William Edward Hodgson Berwick
Encyclopedia
William Edward Hodgson Berwick (11 March 1888 in Dudley Hill, Bradford
– 13 May 1944 in Bangor, Gwynedd
) was a British
mathematician
, specializing in algebra
, who worked on the problem of computing an integral basis for the algebraic integer
s in a simple algebraic extension
of the rationals
.
. He completed his schooling in 1906, securing a Brown Scholarship to assist him in his university studies; he was also awarded an Entrance Scholarship by Clare College, Cambridge
, where he went to study for the Mathematical Tripos. He took Part I of the degree in 1909, placing joint fourth in the class, and Part II in 1910.
During his undergraduate years, under the tutelage of G B Matthews, Berwick became interested in number theory
. He submitted an essay entitled An illustration of the theory of relative corpora for the Smith's Prize in 1911; the essay was placed second in the prize competition. He then co-wrote, with Matthews, a paper On the reduction of arithmetical binary cubics which have a negative determinant: it was published after Berwick had left Cambridge to take up an assistant lectureship at the University of Bristol
, and was the only paper Berwick co-authored in his career.
Berwick taught at Bristol until 1913 when he took up another lectureship at the University College of Bangor. With the outbreak of the First World War in 1914 Berwick began war work on the Technical Staff of the Anti-Aircraft Experimental Section of the Munitions Inventions Department at Portsmouth
. For the 1919–20 academic year Berwick was appointed acting head of the Bangor mathematics department; he then took up a lectureship at the University of Leeds
, earning promotion to a Readership in Mathematical Analysis there in 1921. He was also elected to a fellowship at Clare College, Cambridge, in 1921.
In 1926, with thirteen research papers to his name, Berwick returned to Bangor to serve as Chairman of Mathematics. He had in 1925 become a member of the Council of the London Mathematical Society
; in 1929 he was appointed Vice-President. He retired the post in 1941, at which point he was created Emeritus Professor.
s in a simple algebraic extension
of the rationals
, and studied rings
in algebraic integers. In 1927 he published Integral Bases, an ambitious account that used heavy numerical computations in place of practical proofs.
He published sixteen papers, ten of them — including a 1915 paper giving sufficient conditions for a quintic expression to be solved by radicals — in Proceedings of the London Mathematical Society. Much of his work gained recognition only in the 1960s, when it was republished.
player, participating in the clubs at his various universities. He had a keen interest in teaching, publishing a number of mathematical recreation articles and giving several addresses at meetings of the British Association
.
In 1923, while living in Leeds
, Berwick married Daisy May Thomas, the daughter of Dr W R Thomas. His health began to fail after his 1926 return to Bangor; he published only five further papers after taking up this position. He died in Bangor, Maine
in 1944.
Bradford
Bradford lies at the heart of the City of Bradford, a metropolitan borough of West Yorkshire, in Northern England. It is situated in the foothills of the Pennines, west of Leeds, and northwest of Wakefield. Bradford became a municipal borough in 1847, and received its charter as a city in 1897...
– 13 May 1944 in Bangor, Gwynedd
Bangor, Gwynedd
Bangor is a city in Gwynedd, north west Wales, and one of the smallest cities in Britain. It is a university city with a population of 13,725 at the 2001 census, not including around 10,000 students at Bangor University. Including nearby Menai Bridge on Anglesey, which does not however form part of...
) was a British
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, specializing in algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, who worked on the problem of computing an integral basis for the algebraic integer
Algebraic integer
In number theory, an algebraic integer is a complex number that is a root of some monic polynomial with coefficients in . The set of all algebraic integers is closed under addition and multiplication and therefore is a subring of complex numbers denoted by A...
s in a simple algebraic extension
Algebraic extension
In abstract algebra, a field extension L/K is called algebraic if every element of L is algebraic over K, i.e. if every element of L is a root of some non-zero polynomial with coefficients in K. Field extensions that are not algebraic, i.e...
of the rationals
Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...
.
Academic career
Berwick was educated at a small private school before entering Bradford Grammar SchoolBradford Grammar School
Bradford Grammar School is a co-educational, independent school in Frizinghall, Bradford, West Yorkshire. Headmaster, Stephen Davidson is a member of the Headmasters' and Headmistresses' Conference . The school was founded in 1548 and granted its Charter by King Charles II in 1662...
