David Rodney "Roger" Heath-Brown FRS (born 12 October 1952), 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, mathematical structure, structure, space, Mathematica ...

working in the field of analytic number theory.

Education

He was an undergraduate and graduate student of

Trinity College, Cambridge Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge or Oxford. ...

; his research supervisor was Alan Baker.

Career and research

In 1979 he moved to the

University of Oxford The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the world's second-oldest university in contin ...

, where from 1999 he held a

professorship Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors ...

pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...

. He retired in 2016. Heath-Brown is known for many striking results. He proved that there are infinitely many

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only way ...

s of the form ''x''³ + 2''y''³. In collaboration with S. J. Patterson in 1978 he proved the Kummer conjecture on cubic Gauss sums in its equidistribution form. He has applied Burgess's method on character sums to the ranks of elliptic curves in families. He proved that every non-singular cubic form over the

rational number In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ra ...

s in at least ten variables represents 0. Heath-Brown also showed that Linnik's constant is less than or equal to 5.5. More recently, Heath-Brown is known for his pioneering work on the so-called determinant method. Using this method he was able to prove a conjecture of Serre in the four variable case in 2002. This particular conjecture of Serre was later dubbed the "dimension growth conjecture" and this was almost completely solved by various works of Browning, Heath-Brown, and Salberger by 2009.

Awards and honours

The

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

has awarded Heath-Brown the Junior

Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the ...

(1981), the Senior Berwick Prize (1996), and the Pólya Prize (2009). He was made a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathematic ...

in 1993, and a corresponding member of the Göttingen Academy of Sciences in 1999. He was an invited speaker at

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in 1983 in

Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is official ...

and in 2010 in

Hyderabad Hyderabad ( ; , ) is the capital and largest city of the Indian state of Telangana and the ''de jure'' capital of Andhra Pradesh. It occupies on the Deccan Plateau along the banks of the Musi River (India), Musi River, in the northern part ...

on the topic of "''Number Theory.''" In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

. In 2022 the Royal Society awarded him the

Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry a ...

"for his many important contributions to the study of prime numbers and solutions to equations in integers".

Other

In September 2007, he co-authored (along with

Joseph H. Silverman Joseph Hillel Silverman (born March 27, 1955, New York City) is a professor of mathematics at Brown University working in arithmetic geometry, arithmetic dynamics, and cryptography. Biography Joseph Silverman received an Sc.B. from Brown Unive ...

) the preface to the Oxford University Sixth Edition of ''

An Introduction to the Theory of Numbers ''An Introduction to the Theory of Numbers'' is a classic textbook in the field of number theory, by G. H. Hardy and E. M. Wright. The book grew out of a series of lectures by Hardy and Wright and was first published in 1938. The third edition a ...

'' by G.H. Hardy and

E.M. Wright Sir Edward Maitland Wright (13 February 1906, Farnley – 2 February 2005, Reading) was an English mathematician, best known for co-authoring ''An Introduction to the Theory of Numbers'' with G. H. Hardy. Career He was born in Farnl ...

References

{{DEFAULTSORT:Heath-Brown, Roger Alumni of Trinity College, Cambridge 20th-century British mathematicians 21st-century British mathematicians Fellows of Magdalen College, Oxford Fellows of Worcester College, Oxford Fellows of the Royal Society Fellows of the American Mathematical Society Living people Number theorists 1952 births