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{{short description|American mathematician}}
{{obituary|date=May 2022}}
{{Infobox scientist
| name                    = Martin Kruskal
| image= Martin David Kruskal.jpg
| image_size             =
| caption                 = 
| birth_name = Martin David Kruskal
| birth_date              = {{Birth date|1925|09|28}}
| birth_place             = [[New York City]], [[New York (state)|New York]], US
| death_date              = {{Death date and age|2006|12|26|1925|09|28}}
| death_place             = [[Princeton, New Jersey]], US
| citizenship             = [[United States]]
| nationality             =
| alma_mater              = {{Plainlist|
* [[New York University]]
* [[University of Chicago]]}}
| doctoral_advisor        = [[Richard Courant]]
| doctoral_students       = {{Plainlist|
* [[Robert Sinclair MacKay]]<ref name="mathgene">{{MathGenealogy|id=6194}}</ref>
* [[Steven Orszag]]<ref name="mathgene"/>
*[[Nalini Joshi]]<ref name="mathgene"/>}}
| known_for               = {{Plainlist|[[Kruskal–Szekeres coordinates]]<br/>[[Kruskal–Shafranov instability]]<br/>[[Bernstein–Greene–Kruskal modes]]<br/>[[Kruskal–Schwarzchild instability]]<br/>Theory of [[soliton]]s<br/>[[Kruskal count]]}}
| footnotes               = 
| ethnicity               =
| field                   = [[Mathematical physics]]
| work_institution        = {{Plainlist|
* [[Rutgers University]]
* [[Princeton University]]}}
| prizes                  = {{Plainlist|
* [[Dannie Heineman Prize for Mathematical Physics|Heineman Prize]] {{small|(1983)}}
* [[National Medal of Science]] {{small|(1993)}}
* [[Fellow of the Royal Society|ForMemRS]] (1997)<ref name="Gibbon-Cowley_Joshi-MacCallum_2017"/><ref name="RS_2015"/>
* [[Leroy P. Steele Prizes|Steele Prize]] (2006)}}
| religion                = 
}}

'''Martin David Kruskal''' ({{IPAc-en|ˈ|k|r|ʌ|s|k|əl}}; September 28, 1925 &ndash; December 26, 2006)<ref name="Gibbon-Cowley_Joshi-MacCallum_2017"/> 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]].<ref name="mactutor">{{MacTutor Biography|id=Kruskal_Martin}}</ref>

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 [[American Jews|Jewish]] family<ref>[http://americanjewisharchives.org/publications/journal/PDF/1972_24_01_00_brown.pdf American Jewish Archives: "Two Baltic Families Who Came to America The Jacobsons and the Kruskals, 1870-1970" by Richard D. Brown] January 24, 1972</ref> in [[New York City]] and grew up in [[New Rochelle, New York|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.<ref>{{cite web |url=https://origamiusa.org/thefold/article/%E2%80%98origami-crowns-collection-laura-kruskal-queen-crowns%E2%80%99 |title='Origami Crowns: A Collection by Laura Kruskal, the Queen of Crowns!' |website=Origami USA}}</ref> He was one of five children. 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.<ref>{{Cite web |url=https://www.giladorigami.com/origami-database/Laura+L.+Kruskal |title=Origami laura l. kruskal &#124; Gilad's Origami Page |website=www.giladorigami.com}}</ref> 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.<ref>{{Cite web |date=2018-01-19 |title=Martin Kruskal - School of Natural Sciences {{!}} Institute for Advanced Study |url=https://www.ias.edu/sns/content/martin-kruskal |access-date=2024-12-28 |website=www.ias.edu |language=en}}</ref>{{failed verification|date=October 2022}} Their three children are Karen (an attorney<ref>{{Cite web |title=Karen L. Kruskal |url=http://www.pressman-kruskal.com/jsp2957169.jsp |archive-url=https://web.archive.org/web/20090106155211/http://www.pressman-kruskal.com/jsp2957169.jsp |archive-date=2009-01-06 |access-date=2024-12-28 |website=www.pressman-kruskal.com |url-status=dead }}</ref>), Kerry (an author of children's books<ref>{{Cite web |title=Tewiggly - Wriggley Rex by Kerry Kruskal...Princeton Pedagogical Publications |url=http://www.atlasbooks.com/marktplc/01751.htm |archive-url=https://web.archive.org/web/20090602232315/http://www.atlasbooks.com/marktplc/01751.htm |archive-date=2009-06-02 |access-date=2024-12-28 |website=www.atlasbooks.com |url-status=dead }}</ref>), and [[Clyde Kruskal|Clyde]], a computer scientist.

