# Martin David Kruskal

### Quick Info

New York City, New York, USA

Princeton, New Jersey, USA

**Martin Kruskal**was an American mathematician and physicist who worked in plasma physics as well as soliton equations, asymptotic analysis, and surreal numbers.

### Biography

**Martin Kruskal**'s father was Joseph Kruskal who was a successful businessman, the owner of Kruskal & Kruskal, a major fur wholesale business. William's mother was Lillian Vorhaus who became famous as an expert on origami. Martin was one of five children, having two sisters and two brothers. Both brothers William Kruskal and Joseph Kruskal Jr went on to become famous mathematicians. When Martin was very young, the family moved to New Rochelle, a suburb of New York. Martin attended Fieldston High School in Riverdale, New York, and after graduating entered the University of Chicago. He obtained his B.S. from Chicago in 1945, then went to New York University to study for his Master's Degree with the aim of going on to work for a doctorate.

We mentioned above that the Kruskal family lived in New Rochelle. There was a famous mathematician living in New Rochelle who was a near neighbour, namely Richard Courant. At this time Courant was in the process of building his new Institute of Mathematical Sciences at New York University and was very keen to attract high quality graduate students. He soon persuaded Kruskal that he should undertake research at his new Institute and managed to obtain a position for him as Assistant Instructor in the Mathematics Department. Kruskal became an assistant in 1946 and, after studying for his M.S. was awarded the degree in 1948. He then undertook research advised by Richard Courant and Bernard Friedman. During his time as a research student he married Laura in 1950; they had three children. He submitted his thesis

*The Bridge Theorem for Minimal Surfaces*and was awarded his doctorate in 1952. By this time, however, his assistant instructorship at New York University ended in 1951 and in the same year he had moved to Princeton where he had taken up a post in Project Matterhorn, which today is named the Princeton Plasma Physics laboratory [1]:-

[I]t was among the first places in the world to start research on the possibility of producing useful energy from controlled thermonuclear fusion.In 1956 he was promoted to Associate Head of the Theoretical Division of Project Matterhorn. During this period he wrote a number of highly significant papers on plasma physics with a variety of different colleagues. These include

*Exact nonlinear plasma oscillations*(1957),

*An energy principle for hydrodynamic stability problems*(1958),

*On the stability of plasma in static equilibrium*(1958), and

*Equilibrium of a magnetically confined plasma in a toroid*(1958). In 1959, while continuing to hold his post in Project Matterhorn, Kruskal was also appointed as a lecturer in astronomy at Princeton. An important paper on astronomy was

*Maximal extension of Schwarzschild's metric*(1960) which showed that, using what are now called Kruskal coordinates, certain solutions of the equations of general relativity which are singular at the origin are not singular away from the origin, so allowing the study of black holes.

The award of a National Science Foundation Senior Fellowship saw Kruskal spend 1959-60 at the Max Planck Institute in Munich. In 1961 Kruskal was promoted to Professor of Astronomy at Princeton but continued his position within Project Matterhorn until 1964. He spent the winter of 1965-66 in the USSR as part of an exchange programme. Continuing his different roles at Princeton, Kruskal was appointed as director of the Applied Mathematics programme in 1968, a role he held for 20 years. He had been slowly moving from physics towards pure mathematics and that move became complete in 1979 when he was appointed as Professor of Mathematics. He worked at Princeton until 1979 when he retired. However, he did not give up academic work, but rather was appointed to the newly created David Hilbert Chair of Mathematics at Rutgers University.

Kruskal's later work studied soliton equations, asymptotic analysis, and surreal numbers. He was led to asymptotic analysis in his plasma physics studies and from there to solutions of Hamiltonian equations as in

*Asymptotic theory of Hamiltonian and other systems with all solutions nearly periodic*(1962). Analysing asymptotic series also led Kruskal to become interested in surreal numbers, generalisations of real numbers introduced by John Conway. Kruskal's important paper (written jointly with Clifford S Gardner, John M Greene and Robert M Miura)

*Korteweg-de Vries equation and generalizations. VI. Methods for exact solution*published in 1974 was fundamental, and the ideas developed in it were later extended to dynamical systems, inverse scattering, and symplectic geometry. He was awarded the American Mathematical Society's Steele Prize for a Seminal Contribution to Research in 2006. The prize was awarded jointly to Kruskal and Gardner for the above mentioned Korteweg-de Vries paper. The citation reads:-

This is a fundamental paper in the theory of solitons, inverse scattering transforms, and nonlinear completely integrable systems. Before it, there was no general theory for the exact solution of any important class of nonlinear differential equations. In applications of mathematics, solitons and their descendants (kinks, anti-kinks, instantons, and breathers) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences. Nonlinearity has undergone a revolution: from a nuisance to be eliminated, to a new tool to be exploited.This was certainly not the first honour that Kruskal had received. The American Mathematical Society awarded him their Gibbs lectureship in 1979. He was elected to the National Academy of Sciences in 1980 and to the American Academy of Arts and Sciences in 1983. In the same year he received the Dannie Heineman Prize in Mathematical Physics. In 1986 he received the Potts Gold Medal of the Franklin Institute and then the National Academy of Sciences Award in Applied Mathematics and Numerical Analysis in 1989. He received the President's National Medal of Science in 1993. The medal was presented by President Clinton and Vice President Gore at a ceremony on the White House South Lawn on 30 September:-

For his influence as a leader in nonlinear science for more than two decades as the principal architect of the theory of soliton solutions of nonlinear equations of evolution.In 1997 Kruskal was elected to the Royal Society of London, in 2000 he received an honorary doctorate from Heriot-Watt University in Edinburgh, Scotland, and in 2001 he was elected an Honorary Fellow of the Royal Society of Edinburgh.

The authors of [1] write:-

Finally we mention two of Martin Kruskal's deep interests apart from mathematics: limericks and origami. For years, as director of the Program in Applied Mathematics at Princeton, he wrote an appropriate original limerick to appear on the announcement of the applied mathematics colloquium for each speaker. His interest in origami was motivated by his wife Laura, a world renowned creator and teacher of origami, and his mother, the late Lillian Oppenheimer, who founded the Origami Center of America.

### References (show)

- M J Ablowitz, J Greene and H Segur, Martin D Kruskal receives National Medal of Science,
*Notices Amer. Math. Soc.***41**(3) (1994), 182-184. - I V Andrianov, M Kruskal receives the American 'National Medal of Science' (Russian),
*Priroda*(11) (1994), 110-111.

### Additional Resources (show)

Other pages about Martin Kruskal:

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### Honours (show)

Honours awarded to Martin Kruskal

Written by J J O'Connor and E F Robertson

Last Update November 2006

Last Update November 2006