Harold Calvin Marston Morse (March 24, 1892 – June 22, 1977) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

best known for his work on the ''

calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

in the large'', a subject where he introduced the technique of

differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

now known as Morse theory. The

Morse–Palais lemma In mathematics, the Morse–Palais lemma is a result in the calculus of variations and theory of Hilbert spaces. Roughly speaking, it states that a smooth enough function near a critical point can be expressed as a quadratic form after a suitable c ...

, one of the key results in Morse theory, is named after him, as is the

Thue–Morse sequence In mathematics, the Thue–Morse sequence, or Prouhet–Thue–Morse sequence, is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus ...

, an infinite binary sequence with many applications. In 1933 he was awarded the

Bôcher Memorial Prize The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five year ...

for his work in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied ...

Biography

He was born in

Waterville, Maine Waterville is a city in Kennebec County, Maine, United States, on the west bank of the Kennebec River. The city is home to Colby College and Thomas College. As of the 2020 census the population was 15,828. Along with Augusta, Waterville is ...

to Ella Phoebe Marston and Howard Calvin Morse in 1892. He received his

bachelor's degree A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to si ...

from

Colby College Colby College is a private liberal arts college in Waterville, Maine. It was founded in 1813 as the Maine Literary and Theological Institution, then renamed Waterville College after the city where it resides. The donations of Christian philanth ...

(also in Waterville) in 1914. At

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of highe ...

, he received both his

master's degree A master's degree (from Latin ) is an academic degree awarded by universities or colleges upon completion of a course of study demonstrating mastery or a high-order overview of a specific field of study or area of professional practice.

in 1915 and his

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * '' Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. al ...

in 1917. He wrote his PhD thesis, ''Certain Types of Geodesic Motion of a Surface of Negative Curvature'', under the direction of George David Birkhoff. Morse was a Benjamin Peirce Instructor at Harvard in 1919–1920, after which he served as an assistant professor at

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...

from 1920 to 1925 and at

Brown University Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providenc ...

in 1925–1926. He returned to Harvard in 1926, advancing to professor in 1929, and teaching there until 1935. That year, he accepted a position at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nin ...

, where he remained until his retirement in 1962. He spent most of his career on a single subject, now known as Morse theory, a branch of

that enables one to analyze the

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

of a

smooth manifold In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One ma ...

by studying

differentiable function In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non- vertical tangent line at each interior point in ...

s on that manifold. Morse originally applied his theory to

geodesic In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connecti ...

s ( critical points of the

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...

functional Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional sy ...

on paths); these techniques were used in Raoul Bott's proof of his periodicity theorem. Morse theory is a very important subject in modern

mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developm ...

, such as

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...

. He died on June 22, 1977, at his home in

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of w ...

. Marston Morse should not be confused with either his 5th cousin twice removed

Samuel Morse Samuel Finley Breese Morse (April 27, 1791 – April 2, 1872) was an American inventor and painter. After having established his reputation as a portrait painter, in his middle age Morse contributed to the invention of a single-wire telegraph ...

, famous for

Morse code Morse code is a method used in telecommunication to encode text characters as standardized sequences of two different signal durations, called ''dots'' and ''dashes'', or ''dits'' and ''dahs''. Morse code is named after Samuel Morse, one ...

, nor Anthony Morse, famous for the Morse–Sard theorem.

Selected publications

Articles

* * * * * * * * * * * *

Books

* * * * * with Stewart Cairns: * * * *

Film

"Pits, Peaks, and Passes: A Lecture on Critical Point Theory"
Mathematical Association of America Lecture Films, 1966

Notes

Biographical references

* .

References

* . * (

e-book An ebook (short for electronic book), also known as an e-book or eBook, is a book publication made available in digital form, consisting of text, images, or both, readable on the flat-panel display of computers or other electronic devices. A ...

: ). {{DEFAULTSORT:Morse, Marston 1892 births 1977 deaths 20th-century American mathematicians Colby College alumni Cornell University faculty Differential geometers Harvard University alumni Harvard University faculty Institute for Advanced Study faculty People from Waterville, Maine Princeton University faculty Brown University faculty Topologists National Medal of Science laureates Presidents of the American Mathematical Society Variational analysts Mathematicians from Maine Members of the United States National Academy of Sciences