Bernhard Neumann

Last updated
Bernhard Neumann
Bernhard Neumann.jpg
Born(1909-10-15)15 October 1909
Died20 October 2002(2002-10-20) (aged 93)
NationalityBritish and Australian
Alma mater University of Berlin
University of Cambridge
Known for Petr–Douglas–Neumann theorem
Hahn–Mal'cev–Neumann series
HNN extension
Outer billiard
Absolute presentation of a group
Awards Adams Prize (1952)
Scientific career
Fields Mathematics
Institutions Australian National University
University of Manchester
Doctoral advisor Issai Schur
Philip Hall
Doctoral students Gilbert Baumslag
John Britton
James Wiegold

Bernhard Hermann Neumann AC FRS [1] (15 October 1909 – 21 October 2002) was a German-born British-Australian mathematician who was a leader in the study of group theory. [2] [3]


Early life and education

After gaining a D.Phil. from Friedrich-Wilhelms Universität in Berlin in 1932 he earned a Ph.D. at the University of Cambridge in 1935 and a Doctor of Science at the University of Manchester in 1954. His doctoral students included Gilbert Baumslag, László Kovács, Michael Newman, and James Wiegold. After war service with the British Army, he became a lecturer at University College, Hull, before moving in 1948 to the University of Manchester, where he spent the next 14 years. In 1954 he received a DSc from the University of Cambridge.

In 1962 he migrated to Australia to take up Foundation Chair of the Department of Mathematics within the Institute of Advanced Studies of the Australian National University (ANU), where he served as head of the department until retiring in 1974. In addition he was a senior research fellow at the CSIRO Division of Mathematics and Statistics from 1975 to 1977 and then honorary research fellow from 1978 until his death in 2002.

His wife, Hanna Neumann, and son, Peter M. Neumann, are also notable for their contributions to group theory.

He was an invited speaker of the International Congress of Mathematicians in 1936 at Oslo [4] and in 1970 at Nice. He was elected a Fellow of the Royal Society in 1959. [1] In 1994, he was appointed a Companion of the Order of Australia (AC). [5]

The Australian Mathematical Society awards a student prize named in his honour. [6] The group-theoretic notion of HNN extension (where HNN stands for Higman–Neumann–Neumann) is named in (second) part after him.



Related Research Articles

Martin John Dunwoody is an emeritus professor of Mathematics at the University of Southampton, England.

Keith Devlin

Keith J. Devlin is a British mathematician and popular science writer. Since 1987 he has lived in the United States. He has dual British-American citizenship.

Louis J. Mordell

Louis Joel Mordell was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction.

Ioan Mackenzie James FRS is a British mathematician working in the field of topology particularly in homotopy theory.

Dusa McDuff Mathematician

Dusa McDuff FRS CorrFRSE is an English mathematician who works on symplectic geometry. She was the first recipient of the Ruth Lyttle Satter Prize in Mathematics, was a Noether Lecturer, and is a Fellow of the Royal Society.

Kurt Mahler

Kurt Mahler FRS was a mathematician who worked in the fields of transcendental number theory, diophantine approximation, p-adic analysis, and the geometry of numbers.

Robert Alexander Rankin FRSE FRSAMD was a Scottish mathematician who worked in analytic number theory.

Sydney Goldstein FRS was a British mathematician noted for his contribution to fluid dynamics. He is described as: "... one of those who most influenced progress in fluid dynamics during the 20th century."

P. A. P. Moran

Patrick Alfred Pierce Moran FRS, commonly known as Pat Moran was an Australian statistician who made significant contributions to probability theory and its application to population and evolutionary genetics.

Hanna Neumann German Australian mathematician

Johanna (Hanna) Neumann was a German-born mathematician who worked on group theory.

Peter M. Neumann English mathematician

Peter Michael Neumann OBE was a British mathematician. He was a son of the German-born mathematicians Bernhard Neumann and Hanna Neumann and, after gaining a BA degree from The Queen's College, Oxford in 1963, obtained his DPhil degree from Oxford University in 1966.

