# Harold Calvin Marston Morse

### Quick Info

Waterville, Maine, USA

Princeton, New Jersey, USA

**Morse**developed variational theory in the large with applications to equilibrium problems in mathematical physics, a theory which is now called Morse theory and forms a vital role in global analysis.

### Biography

**Marston Morse**'s mother was Ella Phoebe Marston and his father was Howard Calvin Morse. The name "Marston" by which he wanted to be known, was therefore his mother's maiden name and not a forename. Howard Morse, Marston's father, was a farmer and a real estate agent. Marston attended Coburn Classical Institute until he was eighteen years old, at which time he entered Colby College in Waterville.

Morse received his B.A. from Colby College in 1914, gaining distinction, and from there he entered Harvard to undertake research in mathematics. He obtained a Master's Degree from Harvard in 1915 then continued to work there on his doctoral dissertation which was directed by G D Birkhoff. He was awarded a Ph.D. in 1917 for a thesis entitled

*Certain Types of Geodesic Motion of a Surface of Negative Curvature*. Morse taught briefly at Harvard before entering military service for the period of World War I. For the duration of the war he served as a private in the U.S. Army in France and for his outstanding work in the Ambulance Corps he was awarded the Croix de Guerre with Silver Star. From 1919 to 1924 he was a second lieutenant in the Reserve Coast Artillery Corps but during this time he had renewed his academic career. In fact his wartime service had prevented him publishing his doctoral thesis, and after the war he set about doing so; it appeared in print in 1921.

He was Benjamin Peirce Instructor at Harvard in 1919-20 and he then became an assistant professor at Cornell (1920-1925) and Brown University (1925-1926). From 1926 until 1935 he was at Harvard, serving as assistant professor (1926-28), associate professor (1928-29), and professor from 1929 to 1935. He then moved to the Institute for Advanced Study at Princeton for the rest of his career until he retired in 1962.

During his time at Cornell, Morse had married Céleste Phelps on 20 June 1922. The marriage produced one son and one daughter but ended in divorce in 1930. At the time of the divorce Morse was a professor at Harvard, and there was a scandal in August 1932 when Céleste Phelps married Osgood, a colleague of Morse's at Harvard. Osgood was 28 years older than Morse, and he was 68 years old at the time of the marriage. These events came as a great shock to Morse, and the scandal led to Osgood retiring. In 1940 Morse married Louise Jeffreys, this marriage producing three daughters and two sons.

Morse developed variational theory in the large with applications to equilibrium problems in mathematical physics. This is now called Morse theory and it grew out of a major discovery which Morse made not long after returning to mathematics after the war and published in his important paper

*Relations between the critical points of a real function of $n$ independent variables*in 1925. Morse theory is important in the field of global analysis which is the study of ordinary and partial differential equations from a global or topological point of view. It builds on the classical results in the calculus developed by Hilbert and his students. Cooper writes in [1]:-

He will have enduring fame as the creator of this subject.Morse's major works include

*Calculus of variations in the large*(1934),

*Functional topology and abstract variational theory*(1938),

*Topological methods in the theory of functions of a complex variable*(1947) and

*Lectures on analysis in the large*(1947).

What distinguishes Morse from many other famous mathematicians is his single-minded persistence with a single theme throughout his life. However this theme, Morse theory, is perhaps the single greatest contribution of American mathematics. It was certainly not his only contribution, however, for in all he wrote about 180 papers and eight books on a whole range of topics. These include papers on minimal surfaces, some on the theory of functions of a complex variable where he was particularly interested in applying topological methods, papers on differential topology and on dynamics.

It is slightly surprising that the topics which most captivated Morse do not show up as such in this list, although in many ways they were still the motivation behind much of his work. From the time he undertook research as a postgraduate with Birkhoff he was directed to the major problems which had interested Poincaré such as the three body problem. He also wanted to produce a topological version of quantum theory, but this largely remained a dream which he never achieved.

After his appointment to the Institute for Advanced Study in 1935 he held various positions such as consultant to the Office of Ordnance and the Coast and Geodetic Survey. He served on various councils and commissions for improving mathematics in the United States including the National research Council (1940-42) and the National Commission on Mathematics (1959-63). At an International level he served as vice president of the International Congress of Mathematicians from 1958 to 1962 having earlier in his career given important lectures at the International Congress of Mathematicians in Zürich in 1932 and Cambridge, USA in 1950.

Morse received many awards for his work. These include the Presidential Certificate of Merit for his war work (1947) and the National Medal for Science from the United States for his mathematical contributions, the Legion d'honneur and the Croix de Guerre from France, and a list of twenty honorary degrees from universities throughout the world. In 1933 the American Mathematical Society awarded him the Bôcher Prize for his memoir

*The foundations of a theory of the calculus of variations in the large in m-space*published in

*Transactions of the American Mathematical Society*in 1929 (which he shared with Norbert Wiener). The American Mathematical Society made him Colloquium Lecturer in 1932, vice-president in 1933-34, president in 1941-42, and Gibbs Lecturer in 1952.

Zund, writing in the

*Dictionary of American Biography*, says this of his character:-

Throughout his life Morse retained the stamp of his Maine upbringing in his frugality and industry. He worked long hours and had many collaborators (usually at the postgraduate level) to whom he transmitted his boundless enthusiasm for mathematics.

### References (show)

- Obituary in
*The Times* - R Bott, Marston Morse and his mathematical works,
*Bull. Amer. Math. Soc.***3**(3) (1980), 907-950. - S S Cairns, Marston Morse, 1892-1977,
*Memorial issue for Marston Morse, Bull. Inst. Math. Acad. Sinica***6**(2) (1978), i-xxiii. - V Pöschl, Marston Morse,
*Jbuch. Heidelberger Akad. Wiss.*(1978), 57-58. - S Smale, Marston Morse (1892-1977) : Obituary,
*The Mathematical Intelligencer***1**(1979), 33-34.

### Additional Resources (show)

Other websites about Marston Morse:

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Written by J J O'Connor and E F Robertson

Last Update October 2003

Last Update October 2003