Martin Neil Huxley (born in 1944) is a British

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, working in the field of

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Diric ...

. He was awarded a PhD from the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

in 1970, the year after his supervisor

Harold Davenport Harold Davenport FRS (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory. Early life Born on 30 October 1907 in Huncoat, Lancashire, Davenport was educated at Accrington Grammar Schoo ...

had died. He is a professor at

Cardiff University , latin_name = , image_name = Shield of the University of Cardiff.svg , image_size = 150px , caption = Coat of arms of Cardiff University , motto = cy, Gwirionedd, Undod a Chytgord , mottoeng = Truth, Unity and Concord , established = 1 ...

. Huxley proved a result on

gaps between prime numbers A prime gap is the difference between two successive prime numbers. The ''n''-th prime gap, denoted ''g'n'' or ''g''(''p'n'') is the difference between the (''n'' + 1)-th and the ''n''-th prime numbers, i.e. :g_n = p_ - p_n.\ W ...

, namely that if ''p''_''n'' denotes the ''n''-th prime number and if θ > 7/12, then :

p_ - p_n < p_n^\theta,

for all

sufficiently large In the mathematical areas of number theory and analysis, an infinite sequence or a function is said to eventually have a certain property, if it doesn't have the said property across all its ordered instances, but will after some instances have pa ...

''n''. Huxley also improved the known bound on the

Dirichlet divisor problem Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and ...

References

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* Living people 21st-century British mathematicians 20th-century British mathematicians Number theorists Academics of Cardiff University Alumni of the University of Cambridge 1944 births {{UK-mathematician-stub