==Research==
{{Section cleanup|reason=Too continuous, can be broken down in sections or sub sections.|date=May 2024}}
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 equation]]s and [[nonlinear analysis]] and developed fundamental ideas about [[asymptotic expansion]]s, [[adiabatic invariant]]s, 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 surface|Minimal Surface]]s". 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 [[Kruskal–Shafranov instability]] and the [[Bernstein–Greene–Kruskal modes|Bernstein–Greene–Kruskal (BGK) modes]]. With I. B. Bernstein, E. A. Frieman, and R. M. Kulsrud, he developed the MHD (or [[magnetohydrodynamics|magnetohydrodynamic]]<ref>{{Cite journal |last=Dorch |first=Søren Bertil F. |date=2007-04-13 |title=Magnetohydrodynamics |journal=Scholarpedia |language=en |volume=2 |issue=4 |pages=2295 |doi=10.4249/scholarpedia.2295 |doi-access=free |bibcode=2007SchpJ...2.2295D |issn=1941-6016}}</ref>) Energy Principle. His interests extended to plasma astrophysics as well as laboratory plasmas.

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. In the 1970s, when the [[black hole thermodynamics|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]].

Kruskal's most widely known work was the discovery in the 1960s of the [[integrable system|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). The KdV equation is an asymptotic model of the propagation of nonlinear [[Dispersion (water waves)|dispersive]] waves. But Kruskal and Zabusky made the startling discovery of a "solitary wave" solution of the KdV equation that propagates non-dispersively and even regains its shape after a collision with other such waves. Because of the particle-like properties of such a wave, they named it a "[[soliton]]", a term that caught on almost immediately.

This work was partly motivated by the near-[[Poincaré recurrence theorem|recurrence]] paradox that had been observed in a very early computer simulation<ref>N. J. Zabusky, [http://link.aip.org/link/?CHAOEH/15/015102/1 Fermi–Pasta–Ulam] {{webarchive|url=https://archive.today/20120710231428/http://link.aip.org/link/?CHAOEH/15/015102/1 |date=2012-07-10 }}</ref> of a [[FPUT problem|certain nonlinear lattice]] by [[Enrico Fermi]], [[John Pasta]], [[Stanislaw Ulam]] and [[Mary Tsingou]] at [[Los Alamos National Laboratory|Los Alamos]] in 1955. Those authors had observed long-time nearly recurrent behavior of a one-dimensional chain of anharmonic oscillators, in contrast to the rapid thermalization that had been expected. Kruskal and Zabusky simulated the KdV equation, which Kruskal had obtained as a [[continuum limit]] of that one-dimensional chain, and found solitonic behavior, which is the opposite of thermalization. That turned out to be the heart of the phenomenon.

Solitary wave phenomena had been a 19th-century mystery dating back to work by [[John Scott Russell]] who, in 1834, observed what we now call a soliton, propagating in a canal, and chased it on horseback.<ref>{{Cite web |title=John Scott Russell and the solitary wave |url=http://www.ma.hw.ac.uk/~chris/scott_russell.html |access-date=2024-12-28 |website=www.ma.hw.ac.uk |archive-date=2013-05-25 |archive-url=https://web.archive.org/web/20130525042658/http://www.ma.hw.ac.uk/~chris/scott_russell.html |url-status=dead }}</ref> In spite of his observations of solitons in wave tank experiments, Scott Russell never recognized them as such, because of his focus on the "great wave of translation," the largest amplitude solitary wave. His experimental observations, presented in his Report on Waves to the British Association for the Advancement of Science in 1844, were viewed with skepticism by [[George Airy]] and [[Sir George Stokes, 1st Baronet|George Stokes]] because their linear water wave theories were unable to explain them.  [[Joseph Boussinesq]] (1871) and [[Lord Rayleigh]] (1876) published mathematical theories justifying Scott Russell's observations. In 1895, [[Diederik Korteweg]] and [[Gustav de Vries]] formulated the KdV equation to describe shallow water waves (such as the waves in the canal observed by Russell), but the essential properties of this equation were not understood until the work of Kruskal and his collaborators in the 1960s.

