View source for Peter Lax

{{for|the German ice hockey player|Peter Lax (ice hockey)}}
{{Short description|Hungarian-born American mathematician (1926–2025)}}
{{Eastern name order|Lax Péter Dávid}}
{{Use dmy dates|date=May 2025}}
{{Infobox scientist
| name              = Peter Lax
| image             = Peter Lax in Tokyo.jpg
| image_size        = 210px
| caption           = Lax in Tokyo in 1969
| birth_name        = Péter Dávid Lax
| birth_date        = {{birth date|df=y|1926|5|1}}
| birth_place       = [[Budapest]], [[Kingdom of Hungary|Hungary]]
| death_date        = {{death date and age|2025|5|16|1926|5|1|df=y}}
| death_place       = New York City, U.S.
| nationality       = {{hlist|American|Hungarian}}
| alma_mater        = {{ubil|
* [[New York University]] {{nobr|([[Bachelor of Science|BS]], [[Master of Science|MS]], [[Doctor of Philosophy|PhD]])}}
* [[Texas A&M University]]
* [[University of New Mexico]]
* [[Stanford University]]
}}
| known_for         = {{plainlist|
* [[Lax equivalence theorem]]
* [[Lax pairs]]
* [[Weak formulation|Lax–Milgram theorem]]
* [[Lax–Friedrichs method]]
* [[Lax–Wendroff method]]
* [[Lax–Wendroff theorem]]
* [[Beurling–Lax theorem]]
* [[Riemann_solver#HLLE_solver|HLLE solver]]
* [[Fourier integral operator]]
}}
| prizes            = {{ubil|[[Paul R. Halmos – Lester R. Ford Award|Lester R. Ford]] (1966) | [[John von Neumann Prize]] (1968)|[[Chauvenet Prize]] (1974)| [[Norbert Wiener Prize]] (1975)| [[National Medal of Science]] (1986) |[[Wolf Prize in Mathematics|Wolf Prize]] (1987) |[[Abel Prize]] (2005)|[[Lomonosov Gold Medal]] (2013)}}
| field             = [[Mathematics]]
| work_institutions = [[Courant Institute of Mathematical Sciences|Courant Institute]]
| thesis_title      = Nonlinear System of Hyperbolic Partial Differential Equations in Two Independent Variables
| thesis_url        = <!--(or  | thesis1_url  =   and  | thesis2_url  =  )-->
| thesis_year       = 1949
| doctoral_advisor  = [[Kurt O. Friedrichs|K. O. Friedrichs]]
| doctoral_students = {{plainlist|
* [[Steve Alpern]]
* [[Chen Li-an]]
* [[Gregory Beylkin]]
* [[Alexandre Chorin]]
* [[Charles Epstein (mathematician)|Charles Epstein]]
* [[Michael Ghil]]
* [[Ami Harten]]
* [[James (Mac) Hyman]]
* [[George Logemann]]
* [[Jeffrey Rauch]]
* [[Burton Wendroff]]
}}
}}

'''Peter David Lax''' (1 May 1926 – 16 May 2025) was a Hungarian-born American mathematician and [[Abel Prize]] laureate working in the areas of [[Pure mathematics|pure]] and [[applied mathematics]].

Lax made important contributions to [[integrable system]]s, [[fluid dynamics]] and [[shock wave]]s, [[soliton]]ic physics, [[hyperbolic conservation laws]], and mathematical and [[scientific computing]], among other fields. In a 1958 paper Lax stated a [[conjecture]] about [[Matrix (mathematics)|matrix]] representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the "Lax conjecture" grew as mathematicians working in several different areas recognized the importance of its implications in their field, until it was finally proven to be true in 2003.<ref>{{cite journal|last1=Lewis|first1=Adrian S.|last2=Parrilo|first2=Pablo A.|last3=Ramana|first3=Motakuri V.|year=2005|title=The Lax conjecture is true|journal=[[Proc. Amer. Math. Soc.]]|volume=133|issue=9|pages=2495–2499|arxiv=math/0304104|doi=10.1090/S0002-9939-05-07752-X|mr=2146191|s2cid=17436983}}</ref>

