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Mac Lane graduated from Yale in 1930 and took up a fellowship at Chicago. At the University of Chicago he was influenced by Eliakim Moore . By this time E H Moore was nearly seventy years old but his advice to Mac Lane to study for a doctorate at Göttingen in Germany certainly persuaded Mac Lane to work at the foremost mathematical research centre in the world at that time. Of course Moore had himself studied in Germany as a young man and had created in Chicago an eminent research school of mathematics based on his experiences of German mathematics at that time.

Although Mac Lane went to the greatest mathematics research centre in the world, political events would soon disrupt Göttingen. Mac Lane began to work for his doctorate under Bernays ' supervision but in 1933 the Nazis came to power. They began to remove the top mathematicians from Göttingen, and other universities, who had Jewish connections. Mac Lane had seen that he had to work quickly for his doctorate and leave Germany as soon as possible before things deteriorated further. He defended his thesis Abbreviated Proofs in the Logical Calculus, with Weyl as examiner, on 19 July 1933 and quickly returned to the United States. The article [ ) by Mac Lane give an interesting account of the events at Göttingen in 1933.

On returning to the United States, Mac Lane spent the session 1933/34 at Yale and then the following two years at Harvard. He left Harvard to take up a post of instructor at Cornell for session 1936/37, he spent the following session back at Chicago before accepting an appointment as an assistant professor at Harvard.

It was during these years that he wrote his famous text A survey of modern algebra with G Birkhoff which was published in 1941. Kaplansky writes in about this text:

"A Survey of Modern Algebra" opened to American undergraduates what had until then been largely reserved for mathematicians in van der Waerden 's "Moderne Algebra", published a decade earlier. The impact of Birkhoff and Mac Lane on the content and teaching of algebra in colleges and universities was immediate and long sustained. What we recognise in undergraduate courses in algebra today took much of its start with the abstract algebra which they made both accessible and attractive.

During World War II Mac Lane worked in the Applied Mathematics Groups at Columbia. Then in 1947 he was appointed professor of mathematics at Chicago. The research centre there had Stone , Abraham Albert , Kaplansky , Otto Schilling and Weil on the staff and was led by Stone . In 1952, five years after being appointed, Mac Lane took over the chairmanship of the department from Stone .

Mac Lane's work covered a wide range of mathematics. He worked on and off throughout his career on mathematical logic, no surprise for a student of Bernays , and he did some early work on planar graphs. He studied valuations and their extensions to polynomial rings. In the 1940s he worked on cohomology and introduced the basic notions of category theory.

Kelly, in , writes:

No man could so stimulate others unless, alongside an incisive intellect, he was possessed of enthusiasm and warmth, a deep interest in his fellow man, and a sympathy the more real for being unsentimental. Those who proudly call themselves his friends know these things: others will infer them in reading [his works].

Source:School of Mathematics and Statistics University of St Andrews, Scotland