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 [[Gerald Whitham]] and a fifth one by Kruskal and Zabusky. Several new conservation laws were discovered by hand by [[Robert M. Miura|Robert Miura]], who also showed that many conservation laws existed for a related equation known as the Modified Korteweg–de Vries (MKdV) equation.<ref>[http://tosio.math.toronto.edu/wiki/index.php/Modified_Korteweg-de_Vries_equation Modified Korteweg–de Vries (MKdV) Equation] {{webarchive|url=https://archive.today/20060902100701/http://tosio.math.toronto.edu/wiki/index.php/Modified_Korteweg-de_Vries_equation |date=2006-09-02}}, tosio.math.toronto.edu</ref> With these conservation laws, Miura showed a connection (called the Miura transformation) between solutions of the KdV and MKdV equations. This was a clue that enabled Kruskal, with [[Clifford S. Gardner]], [[John M. Greene]], and Miura (GGKM),<ref>{{cite journal |author-last1=Gardner |author-first1=Clifford S. |author-last2=Greene |author-first2=John M. |author-last3=Kruskal |author-first3=Martin D. |author-last4=Miura |author-first4=Robert M. |date=1967-11-06 |title=Method for Solving the Korteweg-deVries Equation |journal=Physical Review Letters |volume=19 |issue=19 |pages=1095–1097 |doi=10.1103/PhysRevLett.19.1095 |bibcode=1967PhRvL..19.1095G}}</ref> to discover a general technique for exact solution of the KdV equation and understanding of its conservation laws. This was the [[inverse scattering method]], a surprising and elegant method that demonstrates that the KdV equation admits an infinite number of [[Poisson bracket|Poisson-commuting]] conserved quantities and is completely integrable. This discovery gave the modern basis for understanding of the soliton phenomenon: the solitary wave is recreated in the outgoing state because this is the only way to satisfy all of the conservation laws. Soon after GGKM, [[Peter Lax]] famously interpreted the inverse scattering method in terms of [[isospectral deformation]]s and [[Lax pair]]s.

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 [[sine-Gordon equation]]. This led to the discovery of an inverse scattering method for that equation by M. J. [[Ablowitz]], D. J. Kaup, A. C. Newell, and H. Segur (AKNS).<ref>{{cite journal |author-last1=Ablowitz |author-first1=Mark J. |author-last2=Kaup |author-first2=David J. |author-last3=Newell |author-first3=Alan C. |date=1974-12-01 |title=The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems |journal=Studies in Applied Mathematics |language=en |volume=53 |issue=4 |pages=249–315 |doi=10.1002/sapm1974534249 |issn=1467-9590}}</ref> The sine-Gordon equation is a relativistic wave equation in 1+1 dimensions that also exhibits the soliton phenomenon and which became an important model of solvable [[Theory of relativity|relativistic]] field theory. In seminal work preceding AKNS, [[Vladimir E. Zakharov|Zakharov]] and Shabat discovered an inverse scattering method for the nonlinear Schrödinger equation.

Solitons are now known to be ubiquitous in nature, from physics to biology. In 1986, Kruskal and Zabusky shared the [[Howard N. Potts Medal|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<ref>P. A. Griffiths [http://www.ias.ac.in/currsci/sep25/articles16.htm "Mathematics At The Turn Of The Millennium,"] Amer. Mathematical Monthly  Vol. 107, No. 1 (Jan., 2000), pp. 1–14, {{doi|10.1080/00029890.2000.12005154}}</ref> 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 [[Paul Painlevé|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 transcendents|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 number]]s. 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.<ref>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</ref> 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".<ref>Kruskal M. D. [http://bp.pppl.gov/pub_report/1995/MATT160.pdf Asymptotology] {{Webarchive|url=https://web.archive.org/web/20160303214953/http://bp.pppl.gov/pub_report/1995/MATT160.pdf |date=2016-03-03 }}. Proceedings of Conference on Mathematical Models on Physical Sciences. Englewood Cliffs, NJ: Prentice–Hall, 1963, 17–48.</ref> 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.<ref>Barantsev R. G. Asymptotic versus classical mathematics // Topics in Math. Analysis. Singapore e.a.: 1989, 49–64.</ref><ref>Andrianov I. V., Manevitch L. I. Asymptotology: Ideas, Methods, and Applications. Dordrecht, Boston, London: Kluwer Academic Publishers, 2002.</ref><ref>Dewar R. L. Asymptotology – a cautionary tale. [[ANZIAM]] J., 2002, 44, 33–40.</ref>

