Marston Morse

Early Life and Education

Marston Morse, born Harold Calvin Marston Morse on March 24, 1892, in Waterville, Maine, was an influential American mathematician known for his work in the field of calculus of variations. Morse's early education took place in Waterville, where he displayed an early aptitude for mathematics. He pursued his undergraduate studies at Colby College, graduating in 1914. His academic journey continued at Harvard University, where he obtained his Ph.D. in 1917 under the supervision of George David Birkhoff. His doctoral dissertation, "The Foundations of a Theory of the Calculus of Variations in the Large," laid the groundwork for his future contributions to mathematics.

Academic Career

After completing his Ph.D., Morse held several academic positions. He initially taught at Cornell University and later at Brown University. In 1926, he joined the faculty of Harvard University, where he remained until 1935. During his tenure at Harvard, Morse developed the Morse theory, a branch of differential topology that provides a framework for analyzing the topology of manifolds using smooth functions. This theory has had far-reaching implications in various areas of mathematics and theoretical physics.

In 1935, Morse moved to the Institute for Advanced Study in Princeton, New Jersey, where he worked alongside some of the most prominent mathematicians of the time, including Albert Einstein and John von Neumann. He remained at the Institute until his retirement in 1962.

Contributions to Mathematics

Morse Theory

Morse's most significant contribution to mathematics is undoubtedly Morse theory. This theory provides a method for analyzing the topology of smooth manifolds by studying the critical points of smooth functions defined on these manifolds. A critical point of a smooth function is a point where the gradient of the function vanishes. Morse theory relates the topology of the manifold to the nature and distribution of these critical points.

Morse theory has applications in various fields, including differential topology, algebraic topology, and mathematical physics. It has been instrumental in the development of Floer homology, a tool used in the study of symplectic geometry and low-dimensional topology.

Morse-Sard Theorem

Another notable contribution by Morse is the Morse-Sard theorem. This theorem states that the set of critical values of a smooth function on a manifold has measure zero. In other words, almost all values of a smooth function are regular values, meaning that the preimage of these values consists of regular points. The Morse-Sard theorem has important implications in the study of differential topology and the calculus of variations.

Morse-Kelley Set Theory

Morse also made contributions to set theory, particularly in collaboration with John L. Kelley. Together, they developed the Morse-Kelley set theory, an axiomatic set theory that extends the Zermelo-Fraenkel set theory (ZF) by including a stronger form of the axiom of choice and allowing for the existence of proper classes. This set theory has been influential in the study of large cardinals and other areas of mathematical logic.

Personal Life

Marston Morse married Louise Morse in 1918, and the couple had three children. Despite his intense dedication to mathematics, Morse was known for his warm personality and his ability to inspire students and colleagues alike. He was an avid outdoorsman and enjoyed hiking and exploring nature, activities that often provided him with inspiration for his mathematical work.

Awards and Honors

Throughout his career, Morse received numerous awards and honors in recognition of his contributions to mathematics. He was elected to the National Academy of Sciences in 1932 and received the Bôcher Memorial Prize from the American Mathematical Society in 1933. In 1964, he was awarded the National Medal of Science, one of the highest honors bestowed upon scientists in the United States.

Legacy

Marston Morse's work has left a lasting impact on the field of mathematics. His development of Morse theory has influenced a wide range of mathematical disciplines and has inspired subsequent generations of mathematicians. The concepts and techniques he introduced continue to be relevant in contemporary mathematical research.

Morse passed away on June 22, 1977, in Princeton, New Jersey. His legacy lives on through the many mathematical concepts and theories that bear his name, as well as through the continued application of his work in modern mathematical research.

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