Bernd Fischer (18 December 1936 – 13 August 2020) was a German

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 ...

. He is best known for his contributions to the classification of finite

simple group SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are Legal Services, Fiduciary Activities, Banking Intermediation and Corporate Service. The d ...

s, and discovered several of the

sporadic group In the mathematical classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic finite groups, or just the sporadic groups. A simpl ...

s. He introduced 3-transposition groups and constructed the three

Fischer group In the area of modern algebra known as group theory, the Fischer groups are the three sporadic simple groups Fi22, Fi23 and Fi24 introduced by . 3-transposition groups The Fischer groups are named after Bernd Fischer who discovered them ...

s, predicted the existence of the baby monster and

monster group In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group; it has order : : = 2463205976112133171923293 ...

s, and described and computed the

character table In group theory, a branch of abstract algebra, a character table is a two-dimensional table whose rows correspond to irreducible representations, and whose columns correspond to conjugacy classes of group (mathematics), group elements. The entries ...

of the baby monster. He did his

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

in 1963 at the

Johann Wolfgang Goethe University of Frankfurt am Main Goethe University Frankfurt () is a public university, public research university located in Frankfurt am Main, Germany. It was founded in 1914 as a citizens' university, which means it was founded and funded by the wealthy and active liberal cit ...

under the direction of

Reinhold Baer Reinhold Baer (22 July 1902 – 22 October 1979) was a German mathematician, known for his work in algebra. He introduced injective modules in 1940. He is the eponym of Baer rings, Baer groups, and Baer subplanes. Biography Baer studied mecha ...

Career

Fischer went to Goethe University in Frankfurt to study mathematics under Baer in the early 60s, receiving his PhD in 1963. He later moved to the

Bielefeld University Bielefeld University () is a public university in Bielefeld, Germany. Founded in 1969, it is one of the country's newer universities, and considers itself a "reform" university, following a different style of organization and teaching than the e ...

, where he became head of mathematical sciences. In 1970, he classified the almost-simple groups generated by 3-transpositions. In the process, he discovered three new

sporadic groups In the mathematical classification of finite simple groups, there are a number of Group (mathematics), groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic finite groups, or just the spora ...

, which were later called the

Fischer groups In the area of modern algebra known as group theory, the Fischer groups are the three sporadic simple groups Fi22, Fi23 and Fi24 introduced by . 3-transposition groups The Fischer groups are named after Bernd Fischer who discovered them ...

. His proof that the classification was complete was known but not published in a single narrative until Aschbacher published an elementary introduction of 3-transposition groups in 1996. By loosening some of the conditions on his classification, in 1973 he predicted the existence of two larger sporadic simple groups: a -transposition group, now known as the baby monster group, and a -transposition group now known as the

monster A monster is a type of imaginary or fictional creature found in literature, folklore, mythology, fiction and religion. They are very often depicted as dangerous and aggressive, with a strange or grotesque appearance that causes Anxiety, terror ...

group or the Fischer-Griess Monster. These would turn out to be the two largest sporadic groups that could exist.

Robert Griess Robert Louis Griess, Jr. (born 1945, Savannah, Georgia) is a mathematician working on finite simple groups and vertex algebras. He is currently the John Griggs Thompson Distinguished University Professor of mathematics at University of Michigan ...

independently discovered the Monster group and published a description in 1976. Fischer went on to compute the character table for both monsters, in collaboration with Donald Livingstone and Michael Thorne. Leon and Sims first produced a construction of the baby monster in 1977, and Griess produced one for the monster in 1980.

Personal life

Fischer was raised in

Bad Endbach Bad Endbach is the westernmost municipality in Marburg-Biedenkopf district of the state of Hesse in Germany, and borders on the Lahn-Dill district. Geography Location Bad Endbach lies in the Lahn-Dill Bergland (''ie'' Highland) in the foothills o ...

. He later moved to

North Rhine-Westphalia North Rhine-Westphalia or North-Rhine/Westphalia, commonly shortened to NRW, is a States of Germany, state () in Old states of Germany, Western Germany. With more than 18 million inhabitants, it is the List of German states by population, most ...

, where he died in August, 2020.

Notes

20th-century German mathematicians 1936 births 2020 deaths {{Germany-mathematician-stub