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, structure, space, models, and change. History On ...

. 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 mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. A simple group is a group ''G'' that does not have any normal subgroups except for the trivial group and ''G'' itself. The ...

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, having order 246320597611213317192329314147 ...

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 elements. The entries consist of characters ...

of the baby monster. He did his PhD in 1963 at the

Johann Wolfgang Goethe University of Frankfurt am Main Goethe University (german: link=no, Johann Wolfgang Goethe-Universität Frankfurt am Main) is a 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 wealt ...

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 and Baer groups. Biography Baer studied mechanical engineering f ...

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 (german: Universität Bielefeld) is a 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 a ...

, 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 mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. A simple group is a group ''G'' that does not have any normal subgroups except for the trivial group and ''G'' itself. Th ...

, 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 fictional creature found in horror, fantasy, science fiction, folklore, mythology and religion. Monsters are very often depicted as dangerous and aggressive with a strange, grotesque appearance that causes terror and fe ...

group or the

Fischer-Griess Monster 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, having order 24632059761121331719232931414759 ...

. 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 (german: Nordrhein-Westfalen, ; li, Noordrien-Wesfale ; nds, Noordrhien-Westfalen; ksh, Noodrhing-Wäßßfaale), commonly shortened to NRW (), is a States of Germany, state (''Land'') in Western Germany. With more tha ...

, where he died in August, 2020.

Notes

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