Boris Moiseyevich Schein (born June 22, 1938) is a Russian-American

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 ...

, an expert in semigroups, and a Distinguished Professor in the Department of Mathematical Sciences at the

University of Arkansas The University of Arkansas (U of A, UArk, or UA) is a public land-grant research university in Fayetteville, Arkansas. It is the flagship campus of the University of Arkansas System and the largest university in the state. Founded as Arkansas ...

.. Schein was born in

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

on June 22, 1938, and moved to

Saratov Saratov (, ; rus, Сара́тов, a=Ru-Saratov.ogg, p=sɐˈratəf) is the largest city and administrative center of Saratov Oblast, Russia, and a major port on the Volga River upstream (north) of Volgograd. Saratov had a population of 901,36 ...

during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

. He became interested in mathematics as a teenager, and came under the influence of

Viktor Wagner Viktor Vladimirovich Wagner, also Vagner (russian: Виктор Владимирович Вагнер) (4 November 1908 – 15 August 1981) was a Russian mathematician, best known for his work in differential geometry and on semigroups. Wagner wa ...

, a professor of mathematics at

Saratov State University Saratov Chernyshevsky State University (russian: Саратовский государственный университет имени Н. Г. Чернышевского, СГУ, transcribed as SGU) is a major higher education and research inst ...

. Schein did his undergraduate studies in Mechanics-Mathematics at Saratov State, and chose to specialize in

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, Wagner's subject. In 1958 he solved the problem of characterizing the semigroups that could be embedded into an

inverse semigroup In group theory, an inverse semigroup (occasionally called an inversion semigroup) ''S'' is a semigroup in which every element ''x'' in ''S'' has a unique ''inverse'' ''y'' in ''S'' in the sense that ''x = xyx'' and ''y = yxy'', i.e. a regular semig ...

. He graduated summa cum laude in 1960. He continued working as a graduate student with Wagner, and in 1962 defended a

candidacy Candidacy is a rite which takes place during Roman Catholic seminary formation, by which the Church recognizes the seminarian as worthy of being ordained (hence, they become a "candidate" for ordination to the priesthood). With the liturgical ref ...

dissertation on semigroups of transformations at the

Herzen State Pedagogical University of Russia Herzen University, or formally the Russian State Pedagogical University in the name of A. I. Herzen (russian: Российский государственный педагогический университет имени А. И. Герце� ...

Saint Petersburg Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...

. He accepted a faculty position at Saratov in 1963, and defended his

Doctor of Sciences Doctor of Sciences ( rus, доктор наук, p=ˈdoktər nɐˈuk, abbreviated д-р наук or д. н.; uk, доктор наук; bg, доктор на науките; be, доктар навук) is a higher doctoral degree in the Russi ...

thesis in 1966, again at Herzen State Pedagogical University. In 1968, Schein was one of the founding editors of the journal ''

Semigroup Forum Semigroup Forum (print , electronic ) is a mathematics research journal published by Springer. The journal serves as a platform for the speedy and efficient transmission of information on current research in semigroup theory. Coverage in the journ ...

'', published by

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

. However, in the 1970s his connections with Western mathematicians led to political difficulties, his correspondence with mathematicians outside the USSR was cut off, and his students were prevented from graduating. Eventually, in the late 1970s, his mentor Wagner retired from the university and Schein was dismissed. In 1979, Schein was able to travel to

Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...

with his wife and daughter, and immediately he obtained a temporary visiting position at

Tulane University Tulane University, officially the Tulane University of Louisiana, is a private university, private research university in New Orleans, Louisiana. Founded as the Medical College of Louisiana in 1834 by seven young medical doctors, it turned into ...

New Orleans New Orleans ( , ,New Orleans
Merriam-Webster. ; french: La Nouvelle-Orléans , es, Nuev ...

. In 1980, he took his present position at the University of Arkansas. Boris Schein is known for the Schein index, which is the least number of "concepts" necessary to express the

logical matrix A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1) matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets. Matrix representation ...

of a

binary relation In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over Set (mathematics), sets and is a new set of ordered pairs consisting of ele ...

as a Boolean sum, and where a concept is an

outer product In linear algebra, the outer product of two coordinate vector In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers (a tuple) that describes the vector in terms of a particular ordered basis. An ea ...

of logical vectors. In 2011, Schein was named a distinguished reviewer of

Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructur ...

by the European Mathematical Society.Professor Named Distinguished Reviewer
, Univ. of Arkansas Dept. of Mathematical Sciences, retrieved 2012-02-03.

References

{{DEFAULTSORT:Schein, Boris Moiseyevich 1938 births Living people 20th-century American mathematicians 21st-century American mathematicians Soviet mathematicians University of Arkansas faculty Scientists from Saratov Tulane University faculty Soviet emigrants to the United States American people of Russian descent Herzen University alumni