In 1926, Saunders entered Yale University, graduating with Bachelor of Arts degree in 1930.

Gallery of Saunders Mac Lane

5801 S Ellis Ave, Chicago, IL 60637, United States

In 1930, Mac Lane enrolled at the University of Chicago, graduating with a Master of Arts degree in 1931.

Gallery of Saunders Mac Lane

Göttingen, Germany

In 1931, Saunders entered the University of Gottingen, graduating with a Doctor of Philosophy degree in 1934.

Career

Gallery of Saunders Mac Lane

1989

1600 Pennsylvania Ave NW, Washington, DC 20500, United States

Saunders Mac Lane (right) receiving the National Medal of Science from former United States President George H. W. Bush at the White House in 1989. Photo made by Susan Biddle.

Gallery of Saunders Mac Lane

1995

2101 Constitution Ave NW, Washington, DC 20418, United States

From left to right: Isadore Singer, Rob Kirby and Saunders Mac Lane at the National Academy of Sciences of the United States in 1995.

1600 Pennsylvania Ave NW, Washington, DC 20500, United States

Saunders Mac Lane (right) receiving the National Medal of Science from former United States President George H. W. Bush at the White House in 1989. Photo made by Susan Biddle.

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

This classic, written by two young instructors, who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.

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

This book presents modern algebra from first principles. It combines standard materials and necessary algebraic manipulations with general concepts, that clarify meaning and importance.

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

This book records the author's efforts to capture in words a description of the form and function of Mathematics, as a background for the Philosophy of Mathematics.

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

This is Graduate Texts in Mathematics, Book 5. Starting from the foundations, the work illuminates the concepts of category, functor, natural transformation and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories.

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

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

Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions, appropriate to various kinds of manifolds. Sheaves also appear in logic as carriers for models of set theory. This text presents topos theory as it has developed from the study of sheaves. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory, as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.

Saunders Mac Lane was an American mathematician and educator. He expanded modern mathematical thinking with his work on cohomology theory and category theory, on which he collaborated with Samuel Eilenberg. Also, Mac Lane carried out research on what are now called Eilenberg–MacLane spaces. This work opened the way to group cohomology in general. Moreover, it was he, who coined the term Yoneda lemma.

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.

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.

(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.

National Academy of Sciences
,
United States

1949

National Academy of Sciences
,
United States

1963

Mathematical Association of America
,
United States

1953 - 1954

American Mathematical Society
,
United States

1973 - 1974

American Academy of Arts and Sciences
,
United States

1981 - 1985

American Philosophical Society
,
United States

1960 - 1963

American Philosophical Society
,
United States

1968 - 1971

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.