. He completed his schooling in 1906, securing a Brown Scholarship to assist him in his university studies; he was also awarded an Entrance Scholarship by Clare College, Cambridge
Clare College, Cambridge
Clare College is a constituent college of the University of Cambridge in Cambridge, England.The college was founded in 1326, making it the second-oldest surviving college of the University after Peterhouse. Clare is famous for its chapel choir and for its gardens on "the Backs"...
, where he went to study for the Mathematical Tripos. He took Part I of the degree in 1909, placing joint fourth in the class, and Part II in 1910.
During his undergraduate years, under the tutelage of G B Matthews, Berwick became interested in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. He submitted an essay entitled An illustration of the theory of relative corpora for the Smith's Prize in 1911; the essay was placed second in the prize competition. He then co-wrote, with Matthews, a paper On the reduction of arithmetical binary cubics which have a negative determinant: it was published after Berwick had left Cambridge to take up an assistant lectureship at the University of Bristol
University of Bristol
The University of Bristol is a public research university located in Bristol, United Kingdom. One of the so-called "red brick" universities, it received its Royal Charter in 1909, although its predecessor institution, University College, Bristol, had been in existence since 1876.The University is...
, and was the only paper Berwick co-authored in his career.
Berwick taught at Bristol until 1913 when he took up another lectureship at the University College of Bangor. With the outbreak of the First World War in 1914 Berwick began war work on the Technical Staff of the Anti-Aircraft Experimental Section of the Munitions Inventions Department at Portsmouth
Portsmouth
Portsmouth is the second largest city in the ceremonial county of Hampshire on the south coast of England. Portsmouth is notable for being the United Kingdom's only island city; it is located mainly on Portsea Island...
. For the 1919–20 academic year Berwick was appointed acting head of the Bangor mathematics department; he then took up a lectureship at the University of Leeds
University of Leeds
The University of Leeds is a British Redbrick university located in the city of Leeds, West Yorkshire, England...
, earning promotion to a Readership in Mathematical Analysis there in 1921. He was also elected to a fellowship at Clare College, Cambridge, in 1921.
In 1926, with thirteen research papers to his name, Berwick returned to Bangor to serve as Chairman of Mathematics. He had in 1925 become a member of the Council of the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
; in 1929 he was appointed Vice-President. He retired the post in 1941, at which point he was created Emeritus Professor.
Research and publications
Berwick was an algebraist, and worked on the problem of computing an integral basis for the algebraic integerAlgebraic integer
In number theory, an algebraic integer is a complex number that is a root of some monic polynomial with coefficients in . The set of all algebraic integers is closed under addition and multiplication and therefore is a subring of complex numbers denoted by A...
s in a simple algebraic extension
Algebraic extension
In abstract algebra, a field extension L/K is called algebraic if every element of L is algebraic over K, i.e. if every element of L is a root of some non-zero polynomial with coefficients in K. Field extensions that are not algebraic, i.e...
of the rationals
Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...
, and studied rings
Ring (mathematics)
In mathematics, a ring is an algebraic structure consisting of a set together with two binary operations usually called addition and multiplication, where the set is an abelian group under addition and a semigroup under multiplication such that multiplication distributes over addition...
in algebraic integers. In 1927 he published Integral Bases, an ambitious account that used heavy numerical computations in place of practical proofs.
He published sixteen papers, ten of them — including a 1915 paper giving sufficient conditions for a quintic expression to be solved by radicals — in Proceedings of the London Mathematical Society. Much of his work gained recognition only in the 1960s, when it was republished.
Personal life
Berwick was described as a tall man with a distinctive voice and forthright personal style. He was a keen chessChess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
player, participating in the clubs at his various universities. He had a keen interest in teaching, publishing a number of mathematical recreation articles and giving several addresses at meetings of the British Association
British Association for the Advancement of Science
frame|right|"The BA" logoThe British Association for the Advancement of Science or the British Science Association, formerly known as the BA, is a learned society with the object of promoting science, directing general attention to scientific matters, and facilitating interaction between...
.
In 1923, while living in Leeds
Leeds
Leeds is a city and metropolitan borough in West Yorkshire, England. In 2001 Leeds' main urban subdivision had a population of 443,247, while the entire city has a population of 798,800 , making it the 30th-most populous city in the European Union.Leeds is the cultural, financial and commercial...
, Berwick married Daisy May Thomas, the daughter of Dr W R Thomas. His health began to fail after his 1926 return to Bangor; he published only five further papers after taking up this position. He died in Bangor, Maine
Bangor, Maine
Bangor is a city in and the county seat of Penobscot County, Maine, United States, and the major commercial and cultural center for eastern and northern Maine...
in 1944.