==Early life and education==
Lax was born on 1 May 1926 in [[Budapest]], [[Kingdom of Hungary|Hungary]],<ref name=nytimesObit /> to a [[Jewish]] family.<ref>{{Cite web | url=https://www.britannica.com/biography/Peter-Lax |title = Peter Lax &#124; Hungarian-American mathematician}}</ref> He began displaying an interest in mathematics at age twelve, and soon his parents hired [[Rózsa Péter]] as a tutor for him.<ref name="mmp" /> His parents Klara Kornfield and Henry Lax were both physicians and his uncle Albert Kornfeld (also known as Albert Korodi) was a mathematician, as well as a friend of [[Leó Szilárd]]. The family left Hungary on 15 November 1941, and traveled via [[Lisbon]] to the United States. 

As a high school student at [[Stuyvesant High School]], Lax took no math classes but did compete on the school math team. During this time, he met with [[John von Neumann]], [[Richard Courant]], and [[Paul Erdős]], who introduced him to [[Albert Einstein]]. As he was still 17 when he finished high school, he could avoid military service, and was able to study for three semesters at [[New York University]]. He attended a [[complex analysis]] class in the role of a student, but ended up taking over as instructor. He met his future wife, [[Anneli Cahn Lax|Anneli Cahn]] (married to her first husband at that time) in this class.<ref name="mmp" /><ref name="conv" />

Before being able to complete his studies, Lax was drafted into the U.S. Army. After basic training, the Army sent him to [[Texas A&M University]] for more studies. He was then sent to [[Oak Ridge National Laboratory]], and soon afterwards to the [[Manhattan Project]] at [[Los Alamos National Laboratory|Los Alamos]], [[New Mexico]]. At Los Alamos, he began working as a calculator operator, but eventually moved on to higher-level mathematics.<ref>{{cite book
 | last = Hersh | first = Reuben
 | doi = 10.1090/mbk/088
 | isbn = 978-1-4704-1708-6
 | location = Providence, Rhode Island
 | mr = 3243612
 | page = 24
 | publisher = American Mathematical Society
 | title = Peter Lax, mathematician
 | url = https://books.google.com/books?id=ammxBgAAQBAJ&pg=PA24
 | year = 2015}}</ref>

After the war ended, Lax remained with the Army at Los Alamos for another year, while taking courses at the [[University of New Mexico]], then studied at [[Stanford University]] for a semester with [[Gábor Szegő]] and [[George Pólya]].<ref name="mmp" /> Lax returned to NYU for the 1946–1947 academic year, and by pooling credits from the four universities at which he had studied, he graduated that year. He stayed at NYU for his graduate studies, marrying Anneli in 1948 and earning a PhD in 1949 under the supervision of [[Kurt O. Friedrichs]].<ref name="mmp">{{citation|contribution=Peter D. Lax|title=More Mathematical People|editor1-first=Donald J.|editor1-last=Albers|editor2-first=Gerald L.|editor2-last=Alexanderson|editor2-link=Gerald L. Alexanderson|editor3-first=Constance|editor3-last=Reid|editor3-link=Constance Reid|publisher=Harcourt Brace Jovanovich|year=1990|pages=138–159}}.</ref><ref name="conv">{{cite news |url=https://www.nytimes.com/2005/03/29/science/29conv.html |title=A Conversation with Peter Lax – From Budapest to Los Alamos, a Life in Mathematics |first=Claudia |last=Dreifus |author-link=Claudia Dreifus |date=29 March 2005 |work=The New York Times|access-date=31 October 2007}}</ref>

==Career==
In 1954, the [[U.S. Atomic Energy Commission]] put Lax and several of his colleagues at NYU in charge of using an early [[supercomputer]] to calculate the risk of flooding for a major nuclear reactor if a nearby dam were sabotaged; they concluded that the reactor would be safe.<ref name=nytimesObit />

Lax made contributions to the theory of [[hyperbolic partial differential equation]]s. He made breakthroughs in understanding [[shock wave]]s from bombs, [[weather prediction]] and [[aerodynamic design]].<ref name=nytimesObit />