<!-- ==Recreational mathematics== -->

==Awards and honors==
Kruskal's honors and awards included:
{{div col|colwidth=35em}}
* Gibbs Lecturer, [[American Mathematical Society]] (1979);
* [[Dannie Heineman Prize for Mathematical Physics|Dannie Heineman Prize]], [[American Physical Society]] (1983);
* [[Howard N. Potts Medal|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);
* [[Leroy P. Steele Prize|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 [[List of Fellows of the Royal Society elected in 1997|Foreign Member of the Royal Society (ForMemRS) in 1997]]<ref name="Gibbon-Cowley_Joshi-MacCallum_2017"/><ref name="RS_2015"/>
* Elected Foreign Member of the [[Russian Academy of Sciences]](2000)<ref name="Deift_2016"/>
* Elected a [[Fellow of the Royal Society of Edinburgh]] (2001)
{{div col end}}

==See also==
* [[Kruskal count]] in recreational mathematics

==References==
<references>
<ref name="Gibbon-Cowley_Joshi-MacCallum_2017">{{cite journal |author-last1=Gibbon |author-first1=John D. |author-last2=Cowley |author-first2=Steven C. |author-link2=Steven Cowley |author-last3=Joshi |author-first3=Nalini |author-link3=Nalini Joshi |author-last4=MacCallum |author-first4=Malcolm A. H. |title=Martin David Kruskal. 28 September 1925 — 26 December 2006 |journal=[[Biographical Memoirs of Fellows of the Royal Society]] |volume=64 |pages=261–284 |date=2017 |issn=0080-4606 |doi=10.1098/rsbm.2017.0022 |arxiv=1707.00139 |s2cid=67365148}}</ref>
<ref name="RS_2015">{{cite web |title=Fellowship of the Royal Society 1660-2015 |date=2015 |url=https://docs.google.com/spreadsheets/d/1RVVZY00MZNrK2YCTTzVrbTFH2t3RxoAZah128gQR-NM/pubhtml |location=London, UK |publisher=[[Royal Society]] |archive-url=https://web.archive.org/web/20151015185820/https://docs.google.com/spreadsheets/d/1RVVZY00MZNrK2YCTTzVrbTFH2t3RxoAZah128gQR-NM/pubhtml |archive-date=2015-10-15 |url-status=dead}}</ref>
<ref name="Deift_2016">{{cite web |url=http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/kruskal-martin.pdf |title=Martin D. Kruskal, 1925–2006: Biographical Memoirs |author-first=Percy Alec |author-last=Deift |author-link=Percy Alec Deift |date=2016}}</ref>
</references>

==External links==
{{wikiquote}}
* [https://web.archive.org/web/20131212151727/http://www.math.rutgers.edu/docs/kruskal/ In Memoriam: Martin David Kruskal]
* {{cite journal |author-first=Norman J. |author-last=Zabusky |title=Fermi–Pasta–Ulam, Solitons and the Fabric of Nonlinear and Computational Science: History, Synergetics, and Visiometrics |journal=Chaos |volume=15 |issue=1 |page=015102 |date=2005 |doi=10.1063/1.1861554 |pmid=15836279 |bibcode=2005Chaos..15a5102Z}}
* [http://www.math.rutgers.edu/~lebowitz/Kruskal/ Solitons, Singularities, Surreals and Such: A Conference in Honor of Martin Kruskal's Eightieth Birthday]
* [https://www.nytimes.com/2007/01/13/obituaries/13kruskal.html?ex=1326344400&en=8357b31a10c56f61&ei=5088&partner=rssnyt&emc=rss NY Times Obituary, 2007-01-13]
* [https://www.princeton.edu/pr/pwb/07/0205/2a.shtml Princeton University Weekly Bulletin Obituary, 2007-02-05]
* [http://www.ma.hw.ac.uk/~chris/kruskal/ Chris Eilbeck/Heriot–Watt University, Edinburgh, UK]
* [https://www.latimes.com/science/la-sci-kruskal6jan06-story.html Los Angeles Times Obituary, 2007-01-06]
* [https://web.archive.org/web/20110410032825/http://www.siam.org/news/news.php?id=1111 Obituaries – Martin David Kruskal] Society for Industrial and Applied Mathematics, 2007-04-11

{{Winners of the National Medal of Science|math-stat-comp}}
{{John von Neumann Lecturers}}
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{{DEFAULTSORT:Kruskal, Martin David}}
[[Category:1925 births]]
[[Category:2006 deaths]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:20th-century American Jews]]
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[[Category:Fellows of the American Physical Society]]
[[Category:National Medal of Science laureates]]
[[Category:Courant Institute of Mathematical Sciences alumni]]
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[[Category:American relativity theorists]]
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[[Category:Scientists from New Rochelle, New York]]
[[Category:20th-century American physicists]]
[[Category:Howard N. Potts Medal recipients]]
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[[Category:Fellows of the Royal Society of Edinburgh]]
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[[Category:Recreational mathematicians]]