Joachim "Jim" Lambek (5 December 1922 – 23 June 2014) was a German-born Canadian
mathematician. He was Peter Redpath
Emeritus Professor of Pure Mathematics at
McGill University, where he earned his
PhD degree in 1950 with
Hans Zassenhaus
Hans Julius Zassenhaus (28 May 1912 – 21 November 1991) was a German mathematician, known for work in many parts of abstract algebra, and as a pioneer of computer algebra.
Biography
He was born in Koblenz in 1912.
His father was a historian and ...
as advisor.
Biography
Lambek was born in
Leipzig,
Germany, where he attended a
Gymnasium.
He came to England in 1938 as a
refugee on the ''
Kindertransport''.
From there he was interned as an
enemy alien
In customary international law, an enemy alien is any native, citizen, denizen or subject of any foreign nation or government with which a domestic nation or government is in conflict and who is liable to be apprehended, restrained, secured and ...
and deported to a
prison work camp in
New Brunswick,
Canada. There, he began in his spare time a mathematical apprenticeship with Fritz Rothberger, also
interned, and wrote the
McGill Junior Matriculation in fall of 1941. In the spring of 1942, he was released and settled in
Montreal, where he entered studies at McGill University, graduating with an
honours mathematics degree in 1945 and an
MSc
MSC may refer to:
Computers
* Message Sequence Chart
* Microelectronics Support Centre of UK Rutherford Appleton Laboratory
* MIDI Show Control
* MSC Malaysia (formerly known as Multimedia Super Corridor)
* USB mass storage device class (USB MS ...
a year later. In 1950, he completed his doctorate under
Hans Zassenhaus
Hans Julius Zassenhaus (28 May 1912 – 21 November 1991) was a German mathematician, known for work in many parts of abstract algebra, and as a pioneer of computer algebra.
Biography
He was born in Koblenz in 1912.
His father was a historian and ...
becoming McGill's first
PhD in mathematics.
Lambek became assistant professor at McGill; he was made a full professor in 1963. He spent his sabbatical year 1965–66 in at the
Institute for Mathematical Research
The Institute for Mathematical Research (''Forschungsinstitut für Mathematik'', FIM) is a mathematical research institution located at ETH Zurich and founded in 1964 by Beno Eckmann. Its main goals are to promote and facilitating the exchange bet ...
at
ETH Zurich, where
Beno Eckmann
Beno Eckmann (31 March 1917 – 25 November 2008) was a Swiss mathematician who made contributions to algebraic topology, homological algebra, group theory, and differential geometry.
Life
Born in Bern, Eckmann received his master's degree from ...
had gathered together a group of researchers interested in
algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...
and
category theory
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...
, including
Bill Lawvere. There Lambek reoriented his research into category theory.
Lambek retired in 1992 but continued his involvement at
McGill's mathematics department. In 2000 a
festschrift celebrating Lambek's contributions to mathematical structures in
computer science was published. On the occasion of Lambek's 90th birthday, a collection ''Categories and Types in Logic, Language, and Physics'' was produced in tribute to him.
Scholarly work
Lambek's PhD thesis investigated
vector fields using the
biquaternion
In abstract algebra, the biquaternions are the numbers , where , and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group and commute with their coefficients. There are three types of biquaternions c ...
algebra over
Minkowski space, as well as
semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it.
The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'' ...
immersion in a
group
A group is a number of persons or things that are located, gathered, or classed together.
Groups of people
* Cultural group, a group whose members share the same cultural identity
* Ethnic group, a group whose members share the same ethnic ide ...
. The second component was published by the
Canadian Journal of Mathematics
The ''Canadian Journal of Mathematics'' (french: Journal canadien de mathématiques) is a bimonthly mathematics journal published by the Canadian Mathematical Society.
It was established in 1949 by H. S. M. Coxeter and G. de B. Robinson. The c ...
. He later returned to
biquaternion
In abstract algebra, the biquaternions are the numbers , where , and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group and commute with their coefficients. There are three types of biquaternions c ...
s when in 1995 he contributed "If Hamilton had prevailed: Quaternions in Physics", which exhibited the
Riemann–Silberstein bivector In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. If a scalar is considered a degree-zero quantity, and a vector is a degree-one quantity, then a bivector ca ...
to express the free-space electromagnetic equations.
Lambek supervised 17 doctoral students, and has 75 doctoral descendants as of 2020. He has over 100 publications listed in the
Mathematical Reviews, including 6 books. His earlier work was mostly in
module theory
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of ''module'' generalizes also the notion of abelian group, since the abelian groups are exactly the mo ...
, especially torsion theories, non-commutative localization, and
injective modules. One of his earliest papers, , proved the
Lambek–Moser theorem about integer sequences. In 1963 he published an important result, now known as Lambek's theorem, on
character modules characterizing flatness of a module.
His more recent work is in
pregroups and
formal languages; his earliest works in this field were probably and . He is noted, among other things, for the
Lambek calculus, an effort to capture mathematical aspects of natural language syntax in
logical form, and a work that has been very influential in
computational linguistics
Computational linguistics is an interdisciplinary field concerned with the computational modelling of natural language, as well as the study of appropriate computational approaches to linguistic questions. In general, computational linguistics d ...
, as well as for developing the connections between
typed lambda calculus and
cartesian closed categories
In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mat ...
(see
Curry–Howard–Lambek correspondence). His last works were on
pregroup grammar Pregroup grammar (PG) is a grammar formalism intimately related to categorial grammars. Much like categorial grammar (CG), PG is a kind of type logical grammar. Unlike CG, however, PG does not have a distinguished function type. Rather, PG uses in ...
.
Selected works
Books
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Articles
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* Reprinted in
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References
External links
Faculty profile of Joachim Lambekat McGill University
Lambek festival(80th anniversary)
{{DEFAULTSORT:Lambek, Joachim
1922 births
2014 deaths
20th-century Canadian mathematicians
21st-century Canadian mathematicians
21st-century German mathematicians
Algebraists
Canadian logicians
Category theorists
Kindertransport refugees
German emigrants to Canada