Martin David Kruskal facts for kids
Quick facts for kids
Martin Kruskal
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Martin David Kruskal
September 28, 1925 New York City, New York, US
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| Died | December 26, 2006 (aged 81) |
| Citizenship | United States |
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| Fields | Mathematical physics |
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| Doctoral advisor | Richard Courant |
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Martin David Kruskal (born September 28, 1925 – died December 26, 2006) was an American mathematician and physicist. He made very important discoveries in many areas of science. These included plasma physics (the study of superheated gases) and general relativity (Einstein's theory of gravity). He also worked on nonlinear analysis (math for complex systems) and asymptotic analysis (math for understanding things in extreme conditions). His most famous work was on the theory of solitons.
Martin Kruskal studied at the University of Chicago and New York University. He earned his Ph.D. in 1952. He spent most of his career at Princeton University. There, he was a research scientist and later a professor. He also started and led the Program in Applied and Computational Mathematics. After retiring from Princeton in 1989, he joined Rutgers University.
Besides his serious math work, Kruskal was known for fun math tricks. For example, he created the Kruskal Count. This is a magic trick that can even puzzle professional magicians. It works not because of tricky hand movements, but because of a clever math idea.
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About Martin Kruskal's Life
Martin David Kruskal was born in New York City. He grew up in New Rochelle. To his friends, he was Martin, but his family called him David. His father, Joseph B. Kruskal Sr., was a successful fur seller. His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, became famous for promoting the art of origami (paper folding). She even started the Origami Center of America in New York City.
Martin was one of five children. His two brothers, Joseph Kruskal and William Kruskal, were also very famous mathematicians. Joseph discovered multidimensional scaling and Kruskal's algorithm. William discovered the Kruskal–Wallis test.
Martin Kruskal's wife, Laura Kruskal, also taught and wrote about origami. She created many new origami models. They were married for 56 years. Martin Kruskal also invented some origami models himself. One was an envelope for sending secret messages. It was easy to unfold, but very hard to refold perfectly. Their three children are Karen, Kerry, and Clyde.
Martin Kruskal's Discoveries
Martin Kruskal was interested in many topics in pure math and how math applies to science. He always loved partial differential equations (math equations with multiple variables) and nonlinear analysis. He also developed important ideas about asymptotic expansions and adiabatic invariants.
His Ph.D. paper was about "The Bridge Theorem For Minimal Surfaces." He finished this work in 1952.
Plasma Physics Discoveries
In the 1950s and early 1960s, Kruskal mostly worked on plasma physics. Plasma is often called the fourth state of matter, like a superheated gas. He developed many ideas that are now key to this field. His work on adiabatic invariants was very important for fusion research. Fusion is the process that powers the sun.
Important ideas in plasma physics named after him include the Kruskal–Shafranov instability. He also helped create the Bernstein–Greene–Kruskal (BGK) modes. With other scientists, he developed the MHD (or magnetohydrodynamic) Energy Principle. This helps understand how plasmas behave. He studied plasmas in space and in labs.
Black Holes and Wormholes
In 1960, Kruskal made a big discovery about black holes in general relativity. Black holes are areas in space where gravity is so strong that nothing, not even light, can escape. A simple type of black hole can be described by the Schwarzschild solution. But this original solution only showed the area outside the black hole's event horizon.
Kruskal (and George Szekeres at the same time) found a way to describe the entire structure of this black hole. He used what are now called Kruskal–Szekeres coordinates. This led him to an amazing discovery: the inside of a black hole looks like a "wormhole." This wormhole connects two identical universes. This was the first real example of a wormhole in general relativity. However, this wormhole collapses before anyone can travel through it. This is now thought to be what happens to most wormholes.
Later, in the 1970s, scientists found that black holes have a "thermal nature." Kruskal's wormhole idea became very important for understanding this. Today, it helps scientists try to understand quantum gravity, which combines quantum mechanics with general relativity.
The Discovery of Solitons
Kruskal's most famous work was his discovery in the 1960s of how to solve certain complex math equations. These equations describe how waves behave. He started with a computer simulation with Norman Zabusky (and Harry Dym). They studied an equation called the Korteweg–de Vries equation (KdV). This equation describes how certain waves spread out.
But Kruskal and Zabusky made a surprising discovery. They found a "solitary wave" solution to the KdV equation. This wave did not spread out. Even more amazing, it kept its shape after crashing into other similar waves! Because these waves acted like particles, they called them "solitons." This name quickly became popular.
