Background

Ethnicity: His parents were descendants of Mayflower settlers and the Scottish Macleans of Mull.

Saunders Mac Lane was born on August 4, 1909, in Taftville, Connecticut, United States. He was a son of Donald Bradford MacLane, a congregational minister, and Winifred (Saunders) MacLane, a teacher of English, Latin and mathematics. Saunders had two brothers, one of which, Gerald MacLane, became a mathematics professor. Moreover, he had a sister, who died in infancy.

Education

During his years in high school, Saunders' favorite subject was Chemistry. In 1926, he entered Yale University, where he became disillusioned with the subject. At the university, Lester S. Hill was his mathematics instructor, who coached him for a local mathematics competition, which Mac Lane won, setting the direction for his future work.

Saunders continued to study mathematics and physics as a double major, taking classes from many notable physicists and mathematicians, including Jesse Beams, Ernest William Brown, Ernest Lawrence, F. S. C. Northrop, Øystein Ore and others. In the summer of 1929, Mac Lane’s work at General Electric with scientists Irving Langmuir and Katherine Blodgett on the characteristics of filaments of tungsten resulted in his first published paper. In 1930, Mac Lane graduated from Yale University with a Bachelor of Arts degree.

The same year after graduation from Yale University, Saunders entered the University of Chicago on a scholarship, offered by Robert Maynard Hutchins, who was a new president of the university at that time. At the University of Chicago, Mac Lane studied different subjects, including set theory under the guidance of E. H. Moore, number theory under Leonard Eugene Dickson, the calculus of variations under Gilbert Ames Bliss and logic under the tutelage of Mortimer J. Adler. In 1931, Saunders graduated with a Master of Arts degree from the university.

In 1931, Mac Lane entered the University of Göttingen. He attended lectures on non-commutative algebra, given by Emmy Noether, who had a forceful, enthusiastic style, that engaged students in the excitement of mathematics. Mac Lane adopted this style in his own teaching. He also chose to study logic under Paul Bernays. Unfortunately, at this time, Germany was at the beginning of a decade of upheaval with the rise of the Nazi regime. The mathematics departments at Goettingen and other German universities experienced an exodus of faculty throughout the 1930's. Mac Lane’s advisor Bernays was one of many Jews, dismissed from the university. In order to finish his doctorate before the department collapsed, Mac Lane took his examination in the summer of 1933 under Hermann Weyl. In 1934, Saunders received his Doctor of Philosophy degree from the University of Göttingen.

During his lifetime, Mac Lane attained numerous Honorary Doctor of Science degrees from different educational establishments, including Purdue University (1965), Yale University (1969), Coe College (1973), University of Pennsylvania (1977), Union College (1990) and University of Notre Dame (1998). Also, in 1971, Saunders received an Honorary Doctor of Laws degree from the University of Glasgow in Scotland.

Career

Beginning from 1934 till 1938, Mac Lane held appointments at Yale University as a Sterling Fellow, at Harvard University as a Benjamin Pierce Instructor, also working at the University of Chicago and Cornell University during that period. Between 1935 and 1939, he published twenty-three papers in logic and valuation theory. The papers on valuation theory were influenced by the thought of Oystein Ore, who taught Mac Lane two algebra courses at Yale University, and who continued to work with Mac Lane, when he returned to Yale as a Sterling Fellow. Mac Lane made great advancements in the area of valuation theory. In one of his papers, he proved a theorem, known thereafter as Mac Lane’s theorem.

In 1939, he was hired as an assistant professor at Harvard University, a post he held till 1946, when he became a professor. Mac Lane continued to hold a post of a professor at the university until 1947.

In the late 1930's, both Mac Lane and his colleague Garrett Birkhoff taught graduate algebra courses. They agreed to write a text for a standard graduate algebra course. Mac Lane used B. L. van der Waerden’s text, which was based on lectures, presented by Emil Artin and Emmy Noether at the University of Göttingen, and a text, written by a Chicago professor, Adrian Albert, which stressed linear algebra. Mac Lane was also influenced by a lecture, given by Emil Artin on Galois theory, when Artin visited Chicago.

The text Birkhoff and Mac Lane wrote incorporated all of these influences. It was first published in 1941, and in the subsequent years went through numerous editions. The work was a great success, because it reflected the new connections between classical, axiomatic and conceptual ideas about algebra.

In 1941, Mac Lane began a long and productive collaboration with Samuel Eilenberg on the interface between the field of geometry, called topology (the classification of spaces under continuous deformations) and algebra (the manipulation of formulas according to rules). This was the beginning of their cohomology theory, which uses algebraic groups to study the geometric properties of topological spaces, and homological algebra, which attempts to use algebra to compare topological spaces.

Mac Lane and Birkhoff were also solidifying their ideas, concerning the universality of certain mathematical structures. In 1945, their first paper on categories was published. Later, Eilenberg and Mac Lane set out to combine all the theories from the separate structures into one theory. This work was to occupy Mac Lane for the next forty years, and he published more than forty papers on these topics. All in all, he published more than six books and one hundred research articles.