Concepts that bear Lax's name include the Lax equivalence principle, which explained when numerical computer approximations would be reliable, and [[Lax pair]]s, which are helpful in understanding the motion of [[soliton]]s. With [[Ralph Phillips (mathematician)|Ralph Phillips]], Lax developed the Lax-Phillips semigroup in [[scattering theory]], which explained how [[wave]]s move around obstacles and showed how to use the pattern of a wave's frequencies to understand its motion. That theory is helpful in [[Radar signal processing|processing radar signals]].<ref name=nytimesObit />

Lax held a faculty position in the Department of Mathematics, [[Courant Institute of Mathematical Sciences]], [[New York University]].<ref>{{Cite web |title=Peter D. Lax |url=https://math.nyu.edu/faculty/lax/ |access-date=2 March 2023 |website=math.nyu.edu}}</ref> Beginning in 1963, Dr. Lax directed the Courant Institute's computing facilities.<ref name=nytimesObit />

Lax died of [[cardiac amyloidosis]] at his Manhattan home, on 16 May 2025, at the age of 99.<ref name=nytimesObit>{{citation |last1=Barany|first1=Michael J.|last2=Shields|first2=Brit|title=Peter Lax, Pre-eminent Cold War Mathematician, Dies at 99 | newspaper=[[The New York Times]] |date=16 May 2025 |url=https://www.nytimes.com/2025/05/16/science/peter-lax-dead.html | access-date=22 May 2025}}</ref>

==Awards and honors==
He was a member of the [[Norwegian Academy of Science and Letters]]<ref>{{cite web|url=http://www.dnva.no/c26849/artikkel/vis.html?tid=40116|title=Gruppe 1: Matematiske fag|publisher=[[Norwegian Academy of Science and Letters]]|language=no|access-date=7 October 2010|archive-date=10 November 2013|archive-url=https://web.archive.org/web/20131110152102/http://www.dnva.no/c26849/artikkel/vis.html?tid=40116|url-status=dead}}</ref> and the [[National Academy of Sciences, USA]],<ref>{{Cite web|title=Peter D. Lax|url=http://www.nasonline.org/member-directory/members/53419.html|access-date=13 December 2021|website=www.nasonline.org}}</ref> the [[American Academy of Arts and Sciences]],<ref>{{Cite web|title=Peter David Lax|url=https://www.amacad.org/person/peter-david-lax|access-date=13 December 2021|website=American Academy of Arts & Sciences|language=en}}</ref> and the [[American Philosophical Society]].<ref>{{Cite web|title=APS Member History|url=https://search.amphilsoc.org/memhist/search?creator=Peter+D.+Lax&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|access-date=13 December 2021|website=search.amphilsoc.org}}</ref> He won a [[Lester R. Ford Award]] in 1966<ref>{{cite journal|author=Lax, Peter D.|title=Numerical solutions of partial differential equations|journal=Amer. Math. Monthly|volume=72, Part II|issue=2|year=1965|pages=78–84|url=http://www.maa.org/programs/maa-awards/writing-awards/numerical-solutions-of-partial-differential-equations|doi=10.2307/2313313 |jstor=2313313}}</ref> and again in 1973.<ref name="shockdecay">{{cite journal|author=Lax, Peter D.|title=The formation and decay of shock waves|journal=Amer. Math. Monthly|volume=79|issue=3|year=1972|pages=227–241|url=http://www.maa.org/programs/maa-awards/writing-awards/the-formation-and-decay-of-shock-waves|doi=10.2307/2316618|jstor=2316618}}</ref> In 1974, his shock wave article<ref name="shockdecay"/> also won the [[Chauvenet Prize]]. He was awarded the [[National Medal of Science]] in 1986, the [[Wolf Prize]] in 1987, the [[Abel Prize]] in 2005 and the [[Lomonosov Gold Medal]] in 2013.<ref>{{Cite web|url=http://www.ras.ru/win/db/award_dsc.asp?P=id-1.ln-en|title=Большая золотая медаль РАН имени М.В. Ломоносова}}</ref> The [[American Mathematical Society]] selected him as its Gibbs Lecturer for 2007.<ref>{{cite journal|author=Lax, Peter D.|title=Mathematics and physics|journal=[[Bull. Amer. Math. Soc.]]|volume=45|issue=1|pages=135–152|mr=2358380|doi=10.1090/s0273-0979-07-01182-2|year=2008|doi-access=free}}</ref> In 2012, he became a fellow of the [[American Mathematical Society]].<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 27 January 2013.</ref>

