Martin David Kruskal

Martin David Kruskal (September 28, 1925 – December 26, 2006) was an American mathematician and physicist.

He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis.

His most celebrated contribution was in the theory of solitons.

His two brothers, both eminent mathematicians, were Joseph Kruskal (1928–2010; discoverer of multidimensional scaling, the Kruskal tree theorem, and Kruskal's algorithm) and William Kruskal (1919–2005; discoverer of the Kruskal–Wallis test).

Martin Kruskal's wife, Laura Kruskal, was a lecturer and writer about origami and originator of many new models.

They were married for 56 years.

Martin Kruskal also invented several origami models including an envelope for sending secret messages.

The envelope could be easily unfolded, but it could not then be easily refolded to conceal the deed.

Their three children are Karen (an attorney ), Kerry (an author of children's books ), and Clyde, a computer scientist.

Martin Kruskal's scientific interests covered a wide range of topics in pure mathematics and applications of mathematics to the sciences.

He had lifelong interests in many topics in partial differential equations and nonlinear analysis and developed fundamental ideas about asymptotic expansions, adiabatic invariants, and numerous related topics.

His Ph.D. dissertation, written under the direction of Richard Courant and Bernard Friedman at New York University, was on the topic "The Bridge Theorem For Minimal Surfaces".

In the 1950s and early 1960s, he worked largely on plasma physics, developing many ideas that are now fundamental in the field.

His theory of adiabatic invariants was important in fusion research.

Important concepts of plasma physics that bear his name include the Kruskal–Shafranov instability and the Bernstein–Greene–Kruskal (BGK) modes.

With I. B. Bernstein, E. A. Frieman, and R. M. Kulsrud, he developed the MHD (or magnetohydrodynamic ) Energy Principle.

His interests extended to plasma astrophysics as well as laboratory plasmas.

He spent much of his career at Princeton University, as a research scientist at the Plasma Physics Laboratory starting in 1951, and then as a professor of astronomy (1961), founder and chair of the Program in Applied and Computational Mathematics (1968), and professor of mathematics (1979).

He was a student at the University of Chicago and at New York University, where he completed his Ph.D. under Richard Courant in 1952.

He received his Ph.D. in 1952.

In 1960, Kruskal discovered the full classical spacetime structure of the simplest type of black hole in general relativity.

A spherically symmetric spacetime can be described by the Schwarzschild solution, which was discovered in the early days of general relativity.

However, in its original form, this solution only describes the region exterior to the event horizon of the black hole.

Kruskal (in parallel with George Szekeres) discovered the maximal analytic continuation of the Schwarzschild solution, which he exhibited elegantly using what are now called Kruskal–Szekeres coordinates.

This led Kruskal to the astonishing discovery that the interior of the black hole looks like a "wormhole" connecting two identical, asymptotically flat universes.

This was the first real example of a wormhole solution in general relativity.

The wormhole collapses to a singularity before any observer or signal can travel from one universe to the other.

This is now believed to be the general fate of wormholes in general relativity.

Kruskal's most widely known work was the discovery in the 1960s of the integrability of certain nonlinear partial differential equations involving functions of one spatial variable as well as time.

These developments began with a pioneering computer simulation by Kruskal and Norman Zabusky (with some assistance from Harry Dym) of a nonlinear equation known as the Korteweg–de Vries equation (KdV).

In the 1970s, when the thermal nature of black hole physics was discovered, the wormhole property of the Schwarzschild solution turned out to be an important ingredient.

Nowadays, it is considered a fundamental clue in attempts to understand quantum gravity.

He retired from Princeton University in 1989 and joined the mathematics department of Rutgers University, holding the David Hilbert Chair of Mathematics.

Apart from serious mathematical work, Kruskal was known for mathematical diversions.

For example, he invented the Kruskal count, a magical effect that has been known to perplex professional magicians because it was based not on sleight of hand but on a mathematical phenomenon.

Martin David Kruskal was born to a Jewish family in New York City and grew up in New Rochelle.

He was generally known as Martin to the world and David to his family.

His father, Joseph B. Kruskal Sr., was a successful fur wholesaler.

His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, became a noted promoter of the art of origami during the early era of television and founded the Origami Center of America in New York City, which later became OrigamiUSA.

He was one of five children.