MOUNT LAUREL, N.J.-- Martin David Kruskal, a mathematician whose work on the properties of an unusual kind of waves helped lead to the development of fiber optic technology, died Dec. 26 in Princeton after a series of strokes. He was 81.
Until his first stroke earlier last year, Dr. Kruskal remained an active scholar, colleagues said.
"He was a brilliant mathematician and his contributions were extremely original," said Ovidiu Costin, a math professor at Ohio State who was a student of Dr. Kruskal's at Rutgers University. "His interest was in science altogether, not only math but also physics, logic and philosophy."
Dr. Kruskal spent 38 years on the faculty at Princeton University before joining Rutgers in 1989.
Dr. Kruskal's best-known advance came in the 1960s when he was able to use equations to explain a phenomenon 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 2 miles.
Usually, waves that collide deform each other. But this other kind, which Dr. Kruskal and collaborator Norman Zabusky came to call "solitons," do not. Instead, they pass through one another. Light transmitted over fiber optic cables for communication purposes has the same properties.
For his work on solitons and other issues in math -- including using the Theory of General Relativity to help explain black holes, Dr. Kruskal was given a National Medal of Science in 1996 and the Steele Prize for Seminal Contribution to Research by the American Mathematical Society last year, among other awards.
He came to Princeton in 1951 to work on a classified project to produce controlled thermonuclear fusion. He was later a professor of astronomy and held a chair in applied and computational mathematics before becoming a professor of mathematics in 1979.
Dr. Kruskal's scholarship dealt largely with problems related to natural phenomena, but he was also interested in other areas of math. At the end of his life, he was working with what scholars call surreal numbers, for instance "1" followed by an infinite number of zeros.
His versatility as a scholar was noted by colleagues. "It's not unusual for great mathematicians -- and he was one of those," said Joel Lebowitz, a mathematics professor who worked with Dr. Kruskal at Rutgers.
Another of his legacies was better known among magicians than mathematicians. The Kruskal Count is a card trick that employs some deceptively simple math to make it seem as if the magician is reading the mind of a subject who picks a number between one and 10.
Apart from his brilliance, Dr. Kruskal was known to be willing to admit when he was wrong -- on matters dealing with math and other areas of life.
"My father would graciously and with good humor be able to change his thinking about something," said his daughter, Karen, of Brookline, Mass. "It was more important to figure out what was true than was winning a point."
Karen Kruskal said her father doted on his children and grandchildren and loved playing such games as chess with them. He was so passionate about his work that he kept a big blackboard in the living room of their Princeton home so he could work out equations.
Dr. Kruskal, who was born in New Rochelle, N.Y., in 1925, and educated at the University of Chicago and New York University, was from a math-inclined family. His brothers, Joseph and the late William, also became well-known mathematicians. Their late mother, Lillian Oppenheimer, helped popularize origami in the United States.
In addition to his daughter and brother, Dr. Kruskal leaves his wife of 56 years, Laura; two other children; and five grandchildren.
A memorial was being planned for February in Princeton.