# George W. Whitehead Jr.

Published: April 16, 2004

George W. Whitehead Jr. of Winchester, MA, professor emeritus in the Department of Mathematics, died on Monday, April 12. He was 85.

Whitehead served on the MIT faculty from 1949 to 1985. His work was exceptionally important to the development of the field of algebraic topology, "one of the most active areas" in mathematics during "the 20 year period after World War II," said Professor of Mathematics Haynes R. Miller. "He played a major role in the creation of that edifice."

Miller refers to Whitehead as his "academic grandfather," a term for the PhD advisor of one's PhD advisor. Whitehead had 530 "academic descendants," a testament to his impact on academia.

Topology is essentially the intricate study of shape, and mathematicians such as Whitehead dealt with high dimensional shapes. Topology would consider a circle to be one dimensional (a one dimensional line traversible by moving left or right), a sphere two dimensional, and so on. The power of topology expands beyond our everyday physical experiences in three spacial dimensions because it provides abstractions and theorems abstractable to arbitrarily high dimensions.

The ideas of topology translate easily to systems or models with a large number of parameters. A parameter’s constraints in relation to the other parameters of the system would carve out its own specific shape of potential system solutions.

Whitehead specialized in analyzing spheres of large dimensions and finding methods or functions that are able to reduce the number of dimensions. In tabulating the many different ways to perform dimensional reduction, Whitehead’s research led to the J-homomorphism, which defines a family of functions allowing one to collapse a large number of parameters by significant amounts.

It was under Whitehead’s leadership that MIT hired at least six leading thinkers in the field of topology. Some in the Department of Mathematics joked that MIT had become the "Massachusetts Institute of Topology."

Now, Miller mentions, topology is a common tool used by mathematicians. "His thesis was a part of that," he said.

In his later research, Whitehead was involved in designing new algorithms that could carry out the same function of collapsing the number of dimensions.

Whitehead also taught graduate courses during his tenure and delivered now-famous lectures that Miller describe as "beautiful." Though remembered as a very shy in person, "in the class room, he had his script and said what he had to say," said Miller.

The prestigious National Academy of Sciences elected him as a member in 1972. He also received numerous distinctions in his field and served as a National Science Foundation Senior Fellowship from 1965-1966.

Whitehead was an integral part of the mathematics community of the Cambridge area, hosting the annual Christmas party for friends of the department in his Arlington, MA home.

Whitehead is survived by his wife, Kay.