View source for Mark Kac

{{Short description|Polish-American Mathematician}}
{{Infobox scientist
| name=Mark Kac
| image= Mark_Kac.jpg
| birth_date  = {{Birth date|1914|8|3|mf=y}}
| birth_place = [[Krzemieniec]], [[Russian Empire]] (now [[Ukraine]])
| death_date  = {{death date and age|1984|10|26|1914|8|3|mf=y}}
| death_place = [[California]], [[U.S.]]
| nationality = Polish
| citizenship = Poland, USA
| field = [[Mathematics]]
| work_institutions = [[Cornell University]]<br />[[Rockefeller University]]<br />[[University of Southern California]] 
| alma_mater = [[Lviv University|Lwów University]]
| doctoral_advisor = [[Hugo Steinhaus]]
| doctoral_students = [[Harry Kesten]]<br />[[William LeVeque]]<br />[[William Newcomb]]<br />[[Abdulalim A. Shabazz|Lonnie Cross]]<br />[[Daniel Burrill Ray|Daniel B. Ray]]<br />[[Murray Rosenblatt]]<br />[[Daniel Stroock]] 
| known_for  = [[Feynman–Kac formula]]<br />[[Erdős–Kac theorem]]<br />[[Kac–Bernstein theorem]]<br />[[Volterra lattice|Kac–van Moerbeke lattice]]<br/>[[Kac's lemma]]<br />[[Telegraph process|Kac process]]<br />[[Kac ring]]<br>[[Probabilistic number theory]]
| awards = [[Chauvenet Prize]] (1950, 1968)<br>{{no wrap|[[John von Neumann Prize]] (1961)}}<br>[[Josiah Willard Gibbs Lectureship|Gibbs Lecture]] (1967)<br>[[Birkhoff Prize]] (1978)
}}

'''Mark Kac''' ({{IPAc-en|k|ɑː|t|s}} {{respell|KAHTS|'}}; [[Polish Language|Polish]]: ''Marek Kac''; August 3, 1914 – October 26, 1984) was a [[Polish-American]] [[mathematician]]. His main interest was [[probability theory]]. His question, "[[Hearing the shape of a drum|Can one hear the shape of a drum]]?" set off research into [[spectral theory]], the idea of understanding the extent to which the [[spectrum]] allows one to read back the geometry. In the end, the answer was generally "no".

==Early life and education==
He was born to a [[Polish-Jewish]] family; their town, [[Kremenets]] ([[Polish Language|Polish]]: "Krzemieniec"), changed hands from the [[Russian Empire]] (by then [[Soviet Ukraine]]) to [[Second Polish Republic|Poland]] after the [[Peace of Riga]], when Kac was a child.<ref name="rochester">[http://www.math.rochester.edu/people/faculty/rarm/kac.html Obituary] in ''Rochester Democrat & Chronicle'', 11 November 1984</ref>

Kac completed his Ph.D. in mathematics at the Polish [[University of Lwów]] in 1937 under the direction of [[Hugo Steinhaus]].<ref name="mathgen">{{MathGenealogy|id=17851}}</ref> While there, he was a member of the [[Lwów School of Mathematics]]. 

After receiving his degree, he began to look for a position abroad, and in 1938 was granted a scholarship from the Parnas Foundation, which enabled him to go work in the United States. He arrived in [[New York City]] in November 1938.<ref name="autobio">{{cite book |first=Mark |last=Kac |title=Enigmas of Chance: An Autobiography |publisher=Harper and Row |location=New York |year=1985 |isbn=0-06-015433-0 }}</ref>

With the onset of [[World War II in Europe]], Kac was able to stay in the United States, while his parents and brother, who had remained in Kremenets, were [[Holocaust|murdered by the Nazis]] in [[mass execution]]s in August 1942.<ref name="autobio"/>

==Career==
===Cornell University===
From 1939 to 1961, Kac taught at [[Cornell University]], an [[Ivy League]] university in [[Ithaca, New York]], where he was first an instructor. In 1943, he was appointed an assistant professor, and he became a full professor in 1947.<ref name="mactutor">{{MacTutor|id=Kac|title=Mark Kac}}</ref> 

While a professor at Cornell, he became a [[naturalized US citizen]] in 1943. From 1943 to 1945, he also worked with [[George Uhlenbeck]] at the [[MIT Radiation Laboratory]].<ref name="autobio"/> During the 1951–1952 academic year, Kac was on [[sabbatical]] at the [[Institute for Advanced Study]].<ref>[http://www.ias.edu/people/cos/users/mkac01 Kac, Mark, Community of Scholars Profile, IAS] {{webarchive|url=https://web.archive.org/web/20130207025134/http://www.ias.edu/people/cos/users/mkac01 |date=2013-02-07 }}</ref> 