This work was partly inspired by a puzzle from 1955. Scientists Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou had simulated a chain of vibrating particles. They expected the energy to spread out quickly. Instead, they saw the energy almost return to its starting point. Kruskal and Zabusky simulated the KdV equation, which was a simpler version of that particle chain. They found the soliton behavior, which explained why the energy didn't spread out as expected.
Solitary waves had been a mystery since the 1800s. John Scott Russell saw one in a canal in 1834 and even chased it on horseback! But scientists like George Airy and George Stokes didn't believe his observations. Their math theories couldn't explain them. Later, Joseph Boussinesq (1871) and Lord Rayleigh (1876) created math theories that supported Scott Russell's findings. In 1895, Diederik Korteweg and Gustav de Vries wrote the KdV equation. But its true properties weren't understood until Kruskal's work in the 1960s.
The idea of solitons suggested that the KdV equation must have hidden rules, called "conservation laws." These were beyond the usual laws for mass, energy, and momentum. Gerald Whitham found a fourth law, and Kruskal and Zabusky found a fifth. Robert M. Miura found even more. He also showed a link between the KdV equation and another one called the Modified Korteweg–de Vries (MKdV) equation.
This link helped Kruskal, with Clifford S. Gardner, John M. Greene, and Miura (GGKM), find a way to solve the KdV equation exactly. This method is called the inverse scattering method. It showed that the KdV equation has an infinite number of hidden rules and can be solved completely. This discovery explained why solitons keep their shape: it's the only way to follow all these hidden rules. Soon after, Peter Lax explained this method in a new way.
The inverse scattering method has been used in many different areas of math and physics. Kruskal himself helped apply it to other equations, like the sine-Gordon equation. This led to more discoveries about how to solve these equations. The sine-Gordon equation is important for understanding relativistic field theory.
Today, solitons are found everywhere in nature, from physics to biology. In 1986, Kruskal and Zabusky received the Howard N. Potts Medal for their work on solitons. In 2006, the American Mathematical Society gave an award to Gardner, Greene, Kruskal, and Miura. They said that before their work, "there was no general theory for the exact solution of any important class of nonlinear differential equations." They added that solitons have changed fields like optics, plasma physics, and ocean science.
Kruskal received the National Medal of Science in 1993. This was for being a leader in nonlinear science and for his work on solitons.
A famous mathematician, Philip A. Griffiths, wrote that the discovery of how to solve the KdV equation showed "the unity of mathematics." It combined computer work, math analysis, algebraic geometry, and representation theory.
Painlevé Equations and Surreal Numbers
In the 1980s, Kruskal became very interested in the Painlevé equations. These equations often appear when simplifying soliton equations. Kruskal wanted to understand the deep connection between them. He always looked for new and simpler ways to study these equations.
The six Painlevé equations have a special property. Their solutions are "single-valued" around all points where they might become infinite. Kruskal believed this property was key. He worked with Nalini Joshi to study these equations. He also developed a simple way to prove this special property.
Later in his career, Kruskal was very interested in surreal numbers. These numbers are built in a special way. They include all the regular numbers, plus many types of infinities and very tiny numbers. Kruskal helped build the foundation of this theory. He also found a link between surreal numbers and his work on asymptotics. He was writing a book on surreal numbers when he passed away.
Asymptotology
Kruskal created the term asymptotology. He used it to describe the "art of dealing with applied mathematical systems in limiting cases." This means understanding how things behave when they become extremely large or extremely small. He listed seven principles for this art.
The term asymptotology is not as widely known as "soliton." But Kruskal showed that it is a special area of knowledge. It's somewhere between science and art. His ideas have been very helpful.
Awards and Honors
Martin Kruskal received many awards and honors, including:
- Gibbs Lecturer, American Mathematical Society (1979)
- Dannie Heineman Prize, American Physical Society (1983)
- Howard N. Potts Gold Medal, Franklin Institute (1986)
- Award in Applied Mathematics and Numerical Analysis, National Academy of Sciences (1989)
- National Medal Of Science (1993)
- John von Neumann Lectureship, SIAM (1994)
- Honorary DSc, Heriot–Watt University (2000)
- Maxwell Prize, Council For Industrial And Applied Mathematics (2003)
- Steele Prize, American Mathematical Society (2006)
- Member of the National Academy of Sciences (1980)
- Member of the American Academy of Arts and Sciences (1983)
- Elected a Foreign Member of the Royal Society (ForMemRS) in 1997
- Elected Foreign Member of the Russian Academy of Sciences (2000)
- Elected a Fellow of the Royal Society of Edinburgh (2001)
See also
- Kruskal count in recreational mathematics