During World War II, Mac Lane took part in the war effort as director of the applied mathematics group at Columbia University. In 1947, he returned to the University of Chicago as a professor of mathematics, where he stayed until his retirement in 1982. He was also named the Max Mason Distinguished Professor in 1963 of that university.

After his retirement in 1982, Mac Lane continued to influence the mathematical community. His research interests returned to the foundations of mathematics, on which he published a book in 1986. Mac Lane also contributed regularly to the "Notices of the American Mathematical Society" and the "Mathematical Intelligencer" magazines on the topics of the foundation of mathematics, the role of government in mathematics and the directions both mathematics and the mathematical societies should be taking.

Achievements

• Saunders Mac Lane was a prominent mathematician, who became famous as a co-originator of category theory together with Samuel Eilenberg. He is especially known for his work on coherence theorems. Also, he contributed significantly to the philosophy of mathematics and investigations of the algebraic aspects of various fields of geometry.
  
  Mac Lane was an author of Mac Lane’s theorem. Also, he coined the term Yoneda lemma.
  
  During his lifetime, he received many awards, including Chauvenet Prize in 1941, Distinguished Professor Award in 1976, Steele Prize in 1986, National Medal of Science in 1989 and others. Moreover, Mac Lane was a recipient of Guggenheim Fellowship in 1947-1948 and 1972-1973.

Works

More photos

• book

  • A Survey of Modern Algebra

    (This classic, written by two young instructors, who becam...)

    1941
  • Mathematics, Form and Function

    (This book records the author's efforts to capture in word...)

    1986
  • Saunders Mac Lane: A Mathematical Autobiography

    (In this autobiography, Saunders gives his readers a glimp...)

    2005
  • Algebra

    (This book presents modern algebra from first principles. ...)

    1967
  • Saunders MacLane: Selected Papers 1979
  • Homology 1963

• textbook

  • Sheaves in Geometry and Logic: A First Introduction to Topos Theory

    (Sheaves arose in geometry as coefficients for cohomology ...)

    1992
  • Categories for the Working Mathematician

    (This is Graduate Texts in Mathematics, Book 5. Starting f...)

    1971

Views

Mac Lane was a believer in the interconnectedness of all the branches of mathematics, with rigor and abstraction being part of the framework, through which mathematics can be viewed as a whole.

Quotations: "Good general theory does not search for the maximum generality, but for the right generality."

"The notions category and functor were not formulated or put in print until the idea of a natural transformation was also at hand."

"The standard "foundation" for mathematics starts with sets and their elements. It is possible to start differently, by axiomatising not elements of sets but functions between sets. This can be done by using the language of categories and universal constructions."

"The remarkable thing is understanding never stays put. It is important always to get a new understanding...understanding can be improved."

Membership

Saunders was a member of the Royal Society of Edinburgh, Heidelberg Academy of Sciences and Humanities, Royal Danish Academy of Sciences and Letters (foreign member), Sigma Xi and Phi Beta Kappa.

• 

  member

  National Academy of Sciences , United States

  1949

• vice president

  National Academy of Sciences , United States

  1963

• president

  Mathematical Association of America , United States

  1953 - 1954

• 

  president

  American Mathematical Society , United States

  1973 - 1974

• 

  council member

  American Academy of Arts and Sciences , United States

  1981 - 1985

• 

  council member

  American Philosophical Society , United States

  1960 - 1963

• vice president

  American Philosophical Society , United States

  1968 - 1971

• executive committee member

  Association for Symbolic Logic

  1945 - 1947

Personality

Saunders was christened "Leslie Saunders MacLane", but "Leslie" fell into disuse, because his parents came to dislike it. Also, he began inserting a space into his surname, because his first wife found it difficult to type the name without a space.

Interests

• Photography

• Sport & Clubs

  Sailing, skiing

Connections

Saunders married Dorothy M. Jones on July 21, 1933. Their marriage produced two children — Gretchen and Cynthia. Saunders' wife, Dorothy, died in February 1985. Later, on August 16, 1986, he married Osa Skotting Segal.

Father:

Donald Bradford MacLane

Mother:

Winifred (Saunders) MacLane

child:

Cynthia MacLane

child:

Gretchen MacLane

Wife:

Osa Skotting Segal

Wife:

Dorothy M. Jones

Brother:

Gerald MacLane

mentor:

Lester S. Hill

mentor:

Jesse Beams

mentor:

Ernest William Brown

mentor:

Ernest Lawrence

mentor:

F. S. C. Northrop

mentor:

Øystein Ore

mentor:

E. H. Moore

mentor:

Leonard Eugene Dickson

mentor:

Gilbert Ames Bliss

mentor:

Mortimer J. Adler

mentor:

Paul Bernays

mentor:

Hermann Weyl

mentor:

Emmy Noether

colleague:

Samuel Eilenberg