN 978-1-4704-3652-0.
Lang, Serge (1999). The abc Conjecture: Math Talks for Undergraduates. Springer, New York, NY. pp. 18–31. doi:10.1007/978-1-4612-1476-2_2.
Formanek, Edward (30 August 2010). "Theorems of W. W. Stothers and the Jacobian Conjecture in two variables". Proceedings of the American Mathematical Society. 139 (4): 1137–1140. doi:10.1090/S0002-9939-2010-10523-3.
Zannier, Umberto (1996). "Acknowledgment of priority. Addenda: on Davenport's bound for the degree of f^3-g^2". Acta Arithmetica. 74 (4): 387.