Garrett Birkhoff American mathematician Date of Birth: 19.01.1911 Country: USA

Biography of Garrett Birkhoff

Garrett Birkhoff was an American mathematician best known for his research in lattice theory. He was born into a family of renowned mathematicians, with his father being George David Birkhoff. This lineage played a significant role in shaping Garrett's future.

In 1928, Garrett enrolled at Harvard University, where he pursued a standard bachelor's program. He obtained his bachelor's degree in 1932 and then moved to Cambridge to study mathematical physics. However, Garrett's interest in this field was short-lived, and he eventually shifted his focus to abstract algebra under the mentorship of Philip Hall. It was during his time in Munich that he met Constantin Carathéodory, who introduced Garrett to Bartel Leendert van der Waerden's work on abstract algebra and Andreas Speiser's work on group theory, which greatly influenced his future research.

Although Garrett did not receive a master's or doctoral degree, it did not hinder his academic career. He became a member of the Harvard Society and continued to teach at Harvard until the end of his career. In the 1930s, Garrett, along with his colleagues Marshall Stone and Saunders Mac Lane, made significant advancements in American abstract algebra. In 1941, Mac Lane and Birkhoff published the second textbook on abstract algebra in the history of the United States. They also released a series of articles, and in 1940, Garrett's monograph on lattice theory was published.

In 1935, Garrett published the article "On the Structure of Abstract Algebras," which laid the foundation for a new area of mathematics called universal algebra. While he built upon the work of predecessors such as Alfred North Whitehead, Garrett's contributions were significant. During World War II, he shifted his focus to the more "engineering" aspect of mathematics, working on radars and ballistic calculations. He also conducted active research in hydrodynamics, which presented challenging computational problems during the development of new weaponry.

Even after the war, Garrett continued to explore the field of "engineering mathematics." As a close friend of John von Neumann, he closely followed the development of early electronic computing devices. He also found time for less mechanical areas of study, such as supervising David M. Young's doctoral dissertation on numerical solutions of partial differential equations. Young proposed an innovative method of successive relaxations in his work.

In later years, Garrett collaborated with Richard S. Varga, one of his former students, at the Westinghouse Corporation's laboratory in Pittsburgh, working on the development of new nuclear reactors. He also provided consulting services, working with companies like General Motors.

Throughout his career, Garrett Birkhoff made significant contributions to various branches of mathematics, ranging from abstract algebra and lattice theory to engineering mathematics and numerical analysis. His research and teaching have left a lasting impact on the field of mathematics.