Copyright 2005 The New York Times Company The New York Times April 21, 2005 Thursday Late Edition - Final SECTION: Section A; Column 1; National Desk; Pg. 21 LENGTH: 472 words HEADLINE: Saunders Mac Lane, 95, Pioneer of Algebra's Category Theory BYLINE: By JEREMY PEARCE BODY: Dr. Saunders Mac Lane, a mathematician at the University of Chicago who helped to develop category theory, an abstract branch of algebra that has applications in computer science and other fields, died on April 14 at a hospice in San Francisco. He was 95. The cause was internal bleeding, his family said. Dr. Mac Lane wrote and lectured widely about logic, topology and other aspects of mathematics. He began the formulation of category theory in the 1940's. In a seminal paper written in 1945 with Dr. Samuel Eilenberg, a mathematician at Columbia, Dr. Mac Lane laid the foundations of the theory, which provides a framework to show how mathematical structures and families of structures relate to one another. The theory has been used to help define philosophical concepts, and it has applications in linguistics, mathematical physics and computer science. It is often described as having created a universal language for mathematicians. Dr. J. Peter May, a professor of mathematics at Chicago, said that Dr. Mac Lane's ''prescience in category theory and many other directions helped to change the subject of mathematics forever.'' In other work, Drs. Mac Lane and Eilenberg developed a concept of topological space that came to be known as the Eilenberg-Mac Lane space. It is used in the study of mathematical convergence and continuity. Dr. Mac Lane, with Prof. Garrett Birkhoff of Harvard, also helped write popular college mathematics texts, ''Algebra'' and ''A Survey of Modern Algebra.'' In 1963, Dr. Mac Lane published ''Homology,'' on topology and ''ways of describing the shape of something through algebraic calculations,'' said Dr. Steve Awodey, a logician and an associate professor of philosophy at Carnegie Mellon University. Saunders Mac Lane was born in Norwich, Conn. He graduated from Yale and earned a master's at Chicago before receiving his doctorate from the Mathematics Institute at the University of Gottingen in 1934. After teaching at Harvard and Cornell, Dr. Mac Lane was named director of the Columbia Applied Mathematics Group in 1944. He was appointed a professor of mathematics at Chicago in 1947 and remained there for the rest of his career. He retired in 1982, but continued to advise graduate students until the 90's. Dr. Mac Lane was president of the Mathematics Association of America from 1951 to 1953. He was a vice president of the National Academy of Sciences and won the National Medal of Science in 1989. Dr. Mac Lane's first wife, Dorothy Jones Mac Lane, died in 1985. He lived in Hyde Park, Ill., before moving to San Francisco three years ago. He is survived by his wife, Osa Mac Lane; two daughters, Gretchen, of Manhattan, and Cynthia Hay of London; a brother, David, of Portland, Ore.; and one grandchild. URL: http://www.nytimes.com 21-Apr-2005 17:12:26 -0300,1514;000000000001-00000012