His mother, Winifred, studied at Mount Holyoke College and taught English, Latin, and mathematics.

His half-uncle, a lawyer, was determined to send him to Yale University, where many of his relatives had been educated, and paid his way there beginning in 1926.

In 1929, at a party of Yale football supporters in Montclair, New Jersey, Mac Lane (there to be presented with a prize for having the best grade point average yet recorded at Yale) had met Robert Maynard Hutchins, the new president of the University of Chicago, who encouraged him to go there for his graduate studies and soon afterwards offered him a scholarship.

By the time he finished his doctorate in 1934, Bernays had been forced to leave because he was Jewish, and Weyl became his main examiner.

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.

He traveled as a Guggenheim Fellow to ETH Zurich for the 1947–1948 term, where he worked with Heinz Hopf.

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.

[9] 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.