Lax is listed as an [[ISI highly cited researcher]].<ref>{{Cite web
  | last = Thomson ISI
  | title = Lax, Peter D., ISI Highly Cited Researchers
  | url= http://hcr3.isiknowledge.com/author.cgi?&link1=Browse&link2=Results&id=3419
  | access-date =20 June 2009}}
</ref> According to [[György Marx]] he was one of [[The Martians (scientists)|The Martians]].<ref>[http://fizikaiszemle.hu/archivum/fsz9703/marsl.html A marslakók legendája -] {{Webarchive|url=https://web.archive.org/web/20220409175959/http://fizikaiszemle.hu/archivum/fsz9703/marsl.html |date=9 April 2022 }} [[György Marx]]</ref>

Lax also received an Honorary Doctorate from [[Heriot-Watt University]] in 1990.<ref>{{Cite web|url=http://www1.hw.ac.uk/graduation/honorary-graduates.htm|title=Heriot-Watt University Edinburgh: Honorary Graduates|last=|website=www1.hw.ac.uk|access-date=4 April 2016|archive-date=18 April 2016|archive-url=https://web.archive.org/web/20160418163907/http://www1.hw.ac.uk/graduation/honorary-graduates.htm|url-status=dead}}</ref>

==The CDC 6600 incident==
In 1970, as part of an anti-war protest, the [[Transcendental Students]] took hostage a [[CDC 6600]] [[super computer]] at [[NYU|NYU's]] [[Courant Institute]] which Lax had been instrumental in acquiring; the students demanded $100,000 in ransom ({{Inflation|US|100000|1970|fmt=eq|r=-4}}) to provide bail for a member of the [[Black Panthers]]. Some of the students present attempted to destroy the computer with incendiary devices, but Lax and colleagues managed to disable the devices and save the machine.<ref name=siam>{{cite web|title=Peter Lax|work=The History of Numerical Analysis and Scientific Computing |author=Philip Colella |date=26 April 2004 |publisher=Society for Industrial and Applied Mathematics  |url=http://history.siam.org/oralhistories/lax.htm|author-link=Philip Colella }}</ref><ref>{{cite news | last=Barron | first=James | title=The Mathematicians Who Saved a Kidnapped N.Y.U. Computer | newspaper=The New York Times | url=https://www.nytimes.com/2015/12/07/nyregion/the-mathematicians-who-ended-the-kidnapping-of-an-nyu-computer.html | date=7 December 2015}}</ref>

== Books ==
* {{cite book
	| last1 = Lax
	| first1 = Peter D.
    | last2 =  Maria Shea
    | first2 = Terrell
	| date = 2014
	| title = Calculus With Applications 
    | series = Undergraduate Texts in Mathematics
 | edition = 2nd
	| url = https://link.springer.com/book/10.1007/978-1-4614-7946-8
    | doi = 10.1007/978-1-4614-7946-8
	| location = 
	| publisher = Springer New York, NY
	| page = <!-- or pages: -->
	| isbn = 978-1-4614-7945-1
}}

* {{cite book
	| last1 = Lax
	| first1 = Peter D.
    | author-mask=2
    | last2 =  Maria Shea
    | first2 = Terrell
	| date = 2017
	| title = Multivariable Calculus with Applications 
    | series = Undergraduate Texts in Mathematics
 | edition = 1st
	| url = https://link.springer.com/book/10.1007/978-3-319-74073-7
    | doi = 10.1007/978-3-319-74073-7
	| location = 
	| publisher = Springer New York, NY
	| page = <!-- or pages: -->
	| isbn = 978-3-319-74072-0
}}

