Saunders Mac Lane
American mathematician who co-founded category theory.
Saunders Mac Lane was an American mathematician who, together with Samuel Eilenberg, founded category theory, a field that reshaped modern mathematics. Born in Connecticut in 1909, he was originally named Leslie Saunders MacLane, but the first name was dropped by his parents. His father and grandfather were ministers, and his mother, a college graduate, taught English, Latin, and mathematics. In high school, chemistry was his favorite subject, but after his father’s death, a half-uncle funded his education at Yale. There, a mathematics instructor coached him for a competition he won, steering him toward mathematics. He double-majored in mathematics and physics, publishing his first paper in physics. After graduating in 1930, he met University of Chicago president Robert Maynard Hutchins, who offered him a scholarship. Mac Lane arrived without applying and was admitted, studying under notable figures including E. H. Moore and Leonard Eugene Dickson. Earning a master’s degree in 1931, he then studied at the University of Göttingen, where his greatest influences were Paul Bernays and Hermann Weyl. He completed his doctorate in 1934, just as Bernays was forced to leave due to Nazi policies. Mac Lane then held short-term appointments at Yale, Harvard, Cornell, and Chicago before a tenure-track position at Harvard. In 1941, he met Samuel Eilenberg at the University of Michigan, beginning a collaboration that produced category theory in 1945. During World War II, he directed Columbia’s Applied Mathematics Group, working on differential equations for fire-control systems. He returned to Chicago in 1947, later serving as department chair. His contributions include work on valuation theory, Eilenberg–MacLane spaces, and group cohomology. He also led efforts to improve mathematics teaching and advised the government through the National Science Board.
- known_for
- Co-founding category theory with Samuel Eilenberg; Eilenberg–Mac Lane spaces; A Survey of Modern Algebra
Lore & Background
He legally changed his surname to 'Mac Lane' (with a space) in the 1940s to avoid confusion with another mathematician named MacLane; the story about his first wife's typing difficulty is apocryphal. His father and grandfather were both ministers; his grandfather was kicked out of the Presbyterian church for believing in evolution. During World War II he directed Columbia University's Applied Mathematics Group, working on differential equations for fire-control systems. Mac Lane's early work was in field theory and valuation theory. He popularized the term Yoneda lemma and wrote the definitive introduction to category theory, Categories for the Working Mathematician.
Reader's Guide
Saunders Mac Lane’s behavior and approach to mathematics were shaped by a rigorous training across leading institutions. After an early interest in chemistry, he shifted to mathematics and physics at Yale, publishing his first paper in physics. His graduate work at the University of Chicago and the University of Göttingen exposed him to set theory, number theory, logic, and the influences of Paul Bernays and Hermann Weyl. His career included short-term appointments at Yale, Harvard, Cornell, and Chicago before a tenure-track position at Harvard. During World War II, he directed Columbia’s Applied Mathematics Group, working on differential equations for fire-control systems. His collaboration with Samuel Eilenberg, beginning in 1941 at Michigan, produced foundational work in algebraic topology, including Eilenberg–MacLane spaces and the introduction of category theory in 1945. This diagrammatic approach to mathematics, using arrows and objects, became a unifying language across fields. Mac Lane also served as department chair at Chicago, president of the American Mathematical Society, and vice president of the National Academy of Sciences. He initiated efforts to improve mathematics teaching through the Mathematical Association of America and advised the government on the National Science Board. His legacy endures through category theory’s central role in modern mathematics and his accessible, rigorous texts.
Did You Know?
- Mac Lane was christened Leslie Saunders MacLane (no space), but 'Leslie' fell into disuse because his parents came to dislike it.
- He legally changed his surname to 'Mac Lane' (with a space) in the 1940s to avoid confusion with another mathematician named MacLane; the story about his wife's typing difficulty is apocryphal.
- Mac Lane popularized the term 'Yoneda lemma' for a lemma discovered by Nobuo Yoneda, though he did not coin the phrase.
Frequently Asked Questions
What is Saunders Mac Lane most famous for?
He is widely credited with co-founding category theory together with Samuel Eilenberg, creating a structural framework that now unifies many branches of mathematics. His earlier work in homology theory and algebraic topology also remains foundational.
What are Eilenberg–Mac Lane spaces?
These are a family of topological spaces introduced jointly by Eilenberg and Mac Lane that play a central role in algebraic topology and homotopy theory. They give a concrete topological model for cohomology operations and are named after both mathematicians.
Which textbooks did Saunders Mac Lane write?
He co-authored *A Survey of Modern Algebra*, a standard reference that influenced algebra instruction for decades. He also wrote influential texts on homology theory and on category theory itself.
Why is Saunders Mac Lane important to modern mathematics?
By helping create category theory, he provided a general structural language that links previously disconnected fields such as algebra, topology, and logic. His research and teaching materials continue to underpin graduate-level work in pure mathematics.
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