Saunders Mac Lane (August 4, 1909 – April 14, 2005), born Leslie Saunders MacLane, was an American mathematician who co-founded category theory with Samuel Eilenberg.

Early life and education

Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville. He was christened "Leslie Saunders MacLane", but "Leslie" fell into disuse because his parents, Donald MacLane and Winifred Saunders, came to dislike it. He began inserting a space into his surname because his first wife found it difficult to type the name without a space. He was the eldest of three brothers; one of his brothers, Gerald MacLane, also became a mathematics professor at Rice University and Purdue University. Another sister died as a baby. His father and grandfather were both ministers; his grandfather had been a Presbyterian, but was kicked out of the church for believing in evolution, and his father was a Congregationalist. His mother, Winifred, studied at Mount Holyoke College and taught English, Latin, and mathematics.

Career

From 1934 through 1938, Mac Lane held short-term appointments at Yale University, Harvard University, Cornell University, and the University of Chicago. He then held a tenure track appointment at Harvard from 1938 to 1947. In 1941, while giving a series of visiting lectures at the University of Michigan, he met Samuel Eilenberg and began what would become a fruitful collaboration on the interplay between algebra and topology. In 1944 and 1945, he directed Columbia University's Applied Mathematics Group, which was involved in the war effort as a contractor for the Applied Mathematics Panel; the mathematics he worked on in this group concerned differential equations for fire-control systems. he died in 2005

Contributions

thumb|left|MacLane and [[Samuel Eilenberg at a conference in July 1992]]

After a thesis in mathematical logic, Mac Lane's early work was in field theory and valuation theory. He wrote on valuation rings and Witt vectors, and separability in infinite field extensions. He started writing on group extensions in 1942, and in 1943 began his research on what isnow called Eilenberg–MacLane spaces K(G,n), having a single non-trivial homotopy group G in dimension n. This work opened the way to group cohomology in general.

After introducing, via the Eilenberg–Steenrod axioms, the abstract approach to homology theory, he and Eilenberg originated category theory in 1945. He is especially known for his work on coherence theorems. A recurring feature of category theory, abstract algebra, and of some other mathematics as well, is the use of diagrams, consisting of arrows (morphisms) linking objects, such as products and coproducts. According to McLarty (2005), this diagrammatic approach to contemporary mathematics largely stems from Mac Lane (1948), who also coined the term Yoneda lemma for a lemma which is an essential background to many central concepts of category theory and which was discovered by Nobuo Yoneda.

Mac Lane had an exemplary devotion to writing approachable texts, starting with his very influential A Survey of Modern Algebra, coauthored in 1941 with Garrett Birkhoff. From then on, it was possible to teach elementary modern algebra to undergraduates using an English text. His Categories for the Working Mathematician remains the definitive introduction to category theory.

Selected works

  • 1997 (1941). A Survey of Modern Algebra (with Garrett Birkhoff). A K Peters.
  • 1948, "Groups, categories and duality," Proceedings of the Nat. Acad. of Sciences of the USA 34: 263–67.
  • 1963.
  • 1995 (1963). Homology, Springer (Classics in Mathematics) (Originally, Band 114 of Die Grundlehren Der Mathematischen Wissenschaften in Einzeldarstellungen.) AMS review by David Buchsbaum.
  • 1999 (1967). Algebra (with Garrett Birkhoff). Chelsea.
  • 1998 (1972). Categories for the Working Mathematician, Springer (Graduate Texts in Mathematics)
  • 1986. Mathematics, Form and Function. Springer-Verlag.
  • 1992. Sheaves in Geometry and Logic: A First Introduction to Topos Theory (with Ieke Moerdijk).
  • 1995.
  • 2005. Saunders Mac Lane: A Mathematical Autobiography. A K Peters.

See also

  • Foundations of geometry
  • PROP (category theory)
  • SPQR tree

Notes

References

  • (e-book: ).

Biographical references

  • . With selected bibliography emphasizing Mac Lane's philosophical writings.
  • .
  • .
  • Obituary press release from the University of Chicago.
  • Photographs of Mac Lane , 1984–1999.
  • Kutateladze S.S., Saunders Mac Lane, the Knight of Mathematics