Peter Cameron (mathematician) Australian mathematician

Peter Jephson Cameron FRSE is an Australian mathematician who works in group theory, combinatorics, coding theory, and model theory. He is currently half-time Professor of Mathematics at the University of St Andrews, and Emeritus Professor at Queen Mary University of London.

Cheryl Praeger Australian mathematician

Cheryl Elisabeth Praeger is an Australian mathematician. Praeger received BSc (1969) and MSc degrees from the University of Queensland (1974), and a doctorate from the University of Oxford in 1973 under direction of Peter M. Neumann. She has published widely and has advised 27 PhD students. She is currently Emeritus Professor of Mathematics at the University of Western Australia. She is best known for her works in group theory, algebraic graph theory and combinatorial designs.

Department of Mathematics, University of Manchester

The Department of Mathematics at the University of Manchester is one of the largest unified mathematics departments in the United Kingdom, with over 90 academic staff and an undergraduate intake of roughly 400 students per year and approximately 200 postgraduate students in total. The School of Mathematics was formed in 2004 by the merger of the mathematics departments of University of Manchester Institute of Science and Technology (UMIST) and the Victoria University of Manchester (VUM). In July 2007 the department moved from the Mathematics Tower into a purpose-designed building─the first three floors of the Alan Turing Building─on Upper Brook Street. In a Faculty restructure in 2019 the School of Mathematics reverted to the Department of Mathematics. It is one of five Departments that make up the School of Natural Sciences, which together with the School of Engineering now constitutes the Faculty of Science and Engineering at Manchester.

Andrew Majda American mathematician

Andrew Joseph Majda is an American mathematician and the Morse Professor of Arts and Sciences at the Courant Institute of Mathematical Sciences of New York University. He is known for his theoretical contributions to partial differential equations as well as his applied contributions to diverse areas including shock waves, combustion, incompressible flow, vortex dynamics, and atmospheric sciences. Majda is listed as an ISI highly cited researcher in mathematics.

James Wiegold

James "Jim" Wiegold was a Welsh mathematician.

Caroline Series English mathematician

Caroline Mary Series is an English mathematician known for her work in hyperbolic geometry, Kleinian groups and dynamical systems.

Anne Penfold Street Australian mathematician

Anne Penfold Street (1932–2016) was one of Australia's leading mathematicians, specialising in combinatorics. She was the third woman to become a mathematics professor in Australia, following Hanna Neumann and Cheryl Praeger. She was the author of several textbooks, and her work on sum-free sets became a standard reference for its subject matter. She helped found several important organizations in combinatorics, developed a researcher network, and supported young students with interest in mathematics.

Brian Leslie Norman Kennett is a mathematical physicist and seismologist. He is now a professor emeritus at the Australian National University.

Christine Margaret O'Keefe is an Australian mathematician and computer scientist whose research has included work in finite geometry, information security, and data privacy. She is a researcher at CSIRO, and was the lead author of a 2017 report from the Office of the Australian Information Commissioner on best practices for de-identification of personally identifying data.


  1. 1 2 Praeger, C. E. (2010). "Bernhard Hermann Neumann AC. 15 October 1909 -- 21 October 2002". Biographical Memoirs of Fellows of the Royal Society . 56: 285–316. doi: 10.1098/rsbm.2010.0002 .
  2. O'Connor, John J.; Robertson, Edmund F., "Bernhard Neumann", MacTutor History of Mathematics archive , University of St Andrews .
  3. Bernhard Neumann at the Mathematics Genealogy Project
  4. Neumann, B. H. "Identical relations in groups" (PDF). In: Comptes Rendus du Congrès International des Mathématiciens, Oslo, 1936. vol. 2. pp. 18–19.
  5. It's an Honour: AC
  6. "Aust MS : The Bernhard Neumann Prize".
  7. "About Us". World Cultural Council . Retrieved November 8, 2016.