Martin David Kruskal
This article is written like an obituary. (May 2022) |
Martin Kruskal | |
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Born | Martin David Kruskal September 28, 1925 New York City, New York, US |
Died | December 26, 2006 | (aged 81)
Citizenship | United States |
Alma mater | |
Known for | |
Awards |
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Scientific career | |
Fields | Mathematical physics |
Institutions | |
Doctoral advisor | Richard Courant |
Doctoral students |
Martin David Kruskal (
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 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 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.
Personal life
Martin David Kruskal was born to a
Martin Kruskal's wife, Laura Kruskal, was a lecturer and writer about origami and originator of many new models.[7] 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.[8][failed verification] Their three children are Karen (an attorney[9]), Kerry (an author of children's books[10]), and Clyde, a computer scientist.
Research
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
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". He received his Ph.D. in 1952.
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
In 1960, Kruskal discovered the full classical spacetime structure of the simplest type of
This led Kruskal to the astonishing discovery that the interior of the black hole looks like a "
Kruskal's most widely known work was the discovery in the 1960s of the
This work was partly motivated by the near-
Solitary wave phenomena had been a 19th-century mystery dating back to work by
Solitonic behavior suggested that the KdV equation must have conservation laws beyond the obvious conservation laws of mass, energy, and momentum. A fourth conservation law was discovered by
The inverse scattering method has had an astonishing variety of generalizations and applications in different areas of mathematics and physics. Kruskal himself pioneered some of the generalizations, such as the existence of infinitely many conserved quantities for the
Solitons are now known to be ubiquitous in nature, from physics to biology. In 1986, Kruskal and Zabusky shared the Howard N. Potts Gold Medal from the Franklin Institute "for contributions to mathematical physics and early creative combinations of analysis and computation, but most especially for seminal work in the properties of solitons". In awarding the 2006 Steele Prize to Gardner, Greene, Kruskal, and Miura, the American Mathematical Society stated that before their work "there was no general theory for the exact solution of any important class of nonlinear differential equations". The AMS added, "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."
Kruskal received the National Medal of Science in 1993 "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 an article [17] surveying the state of mathematics at the turn of the millennium, the eminent mathematician Philip A. Griffiths wrote that the discovery of integrability of the KdV equation "exhibited in the most beautiful way the unity of mathematics. It involved developments in computation, and in mathematical analysis, which is the traditional way to study differential equations. It turns out that one can understand the solutions to these differential equations through certain very elegant constructions in algebraic geometry. The solutions are also intimately related to representation theory, in that these equations turn out to have an infinite number of hidden symmetries. Finally, they relate back to problems in elementary geometry."
In the 1980s, Kruskal developed an acute interest in the Painlevé equations. They frequently arise as symmetry reductions of soliton equations, and Kruskal was intrigued by the intimate relationship that appeared to exist between the properties characterizing these equations and completely integrable systems. Much of his subsequent research was driven by a desire to understand this relationship and to develop new direct and simple methods for studying the Painlevé equations. Kruskal was rarely satisfied with the standard approaches to differential equations.
The six Painlevé equations have a characteristic property called the Painlevé property: their solutions are single-valued around all singularities whose locations depend on the initial conditions. In Kruskal's opinion, since this property defines the Painlevé equations, one should be able to start with this, without any additional unnecessary structures, to work out all the required information about their solutions. The first result was an asymptotic study of the Painlevé equations with Nalini Joshi, unusual at the time in that it did not require the use of associated linear problems. His persistent questioning of classical results led to a direct and simple method, also developed with Joshi, to prove the Painlevé property of the Painlevé equations.
In the later part of his career, one of Kruskal's chief interests was the theory of surreal numbers. Surreal numbers, which are defined constructively, have all the basic properties and operations of the real numbers. They include the real numbers alongside many types of infinities and infinitesimals. Kruskal contributed to the foundation of the theory, to defining surreal functions, and to analyzing their structure. He discovered a remarkable link between surreal numbers, asymptotics, and exponential asymptotics. A major open question, raised by Conway, Kruskal and Norton in the late 1970s, and investigated by Kruskal with great tenacity, is whether sufficiently well behaved surreal functions possess definite integrals. This question was answered negatively in the full generality, for which Conway et al. had hoped, by Costin, Friedman and Ehrlich in 2015.[18] However, the analysis of Costin et al. shows that definite integrals do exist for a sufficiently broad class of surreal functions for which Kruskal's vision of asymptotic analysis, broadly conceived, goes through. At the time of his death, Kruskal was in the process of writing a book on surreal analysis with O. Costin.
