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Canadian mathematician (1922–2014)
Joachim "Jim" Lambek FRSC (5 December 1922 – 23 June 2014)[2] was a 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 as advisor.
Biography
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Lambek was born in Leipzig , Germany , where he attended a Gymnasium .[3] He came to England in 1938 as a refugee on the Kindertransport .[2] From there he was interned as an enemy alien 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.[3] 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 a year later.[4] In 1950, he completed his doctorate under Hans Zassenhaus 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 at ETH Zurich , where Beno Eckmann had gathered together a group of researchers interested in algebraic topology and category theory , including Bill Lawvere . There Lambek reoriented his research into category theory.[5]
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.[6] On the occasion of Lambek's 90th birthday, a collection Categories and Types in Logic, Language, and Physics was produced in tribute to him.[7]
Scholarly work
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Lambek's PhD thesis investigated vector fields using the biquaternion algebra over Minkowski space , as well as semigroup immersion in a group . The second component was published by the Canadian Journal of Mathematics .[8] He later returned to biquaternions when in 1995 he contributed "If Hamilton had prevailed: Quaternions in Physics", which exhibited the Riemann–Silberstein bivector to express the free-space electromagnetic equations.
Lambek supervised 17 doctoral students, and has 75 doctoral descendants as of 2020.[9] He has over 100 publications listed in the Mathematical Reviews , including 6 books. His earlier work was mostly in module theory , especially torsion theories, non-commutative localization, and injective modules . One of his earliest papers, Lambek & Moser (1954) , 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.[10] His more recent work is in pregroups and formal languages ; his earliest works in this field were probably Lambek (1958) and Lambek (1979) . 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 , as well as for developing the connections between typed lambda calculus and cartesian closed categories (see Curry–Howard–Lambek correspondence ). His last works were on pregroup grammar .
Selected works
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Books
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Lambek, Joachim (2009) [1966]. Lectures on rings and modules (3rd ed.). Blaisdell Publishing. ISBN 9780821849002 . MR 0206032 .
Fine, N. J. ; Gillman, Leonard ; — (1966). Rings of quotients of rings of functions . McGill University Press. MR 0200747 .
— (1966). Completions of categories . Seminar lectures given in 1966 in Zürich. Lecture Notes in Mathematics, No. 24. Berlin, New York: Springer-Verlag . MR 0209330 .
— (1971). Torsion theories, additive semantics, and rings of quotients . Lecture Notes in Mathematics. Vol. 177. Berlin, New York: Springer-Verlag . MR 0284459 .
—; Scott, P. J. (1986). Introduction to Higher Order Categorical Logic . Cambridge University Press . ISBN 978-0-521-35653-4 . MR 0856915 .
Anglin, W. S.; — (1995). The heritage of Thales . Undergraduate Texts in Mathematics . Berlin, New York: Springer-Verlag . ISBN 978-0-387-94544-6 . MR 1369087 .
Casadio, Claudia; — (2008). Computational Algebraic Approaches to Natural Language . Polimetrica. ISBN 978-88-7699-125-7 .
— (2008). From word to sentence: a computational algebraic approach to grammar . Polimetrica. ISBN 978-88-7699-117-2 .
Articles
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Lambek, Joachim (1951), "The immersibility of a semigroup into a group", Canadian Journal of Mathematics , 3 : 34–43, doi :10.4153/CJM-1951-005-8 , S2CID 124979541
—; Moser, L. (1954), "Inverse and Complementary Sequences of Natural Numbers", The American Mathematical Monthly , 61 (7 ): 454–458, doi :10.2307/2308078 , ISSN 0002-9890 , JSTOR 2308078 , MR 0062777
— (1958), "The Mathematics of Sentence Structure" (PDF) , The American Mathematical Monthly , 65 (3 ): 154–170, doi :10.2307/2310058 , ISSN 0002-9890 , JSTOR 1480361
— (1961), "How to program an infinite abacus", Canadian Mathematical Bulletin , 4 (3 ): 295–302, doi :10.4153/CMB-1961-032-6 , S2CID 121506469
— (1969). "Deductive systems and categories II. Standard constructions and closed categories". Lecture Notes in Mathematics . Vol. 86. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 76–122. doi :10.1007/bfb0079385 . ISBN 978-3-540-04605-9 . ISSN 0075-8434 .
— (1972), "Bicommutators of nice injectives", Journal of Algebra , 21 : 60–73, doi :10.1016/0021-8693(72 )90034-8 , ISSN 0021-8693 , MR 0301052
— (1972), "Localization and completion", Journal of Pure and Applied Algebra , 2 (4 ): 343–370, doi :10.1016/0022-4049(72 )90011-4 , ISSN 0022-4049 , MR 0320047
— (1979), "A mathematician looks at Latin conjugation", Theoretical Linguistics , 6 (2 ): 221–234, doi :10.1515/thli.1979.6.1-3.221 , ISSN 0301-4428 , MR 0589163 , S2CID 62697835
— (1995). "If Hamilton had prevailed: Quaternions and Physics". Mathematical Intelligencer . 17 (4 ): 7–15. doi :10.1007/BF03024783 . S2CID 120099630 . Reprinted in Wilson, Robin; Gray, Jeremy, eds. (2001). Mathematical Conversations . Springer-Verlag . ISBN 978-1-4613-0195-0 .
—; Barr, Michael (2013), In Praise of Quaternions (PDF) , McGill University
See also
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References
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^ a b "Joachim Lambek" . Montreal Gazette . Legacy.com. 27 June 2014. Retrieved 31 October 2018 .
^ a b Darmon, Henri (2 December 2014). Resolution on the Death of Emeritus Professor Joachim (Jim) Lambek, Department of Mathematics and Statistics (PDF) . Faculty of Science: Meeting of Faculty. Montreal: McGill University . p. 2.
^ Müller-Hoissen, Folkert; Pallo, Jean Marcel; Stasheff, Jim, eds. (2012). Associahedra, Tamari Lattices and Related Structures . Progress in Mathematics. Vol. 299. Birkhäuser. p. 18. doi :10.1007/978-3-0348-0405-9 . ISBN 978-3-0348-0404-2 . LCCN 2012942603 .
^ Barr, Michael (5 December 1997). An appreciation of Jim Lambek at McGill . LambekFest. Montreal.
^ Barr, Michael ; Scott, P. J.; Seely, R. A. G., eds. (2000), The Lambek Festschrift: mathematical structures in computer science , Cambridge University Press , MR 1770227
^ Casadio, Claudia; Coeke, Bob; Moortgat, Michael; Scott, Philip, eds. (2014), Categories and Types in Logic, Language, and Physics: Essays Dedicated to Jim Lambek on the Occasion of His 90th Birthday , Springer-Verlag
^ Lambek, J. (1951). "The immersibility of a semigroup into a group" . Canadian Journal of Mathematics . 3 : 34–43. doi :10.4153/CJM-1951-005-8 . S2CID 124979541 .
^ Joachim Lambek at the Mathematics Genealogy Project
^ Lambek, J. (1964). "A Module is Flat if and Only if its Character Module is Injective" . Canadian Mathematical Bulletin . 7 (2 ): 237–243. doi :10.4153/CMB-1964-021-9 . ISSN 0008-4395 .
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