Israel Kleiner (mathematician)

Israel Kleiner is a Canadian mathematician and historian of mathematics.

Kleiner earned his PhD in 1967 at McGill University under Joachim Lambek with thesis Lie modules and rings of quotients. Before his retirement as professor emeritus, he spent his career as a mathematics professor at York University, where he was a member of the faculty since 1965 and where he coordinated the training program for mathematics teachers teaching at the secondary school level. He is noted for his work on the history of algebra and with the combination of the history of mathematics and mathematics education.

He received the Carl B. Allendoerfer Award in 1987 and again in 1992, the George Pólya Award in 1990, and the Lester Randolph Ford Award in 1995. He was in the mid 2000s vice-president of the Canadian Society for the Philosophy and History of Mathematics.

Works

• Excursions in the history of mathematics, Springer 2011
• A history of abstract algebra, Birkhäuser 2007
• Rigor and proof in mathematics - a historical perspective, Mathematics Magazine, Vol. 64, 1991, pp. 291-314 (1992 Allendoerfer Award)
• The Evolution of Group Theory: A Brief Survey, Mathematics Magazine, Vol. 59, 1986, pp. 195-215 (1987 Allendoerfer Award, reprinted in Alexanderson The harmony of the world - 75 years of Mathematics Magazine, MAA 2007)
• Evolution of the function concept: a brief survey, College Mathematics Journal, Vol. 20, 1989, No. 4 (1990 Polya Award)
• with Nitsa Movshovitz-Hadar The role of paradoxes in the evolution of mathematics, The American Mathematical Monthly, Vol. 101, 1994, p. 963 (1995 Lester R. Ford Award)
• The roots of commutative algebra in algebraic number theory, Mathematics Magazine, Vol. 68, 1995, pp. 3–15, reprinted (with The evolution of group theory and Evolution of the function concept) in Victor Katz, Robin Wilson, Marlow Anderson Who gave you the epsilon? And other tales of mathematical history, MAA, Spectrum Series, 2009
• The genesis of the abstract ring concept, American Mathematical Monthly, Vol. 103, 1996, p. 423
• A sketch of the evolution of (non-commutative) ring theory, L´Enseignement Mathematique, Vol. 33, 1987, pp. 227–267
• From numbers to rings - an early history of ring theory, Elemente der Mathematik, Vol. 53, 1998, pp. 18–35
• Field theory: from equations to axiomatization, Part 2, American Mathematical Monthly, Vol. 106, 1999, pp. 677–684, 859-863
• Emmy Noether- highlights in her life and work, L´Enseignement Mathematique, Vol. 38, 1992, pp. 103–124
• From Fermat to Wiles, Elemente der Mathematik, Vol. 55, 2000, pp. 19–37
• Thinking the unthinkable - the story of complex numbers (with a moral), Mathematics Teacher, Vol. 81, 1988, pp. 583–582
• The teaching of abstract algebra - an historical perspective, in Frank Swetz, Otto Bekken, Bengt Johansson, John Fauvel, Victor Katz (eds.) Learn from the masters, MAA 1994
• A historically focused course on abstract algebra, Mathematics Magazine, Vol. 71, 1998, pp. 105–111
• The principle of continuity- a brief history, Mathematical Intelligencer, 2006, No. 4

External links

• brief biography
• additional brief biography