Martin Kruskal, pre-eminent applied mathematician, dies


Martin Kruskal doted on his three children and loved to think about mathematics as much as possible. So he did the most obvious thing he could think of to combine both worlds.

He dragged an 8-by-4-foot blackboard into the center of his Princeton, N.J., living room and set it on a large wooden stand.

The table-sized slate was usually plastered with what looked like hieroglyphics, but were actually new kinds of math equations, rendering in abstract form the strange behavior of the physical world.

“I was pretty old by the time I realized that blackboards were not in everyone’s living room,” said Mr. Kruskal’s daughter, Karen, now an attorney in Brookline, Mass.

Mr. Kruskal, one of the world’s pre-eminent applied mathematicians and mathematical physicists, died Dec. 26 at Princeton Medical Center after suffering a stroke in mid-December. He was 81.

He had suffered an earlier stroke in August, but had fought his way back to health and was working as an active scholar when he was felled again last month.

Officials at Princeton University announced his death on Thursday. Mr. Kruskal spent 38 years on the Princeton faculty before moving to Rutgers University in 1989.

Brilliant, independent, a night owl and a casual dresser, Mr. Kruskal is best known for his work in the 1960s in which he pioneered the understanding of the soliton, a powerful energy wave. His mathematical analysis of solitons, conducted with colleague Norman Zabusky, proved that such waves were possible and brought them within the realm of practical use, including their use as boosters of the signals conveyed along long-distance, undersea, fiber optic communication cables.

“We have lost a great man, but he left a great legacy for us to celebrate,” said Ingrid Daubechies, the William R. Kenan Jr. Professor of Mathematics and Applied and Computational Mathematics at Princeton.

The phenomenon of solitons was first recorded in 1834, when Scottish scientist John Scott Russell noticed a bump of water traveling through a canal near Edinburgh. On his horse, Russell followed the bump for about two miles.

In the 1950s, Mr. Kruskal made a number of seminal contributions that laid the theoretical foundations of controlled nuclear fusion and the developing field of plasma physics. In 1960, he devised what became known as Kruskal Coordinates used in the theory of relativity to develop black holes.

He also had a fun side. He is renowned among magicians for his invention of a card trick called “The Kruskal Count.”

Raised in New Rochelle, N.Y., Mr. Kruskal’s father was a furrier and his mother a homemaker with a passion for origami. He launched his research career in 1951 at the Princeton Plasma Physics Laboratory and ultimately joined the faculty at Princeton University. In 1989, he transferred to emeritus status as a professor of mathematics and astrophysical sciences at Princeton. He then joined the mathematics department at Rutgers.

There, he filled his office with waist-high piles of papers and texts, studied and taught.

“We would spend hours discussing logic, physics and even philosophy,” said Ovidiu Costin, a former Rutgers student now on the faculty at Ohio State University. “By doing so, he gave me a new vision of mathematics.”

Mr. Kruskal wasn’t the only mathematician in his family.

His older brother, William, was a statistician, best known to the public for the Kruskal-Wallis test, part of every major statistical computation system. His younger brother, Joseph, is well known for deducing some of the intellectual mainstays of computer science, including Kruskal’s Algorithm and the Kruskal Tree Theorem.

His daughter remembers a parade of visitors filing into their home and gathering around the infamous blackboard for scribbling sessions.

She said her father’s day, which began in the afternoon and ended when most other people were having breakfast, worked out well for seeing his wife and three children. He would wake, go teach, and return home for dinner.

The early hours of the evening were spent playing strategy games like chess and backgammon. He wouldn’t let his children win on purpose, but he would calculate a handicap to improve their odds.

After, his research would continue well into the night. Sometimes, he would sit alone, scratching at the blackboard for hours. At other times, he would go to campus and work.

In addition to his daughter, he is survived by his wife, Laura; two sons, Clyde of Maryland and Kerry of New Mexico; and five grandchildren.

A memorial is being planned for mid-February in Princeton. Details will appear online at as they become available.