* {{cite book | last=Lax | first=Peter D. | author-mask=2 | last2=Terrell | first2=Maria Shea | title=Calculus With Applications | publisher=Springer | publication-place=New York, NY | date=21 September 2013 | isbn=978-1-4614-7945-1}}
* {{cite book | last=Lax | first=Peter D. | author-mask=2 | last2=Zalcman | first2=Lawrence | title=Complex Proofs of Real Theorems | publisher=American Mathematical Soc. | publication-place=Providence, R.I | date=21 December 2011 | isbn=978-0-8218-7559-9}}
* ''Decay of Solutions of Systems of Nonlinear Hyperbolic Conservation Laws'', with [[James Glimm|J. Glimm]], American Mathematical Society (1970).
* {{cite book | last=Lax | first=Peter D. | author-mask=2 | title=Functional Analysis | publisher=John Wiley & Sons | publication-place=New York | date=4 April 2002 | isbn=978-0-471-55604-6}} (Review<ref>{{cite journal|author=Zhu, Meijun|title=Review: ''Functional analysis'', by Peter D. Lax|journal=Bull. Amer. Math. Soc. (N.S.)|year=2006|volume=43|issue=1|pages=123–126|url=https://www.ams.org/journals/bull/2006-43-01/S0273-0979-05-01073-6/S0273-0979-05-01073-6.pdf|doi=10.1090/s0273-0979-05-01073-6|doi-access=free}}</ref>)
* {{cite book | last=Lax | first=Peter D. | author-mask=2 | title=Hyperbolic Partial Differential Equations | publisher=American Mathematical Soc. | publication-place=New York | date=2006 | isbn=978-0-8218-3576-0}}
* {{cite book | last=Lax | first=Peter D. | author-mask=2 | title=Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves | publisher=SIAM | publication-place=Philadelphia, Pa | date=1 January 1973 | isbn=978-0-89871-177-6}}
* {{cite book | last=Lax | first=Peter D. | author-mask=2 | title=Linear Algebra and Its Applications | publisher=John Wiley & Sons | publication-place=Hoboken, N.J | date=10 September 2007 | isbn=978-0-471-75156-4}}
* {{cite book | last=Lax | first=Peter D. | author-mask=2 | title=Mathematical Aspects of Production and Distribution of Energy | publisher=American Mathematical Soc. | publication-place=Providence | date=1977 | isbn=978-0-8218-0121-5}}
* {{cite book | last=Fujita | first=H. | last2=Lax | first2=P.D. | author-mask2=2 | last3=Strang | first3=G. | title=Nonlinear Partial Differential Equations in Applied Science | publisher=Elsevier | publication-place=Amsterdam | date=1 April 2000 | isbn=978-0-08-087192-9}}
* {{cite book | last=Lax | first=Peter D. | author-mask=2 | last2=Nirenberg | first2=L. | last3=Spigler | first3=Renato | title=Recent Advances in Partial Differential Equations, Venice 1996 | publisher=American Mathematical Soc. | publication-place=Providence, R.I | date=1998 | isbn=978-0-8218-0657-9}}
* {{cite book | last=Boillat | first=Guy | last2=Dafermos | first2=Constantin M. | last3=Lax | first3=Peter D. | author-mask3=2 | last4=Liu | first4=Tai-Ping | title=Recent Mathematical Methods in Nonlinear Wave Propagation | publisher=Springer | publication-place=Berlin, Heidelberg | date=14 November 2006 | isbn=978-3-540-49565-9}}
* {{cite book | last=Lax | first=Peter D. | author-mask=2 | last2=Phillips | first2=Ralph S. | title=Scattering Theory, Revised Edition | publisher=Academic Press | publication-place=Boston San Diego New York [etc.] | date=1989 | isbn=0-12-440051-5}}
* {{cite book | last=Lax | first=Peter D. | author-mask=2 | last2=Phillips | first2=Ralph S. | title=Scattering Theory for Automorphic Functions | publisher=Princeton University Press | publication-place=Princeton, NJ | date=1976 | isbn=978-0-691-08184-7}}
* {{Cite book | last1=Lax | first1=Peter D. | author-mask=2 | title=Selected papers. Vol. I | url=https://www.springer.com/us/book/9781461494324 | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-0-387-22925-6 | mr=2164867 | year=2005 }}<ref>{{cite journal|author=Hersh, Reuben|author-link=Reuben Hersh|title=Review of ''Selected papers of Peter Lax'', Vol. I, edited by Peter Sarnak and Andrew Majda|journal=Bull. Amer. Math. Soc.|year=2006|volume=43|pages=605–608|doi=10.1090/s0273-0979-06-01117-7|doi-access=free}}</ref>
* {{Cite book | last1=Lax | first1=Peter D. | author-mask=2 | title=Selected papers. Vol. II | url=https://www.springer.com/us/book/9781461494317 | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-0-387-22926-3 | mr=2164868 | year=2005 }}