In 1952, Kac, with [[Theodore H. Berlin]], introduced the spherical model of a [[ferromagnet]], a variant of the [[Ising model]],<ref>{{cite journal|author=Berlin, T. H.|author2=Kac, M.|title=The spherical model of a ferromagnet|journal=Phys. Rev.|volume=86|pages=821–35|year=1952|issue=6|doi=10.1103/PhysRev.86.821|url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.86.821|bibcode=1952PhRv...86..821B}}</ref> and, with [[John Clive Ward|J. C. Ward]], found an exact solution of the Ising model using a combinatorial method.<ref>{{cite journal|author=Kac, M.|author2=Ward, J. C.|title=A combinatorial solution of the two-dimensional Ising model|journal=Phys. Rev.|volume=88|pages=1332–1337|year=1952|issue=6|doi=10.1103/physrev.88.1332|bibcode=1952PhRv...88.1332K}}</ref> 

In 1956, he introduced a simplified mathematical model known as the [[Kac ring]], which features the emergence of [[macroscopic scale|macroscopic]] irreversibility from completely [[T-symmetry|time-symmetric]] [[microscopic scale|microscopic]] laws. Using the model as an analogy to molecular motion, he provided an explanation for [[Loschmidt's paradox]].<ref>{{cite journal |last1=Thompson |first1=Colin J |title=The contributions of Mark Kac to mathematical physics |journal=The Annals of Probability |date=1986 |volume=14 |issue=4 |pages=1129–1138|doi=10.1214/aop/1176992357 }}</ref>

===Rockefeller University===
In 1961, Kac left Cornell and went to [[The Rockefeller University]] in [[New York City]]. 

He worked with [[George Uhlenbeck]] and [[Per Christian Hemmer|P. C. Hemmer]] on the mathematics of a [[Van der Waals equation|van der Waals gas]].<ref>{{cite journal|author=Cohen, E. G. D.|author-link=E.G.D. Cohen|title=Obituary: Mark Kac|journal=Physics Today|date=April 1985|volume=38|issue=4|pages=99–100|url=http://www.physicstoday.org/resource/1/phtoad/v38/i4/p99_s2?bypassSSO=1|archive-url=https://archive.today/20130930194330/http://www.physicstoday.org/resource/1/phtoad/v38/i4/p99_s2?bypassSSO=1|url-status=dead|archive-date=2013-09-30|doi=10.1063/1.2814542|bibcode=1985PhT....38d..99C}}</ref> After twenty years at Rockefeller, he moved to the [[University of Southern California]] where he spent the rest of his career.

In his 1966 article, "[[Hearing the shape of a drum|Can one hear the shape of the drum]]", Kac asked whether the [[geometric shape]] of a drum is uniquely defined by its sound. The answer was negative, meaning two different [[resonator]]s can have identical set of [[eigenfrequency|eigenfrequencies]].

===Human rights===
Kac was the co-chair of the [[Committee of Concerned Scientists]].<ref>{{cite journal|author=Benguria, Rafael|title=The centenary of Mark Kac (1914–1984)|journal=IAMP News Bulletin|date=July 2014|pages=5–18|url=http://www.iamp.org/bulletins/old-bullletins/201407.pdf}} (See pages 14–15.)</ref> He co-authored a letter which publicized the case of the scientist Vladimir Samuilovich Kislik<ref>{{cite journal|date=January 1980|title=A legacy and a hope|author=Gottesman, Max|author2=Kac, Mark Kac|author3=Langer, James|journal=Physics Today|volume=33|issue=1|pages=102|doi=10.1063/1.2913884|bibcode=1980PhT....33a.102G }}</ref> and a letter which publicized the case of the applied mathematician [[Yosif Begun]].<ref>{{cite journal|author=Kac, Mark|author2=Lebowitz, Joel L.|author3=Plotz, Paul H.|title=Yosif Begun|date=12 October 1984|journal=Science|volume=226|issue=4671|pages=114–116|doi=10.1126/science.226.4671.114.c|pmid=17814316 |s2cid=239881402 }}</ref>