Kruskal coined the term asymptotology to describe the "art of dealing with applied mathematical systems in limiting cases".[19] He formulated seven Principles of Asymptotology: 1. The Principle of Simplification; 2. The Principle of Recursion; 3. The Principle of Interpretation; 4. The Principle of Wild Behaviour; 5. The Principle of Annihilation; 6. The Principle of Maximal Balance; 7. The Principle of Mathematical Nonsense.
The term asymptotology is not so widely used as the term soliton. Asymptotic methods of various types have been successfully used since almost the birth of science itself. Nevertheless, Kruskal tried to show that asymptotology is a special branch of knowledge, intermediate, in some sense, between science and art. His proposal has been found to be very fruitful.[20][21][22]
Awards and honors
Kruskal's honors and awards included:
- 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) and the American Academy of Arts and Sciences (1983)
- Elected a
- Elected Foreign Member of the Russian Academy of Sciences(2000)[23]
- Elected a Fellow of the Royal Society of Edinburgh(2001)
See also
- Kruskal count in recreational mathematics
References
- ^ S2CID 67365148.
- ^ a b "Fellowship of the Royal Society 1660-2015". London, UK: Royal Society. 2015. Archived from the original on 2015-10-15.
- ^ a b c Martin David Kruskal at the Mathematics Genealogy Project
- ^ O'Connor, John J.; Robertson, Edmund F., "Martin David Kruskal", MacTutor History of Mathematics Archive, University of St Andrews
- ^ American Jewish Archives: "Two Baltic Families Who Came to America The Jacobsons and the Kruskals, 1870-1970" by Richard D. Brown January 24, 1972
- ^ "'Origami Crowns: A Collection by Laura Kruskal, the Queen of Crowns!'". Origami USA.
- ^ "Origami laura l. kruskal | Gilad's Origami Page". www.giladorigami.com.
- ^ Edward Witten, Reminiscenses
- ^ Karen Kruskal Archived 2009-01-06 at the Wayback Machine, pressman-kruskal.com
- ^ Kerry Kruskal, atlasbooks.com
- ^ Magnetohydrodynamics, scholarpedia.org
- ^ N. J. Zabusky, Fermi–Pasta–Ulam Archived 2012-07-10 at archive.today
- ^ Soliton Propagating in a Canal, www.ma.hw.ac.uk
- ^ Modified Korteweg–de Vries (MKdV) Equation Archived 2006-09-02 at archive.today, tosio.math.toronto.edu
- .
- ISSN 1467-9590.
- ^ Ovidiu Costin, Philip Ehrlich, and Harvey M. Friedman, Integration on the surreals: A conjecture of Conway, Kruskal and Norton, 2015, arXiv.org/abs/1505.02478
- ^ Kruskal M. D. Asymptotology Archived 2016-03-03 at the Wayback Machine. Proceedings of Conference on Mathematical Models on Physical Sciences. Englewood Cliffs, NJ: Prentice–Hall, 1963, 17–48.
- ^ Barantsev R. G. Asymptotic versus classical mathematics // Topics in Math. Analysis. Singapore e.a.: 1989, 49–64.
- ^ Andrianov I. V., Manevitch L. I. Asymptotology: Ideas, Methods, and Applications. Dordrecht, Boston, London: Kluwer Academic Publishers, 2002.
- ANZIAMJ., 2002, 44, 33–40.
- Deift, Percy Alec (2016). "Martin D. Kruskal, 1925–2006: Biographical Memoirs"(PDF).
External links
- In Memoriam: Martin David Kruskal
- Zabusky, Norman J. (2005). "Fermi–Pasta–Ulam, Solitons and the Fabric of Nonlinear and Computational Science: History, Synergetics, and Visiometrics". Chaos. 15 (1): 015102. PMID 15836279.
- Solitons, Singularities, Surreals and Such: A Conference in Honor of Martin Kruskal's Eightieth Birthday
- NY Times Obituary, 2007-01-13
- Princeton University Weekly Bulletin Obituary, 2007-02-05
- Chris Eilbeck/Heriot–Watt University, Edinburgh, UK
- Los Angeles Times Obituary, 2007-01-06
- Obituaries – Martin David Kruskal Society for Industrial and Applied Mathematics, 2007-04-11