==See also==
*[[Babuška–Lax–Milgram theorem]]
*[[Lions–Lax–Milgram theorem]]
*[[The Martians (scientists)]]

==References==
{{reflist}}

==External links==
* [http://manhattanprojectvoices.org/oral-histories/peter-laxs-interview 2016 Video Interview with Peter Lax by Atomic Heritage Foundation] Voices of the Manhattan Project
* {{MathGenealogy|id=13415}}
*{{MacTutor Biography|id=Lax_Peter}}
* [http://www.abelprisen.no/en/prisvinnere/2005/documents/popular2005eng9.pdf Elements from his contributions to mathematics]. Popularised presentation of Peter Lax by [[Helge Holden]], published on the Abel Prize website.
* [http://www.abelprisen.no/en/prisvinnere/2005/documents/abelprize_2005_EN.pdf Abel Prize press release and biography]
* {{cite news |author=Dreifus, C. |title=A Conversation with Peter Lax: From Budapest to Los Alamos, a Life in Mathematics |newspaper=The New York Times|date=29 March 2005 |url=https://www.nytimes.com/2005/03/29/science/29conv.html?_r=0&th=&emc=th&pagewanted=all&position=}}
* {{ cite journal
  | last = Raussen
  | first = Martin
  | author2=Christian Skau
  | title = Interview with Peter D. Lax
  | journal=[[Notices of the American Mathematical Society]]
  | date=February 2006
  | volume = 53
  | issue = 2
  | pages = 223–9
  | url = https://www.ams.org/notices/200602/comm-lax.pdf
  }}

{{Wolf Prize in Mathematics}}
{{Abel Prize laureates}}
{{Winners of the National Medal of Science|math-stat-comp}}
{{Chauvenet Prize recipients}}
{{John von Neumann Lecturers}}
{{AMS Presidents|state=collapsed}}
{{Authority control}}

{{DEFAULTSORT:Lax, Peter}}
[[Category:20th-century American academics]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Fluid dynamicists]]
[[Category:Numerical analysts]]
[[Category:Partial differential equation theorists]]
[[Category:Mathematicians from New York (state)]]
[[Category:Jewish American scientists]]
[[Category:Jewish American academics]]
[[Category:Courant Institute of Mathematical Sciences faculty]]
[[Category:Presidents of the American Mathematical Society]]
[[Category:American textbook writers]]
[[Category:Abel Prize laureates]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:National Medal of Science laureates]]
[[Category:Recipients of the Lomonosov Gold Medal]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Fellows of the Society for Industrial and Applied Mathematics]]
[[Category:Members of the American Philosophical Society]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Members of the Norwegian Academy of Science and Letters]]
[[Category:Foreign members of the USSR Academy of Sciences]]
[[Category:Foreign members of the Russian Academy of Sciences]]
[[Category:Courant Institute of Mathematical Sciences alumni]]
[[Category:Stuyvesant High School alumni]]
[[Category:United States Army personnel of World War II]]
[[Category:Deaths from amyloidosis]]
[[Category:American people of Hungarian-Jewish descent]]
[[Category:Jews who immigrated to the United States to escape Nazism]]
[[Category:Hungarian emigrants to the United States]]
[[Category:20th-century Hungarian Jews]]
[[Category:1926 births]]
[[Category:2025 deaths]]