==Awards and honors==
* 1950 — [[Chauvenet Prize]] for 1947 expository article<ref>{{cite journal|author=Kac, Mark|title=Random walk and the theory of Brownian motion|journal=Amer. Math. Monthly|year=1947|volume=54|issue=7|pages=369–391|url=http://www.maa.org/programs/maa-awards/writing-awards/random-walk-and-the-theory-of-brownian-motion|doi=10.2307/2304386|jstor=2304386|bibcode=1947AmMM...54..369K}}</ref>
* 1959 – member of the [[American Academy of Arts and Sciences]]<ref>{{Cite web |title=Mark Kac |url=https://www.amacad.org/person/mark-kac |access-date=2022-09-13 |website=American Academy of Arts & Sciences |language=en}}</ref>
* 1965 – member of the [[National Academy of Sciences]]<ref>{{Cite web |title=Mark Kac |url=http://www.nasonline.org/member-directory/deceased-members/54016.html |access-date=2022-09-13 |website=www.nasonline.org}}</ref>
* 1968 – [[Chauvenet Prize]] (and 1967 [[Lester R. Ford Award]]) for 1966 expository article<ref>{{cite journal|author=Kac, Mark|title=Can one hear the shape of a drum?|journal=Amer. Math. Monthly|volume=73, Part II|year=1966|issue=4|pages=1–23|url=http://www.maa.org/programs/maa-awards/writing-awards/can-one-hear-the-shape-of-a-drum-0|doi=10.2307/2313748|jstor=2313748}}</ref>
* 1969 – member of the [[American Philosophical Society]]<ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=Mark+Kac&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=2022-09-13 |website=search.amphilsoc.org}}</ref>
* 1971 – Solvay Lecturer at Brussels
* 1980 – Fermi Lecturer at the [[Scuola Normale Superiore di Pisa|Scuola Normale, Pisa]]

==Books==
* Mark Kac and [[Stanislaw Ulam]]: ''Mathematics and Logic: Retrospect and Prospects'', Praeger, New York (1968)<ref>{{cite journal|author=May, Kenneth O.|author-link=Kenneth O. May|title=Review of ''Mathematics and Logic'' by Mark Kac and Stanislaw Ulam|date=Spring 1969|journal=Isis|volume=60|issue=1|pages=112–113|doi=10.1086/350456}}</ref> [https://books.google.com/books/about/Mathematics_and_Logic.html?id=dZW7_8cpjykC 1992 Dover paperback reprint.] {{isbn|0-486-67085-6}}
* Mark Kac, ''Statistical Independence in Probability, Analysis and Number Theory'', [[Carus Mathematical Monographs]], Mathematical Association of America, 1959.<ref>{{cite journal|author=LeVeque, W. L.|title=Review: ''Statistical independence in probability, analysis and number theory'', by Mark Kac. Carus Mathematical Monographs, no. 12|journal=Bull. Amer. Math. Soc.|year=1960|volume=66|issue=4|pages=265–266|url=https://www.ams.org/journals/bull/1960-66-04/S0002-9904-1960-10459-4/|doi=10.1090/S0002-9904-1960-10459-4|doi-access=free}}</ref>
* Mark Kac, ''Probability and related topics in the physical sciences.'' 1959 (with contributions by [[George Uhlenbeck|Uhlenbeck]] on the Boltzmann equation, [[Albert Hibbs|Hibbs]] on quantum mechanics, and [[Balthasar van der Pol|van der Pol]] on finite difference analogues of the wave and potential equations, Boulder Seminar 1957).<ref>{{cite journal|author=Baxter, Glen|author-link=Glen E. Baxter|title=Review: ''Probability and related topics in the physical sciences'', by Mark Kac|journal=Bull. Amer. Math. Soc.|year=1960|volume=66|issue=6|pages=472–475|url=https://www.ams.org/journals/bull/1960-66-06/S0002-9904-1960-10500-9/|doi=10.1090/s0002-9904-1960-10500-9|doi-access=free}}</ref>
* Mark Kac, ''Enigmas of Chance: An Autobiography'', Harper and Row, New York, 1985. Sloan Foundation Series. Published posthumously with a memoriam note by [[Gian-Carlo Rota]].<ref>{{cite journal|author=Birnbaum, Z. W.|author-link=Z. W. Birnbaum|title=Review: ''Enigmas of chance; an autobiography'', by Mark Kac|journal=Bull. Amer. Math. Soc. (N.S.)|year=1987|volume=17|issue=1|pages=200–202|url=https://www.ams.org/journals/bull/1987-17-01/S0273-0979-1987-15563-7/|doi=10.1090/s0273-0979-1987-15563-7|doi-access=free}}</ref> {{isbn|0-06-015433-0}}

==References==
{{Reflist}}

==External links==
{{Category commons}}
{{wikiquote}}
* {{MacTutor Biography|id=Kac}}
* {{MathGenealogy|id=17851}}
*[http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/kac-mark.pdf National Academy of Sciences Biographical Memoir]

{{Chauvenet Prize recipients}}
{{John von Neumann Lecturers}}
{{Authority control}}

{{DEFAULTSORT:Kac, Mark}}
[[Category:1914 births]]
[[Category:1984 deaths]]
[[Category:20th-century American mathematicians]]
[[Category:American people of Polish-Jewish descent]]
[[Category:Cornell University faculty]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Lwów School of Mathematics]]
[[Category:Members of the American Philosophical Society]]
[[Category:People from Kremenets]]
[[Category:Naturalized citizens of the United States]]
[[Category:Polish emigrants to the United States]]
[[Category:Presidents of the Institute of Mathematical Statistics]]
[[Category:Probability theorists]]
[[Category:Mathematical physicists]]
[[Category:University of Southern California faculty]]