Sheila Oates Williams (1939 – 12 August 2024, also published as Sheila Oates and Sheila Oates Macdonald) was a British and Australian mathematician specializing in

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

. She was the namesake of the Oates–Powell theorem in

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

, and a winner of the B. H. Neumann Award.

Education and career

Sheila Oates was originally from

Cornwall Cornwall (; or ) is a Ceremonial counties of England, ceremonial county in South West England. It is also one of the Celtic nations and the homeland of the Cornish people. The county is bordered by the Atlantic Ocean to the north and west, ...

, where her father was a primary school headmaster in

Tintagel Tintagel () or Trevena (, meaning ''Village on a Mountain'') is a civil parishes in England, civil parish and village situated on the Atlantic Ocean, Atlantic coast of Cornwall, England, United Kingdom. The village and nearby Tintagel Castle ...

. She was educated at Sir James Smith's Grammar School, and inspired to become a mathematician by a teacher there, Alfred Hooper. She read mathematics at

St Hugh's College, Oxford St Hugh's College is a Colleges of the University of Oxford, constituent college of the University of Oxford. It is located on a site on St Margaret's Road, to the north of the city centre. It was founded in 1886 by Elizabeth Wordsworth as a ...

, with

Ida Busbridge Ida Winifred Busbridge (1908–1988) was a British mathematician who taught at the University of Oxford from 1935 until 1970. She was the first woman to be appointed to an Oxford fellowship in mathematics. Early life and education Ida Busbridg ...

as her tutor, and continued at Oxford as a doctoral student of

Graham Higman Graham Higman FRS (19 January 1917 – 8 April 2008) was a prominent English mathematician known for his contributions to group theory. Biography Higman was born in Louth, Lincolnshire, and attended Sutton High School, Plymouth, winning ...

. She completed her doctorate (D.Phil.) in 1963. She became a lecturer and fellow at

St Hilda's College, Oxford St Hilda's College (full name = Principal and Council of St. Hilda's College, Oxford) is a constituent college of the University of Oxford in England. The college is named after the Anglo-Saxon saint Hilda of Whitby and was founded in 1893 as a ...

, before moving to Australia in 1965. In 1966, she took a position as senior lecturer at the University of Newcastle and later moved to the

University of Queensland The University of Queensland is a Public university, public research university located primarily in Brisbane, the capital city of the Australian state of Queensland. Founded in 1909 by the Queensland parliament, UQ is one of the six sandstone ...

as reader. She retired in 1997.

Contributions

As a student at Oxford, with Martin B. Powell, another student of Higman, she proved the Oates–Powell theorem. This is an analogue for

Hilbert's basis theorem In mathematics Hilbert's basis theorem asserts that every ideal (ring theory), ideal of a polynomial ring over a field (mathematics), field has a finite generating set of an ideal, generating set (a finite ''basis'' in Hilbert's terminology). In ...

, and states that all

finite group In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving tra ...

s have a finite system of axioms from which can be derived all equations that are true of the group. That is, every finite group is finitely based. As well as for her research, Williams was known for her work setting Australian mathematics competitions, including the

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the wor ...

in 1988 and the

Australian Mathematics Competition The Australian Mathematics Competition is a mathematics competition run by the Australian Maths Trust for students from year 3 to year 12, in Australia, and their equivalent grades in other countries. History The forerunner of the competition, ...

. She also participated several times in the Australian edition of the ''

Mastermind Mastermind, Master Mind or The Mastermind may refer to: Fictional characters * Mastermind (Jason Wyngarde), a fictional supervillain in Marvel Comics, a title also held by his daughters: ** Martinique Jason, the first daughter and successor of the ...

'' television quiz show.

Recognition

Williams was a 2002 recipient of the B. H. Neumann Award for Excellence in Mathematics Enrichment of the Australian Maths Trust.

References

{{DEFAULTSORT:Williams, Sheila Oates 1939 births 2024 deaths Australian mathematicians Australian women mathematicians British mathematicians 21st-century British women mathematicians Alumni of St Hugh's College, Oxford Fellows of St Hilda's College, Oxford Academic staff of the University of Newcastle (Australia) Academic staff of the University of Queensland People from Tintagel