**Garrett Birkhoff** was an American mathematician best known for the algebra book he wrote with Saunders Mac Lane.

- Garrett was educated at home until he was eight years old when he began to attend school.
- Again, as at his primary school, Garrett progressed very rapidly and despite going to Europe with his parents during his third year of study he was still ready to take the examinations a year early.
- His parents had encouraged him to do this because they were going on a major year long tour and so, after passing the examinations, Garrett attended a boarding school at Lake Placid for a year, spending much time on sport, before he entered Harvard University in 1928.
- With lecturers such as Morse and Whitney, Birkhoff certainly had inspiring teachers at Harvard.
- Birkhoff graduated from Harvard in 1932 and was awarded a Henry Fellowship to study at Cambridge University in England.
- Birkhoff published a joint paper will Hall, On the order of groups of automorphisms which appeared in 1936.
- From Cambridge Birkhoff went to Munich for a month in July 1933 and worked on his own on group theory, but while he was there he visited Carathéodory who pointed him towards van der Waerden's algebra text and Speiser's group theory book.
- Returning to the United States, Birkhoff was a member of the Society of Fellows at Harvard from 1933 to 1936, and then he was appointed as an instructor at Harvard in 1936.
- Mac Lane had been at Harvard during 1934-36 and in 1937 Birkhoff taught his first undergraduate course on abstract algebra.
- When Mac Lane returned to Harvard in 1938 he took over teaching Birkhoff's undergraduate algebra course, then Mac Lane took the course back in 1939.
- The impact of Birkhoff and Mac Lane on the content and teaching of algebra in colleges and universities was immediate and long sustained.
- Perhaps this is rather misleading for Birkhoff did not consider this work closely related to the mathematical physics which he had started out on.
- Later Birkhoff was involved in war work at the Ballistic Research Laboratory at the Aberdeen Proving Ground investigating the effectiveness of exploding shells.
- Birkhoff's work also took him into computing and his friendship with von Neumann led to many interesting discussions on this topic.
- This led to Birkhoff's interest in numerical linear algebra.
- Another piece of consultancy work led Birkhoff into yet another area of mathematics.
- Garrett was quick to recommend the use of cubic splines (i.e. piecewise cubic polynomials with two continuous derivatives) for the representation of smooth curves.
- In 1969 Birkhoff was appointed George Putnam Professor of Pure and Applied Mathematics at Harvard.
- Birkhoff received many honours.

Born 19 January 1911, Princeton, New Jersey, USA. Died 22 November 1996, Water Mill, New York, USA.

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Group Theory, Origin Usa

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive