Robert John Aumann (Yisrael Aumann, ; born June 8, 1930) is an

Israeli-American Israeli Americans () are Americans who are of full or partial Israeli descent. The Israeli-American community, while predominantly Jewish, also includes various ethnic and religious minorities reflective of Israel's diverse demographics. This c ...

mathematician, and a member of the

United States National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

. He is a professor at the Center for the Study of Rationality in the

Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; ) is an Israeli public university, public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. ...

. He also holds a visiting position at

Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public university, public research university in Stony Brook, New York, United States, on Long Island. Along with the University at Buffalo, it is on ...

, and is one of the founding members of the Stony Brook Center for Game Theory. Aumann received the

Nobel Memorial Prize in Economic Sciences The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (), commonly referred to as the Nobel Prize in Economics(), is an award in the field of economic sciences adminis ...

in 2005 for his work on conflict and cooperation through

game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

analysis. He shared the prize with

Thomas Schelling Thomas Crombie Schelling (April 14, 1921 – December 13, 2016) was an American economist and professor of foreign policy, national security, nuclear strategy, and arms control at the School of Public Policy at the University of Maryland, Coll ...

Early life and education

Aumann was born in

Frankfurt am Main Frankfurt am Main () is the most populous city in the States of Germany, German state of Hesse. Its 773,068 inhabitants as of 2022 make it the List of cities in Germany by population, fifth-most populous city in Germany. Located in the forela ...

, Germany, and fled to the

United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...

with his family in 1938, two weeks before the

Kristallnacht ( ) or the Night of Broken Glass, also called the November pogrom(s) (, ), was a pogrom against Jews carried out by the Nazi Party's (SA) and (SS) paramilitary forces along with some participation from the Hitler Youth and German civilia ...

pogrom. He attended the

Rabbi Jacob Joseph School The Rabbi Jacob Joseph School is an Orthodox Jewish day school located in Staten Island, New York that serves students from nursery through twelfth grade, with another branch in Edison, New Jersey. The school was founded in 1903 by Rabbi Shmuel ...

, a

yeshiva A yeshiva (; ; pl. , or ) is a traditional Jewish educational institution focused on the study of Rabbinic literature, primarily the Talmud and halacha (Jewish law), while Torah and Jewish philosophy are studied in parallel. The stu ...

high school in New York City. Aumann graduated from the

City College of New York The City College of the City University of New York (also known as the City College of New York, or simply City College or CCNY) is a Public university, public research university within the City University of New York (CUNY) system in New York ...

in 1950 with a B.S. in

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. He received his

M.S. A Master of Science (; abbreviated MS, M.S., MSc, M.Sc., SM, S.M., ScM or Sc.M.) is a master's degree. In contrast to the Master of Arts degree, the Master of Science degree is typically granted for studies in sciences, engineering and medicine ...

in 1952, and his Ph.D. in Mathematics in 1955, both from the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

. His doctoral dissertation, ''Asphericity of Alternating Linkages'', concerned

knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...

. His advisor was George Whitehead, Jr.

Academic career

In 1956 he joined the Mathematics faculty of the

and has been a visiting professor at

since 1989. He has held visiting professorship at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

(1971, 1985–1986),

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

(1975–1976, 1980–1981), and

Universite Catholique de Louvain UCLouvain (or Université catholique de Louvain , French for Catholic University of Louvain, officially in English the University of Louvain) is Belgium's largest French-speaking university and one of the oldest in Europe (originally establishe ...

(1972, 1978, 1984).

Mathematical and scientific contribution

Aumann's greatest contribution was in the realm of

repeated game In game theory, a repeated game (or iterated game) is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capt ...

s, which are situations in which players encounter the same situation over and over again. Aumann was the first to define the concept of

correlated equilibrium In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. It was first discussed by mathematician Robert Aumann in 1974. The idea is that each player chooses their action according ...

in game theory, which is a type of equilibrium in

non-cooperative game In game theory, a non-cooperative game is a game in which there are no external rules or binding agreements that enforce the cooperation of the players. A non-cooperative game is typically used to model a competitive environment. This is stated in ...

s that is more flexible than the classical

Nash equilibrium In game theory, the Nash equilibrium is the most commonly used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed) ...

. Furthermore, Aumann has introduced the first purely formal account of the notion of

common knowledge Common knowledge is knowledge that is publicly known by everyone or nearly everyone, usually with reference to the community in which the knowledge is referenced. Common knowledge can be about a broad range of subjects, such as science, litera ...

in game theory. He collaborated with

Lloyd Shapley Lloyd Stowell Shapley (; June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Memorial Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally conside ...

on the Aumann–Shapley value. He is also known for

Aumann's agreement theorem Aumann's agreement theorem states that two Bayesian agents with the same prior beliefs cannot "agree to disagree" about the probability of an event if their individual beliefs are common knowledge. In other words, if it is commonly known what eac ...

, in which he argues that under his given conditions, two

Bayesian Thomas Bayes ( ; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian minister. Bayesian ( or ) may be either any of a range of concepts and approaches that relate to statistical methods based on Bayes' theorem Bayes ...

rationalists with common prior beliefs cannot agree to disagree. Aumann and Maschler used game theory to analyze

Talmud The Talmud (; ) is the central text of Rabbinic Judaism and the primary source of Jewish religious law (''halakha'') and Jewish theology. Until the advent of Haskalah#Effects, modernity, in nearly all Jewish communities, the Talmud was the cen ...

ic dilemmas. They were able to solve the mystery about the "division problem", a long-standing dilemma of explaining the Talmudic rationale in dividing the heritage of a late husband to his three wives depending on the worth of the heritage compared to its original worth. The article in that matter was dedicated to a son of Aumann, Shlomo, who was killed during the

1982 Lebanon War The 1982 Lebanon War, also called the Second Israeli invasion of Lebanon, began on 6 June 1982, when Israel invaded southern Lebanon. The invasion followed a series of attacks and counter-attacks between the Palestine Liberation Organization ...

, while serving as a tank gunner in the Israel Defense Forces's armored corps. Aumann's Ph.D. students include

David Schmeidler David Schmeidler (; 1939 – 17 March 2022) was an Israeli mathematician and economic theorist. He was a Professor Emeritus at Tel Aviv University and the Ohio State University. Biography David Schmeidler was born in 1939 in Kraków, Poland. ...

, Sergiu Hart,

Abraham Neyman Abraham Neyman (; born June 14, 1949) is an Israeli mathematician and game theorist, Professor of Mathematics at the Federmann Center for the Study of Rationality and the Einstein Institute of Mathematics at the Hebrew University of Jerusalem. ...

, and

Yair Tauman Yair Tauman (; born January 20, 1948) is a professor of Economics at State University of New York, Stony Brook and the Director of the Stony Brook Center for Game Theory. He studied at the Hebrew University of Jerusalem where he obtained his B.S ...

Torah codes controversy

Aumann has entered the controversy of

Bible code The Bible code (, ), also known as the Torah code, is a purported set of encoded words within a Hebrew text of the Torah that, according to proponents, has predicted significant historical events. The statistical likelihood of the Bible code a ...

s research. In his position as both a religious Jew and a man of science, the codes research holds special interest to him. He has partially vouched for the validity of the " Great Rabbis Experiment" by Doron Witztum,

Eliyahu Rips Eliyahu Rips (; ; ; 12 December 1948 – 19 July 2024) was an Israeli mathematician of Latvian origin known for his research in geometric group theory. He became known to the general public following his co-authoring a paper on what is popularl ...

, and Yoav Rosenberg, which was published in ''Statistical Science''. Aumann not only arranged for Rips to give a lecture on Torah codes in the

Israel Academy of Sciences and Humanities Israel Academy of Sciences and Humanities, based in Jerusalem, was established in 1961 by the State of Israel to foster contact between Israeli scholars in the sciences and humanities and create a think tank for advising the government on res ...

, but sponsored the Witztum-Rips-Rosenberg paper for publication in the

Proceedings of the National Academy of Sciences ''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of Scie ...

. The academy requires a member to sponsor any publication in its Proceedings; the paper was turned down however. In 1996, a committee consisting of

Robert J. Aumann Robert John Aumann (Yisrael Aumann, ; born June 8, 1930) is an Israeli-American mathematician, and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University o ...

Dror Bar-Natan Dror Bar-Natan (; born January 30, 1966) is a professor at the University of Toronto Department of Mathematics, Canada. His main research interests include knot theory, finite type invariants, and Khovanov homology. Education Bar-Natan earned his ...

Hillel Furstenberg Hillel "Harry" Furstenberg (; born September 29, 1935) is a German-born American-Israeli mathematician and professor emeritus at the Hebrew University of Jerusalem. He is a member of the Israel Academy of Sciences and Humanities and U.S. Natio ...

, Isaak Lapides, and Rips, was formed to examine the results that had been reported by H.J. Gans regarding the existence of "encoded" text in the Bible foretelling events that took place many years after the Bible was written. The committee performed two additional tests in the spirit of the Gans experiments. Both tests failed to confirm the existence of the putative code. After a long analysis of the experiment and the dynamics of the controversy, stating for example that "almost everybody included n the controversymade up their mind early in the game," Aumann concluded: "''A priori'', the thesis of the Codes research seems wildly improbable... Research conducted under my own supervision failed to confirm the existence of the codes – though it also did not establish their non-existence. So I must return to my ''a priori'' estimate, that the Codes phenomenon is improbable".

Political views

These are some of the themes of Aumann's Nobel lecture, named "War and Peace": # War is not irrational, but must be scientifically studied in order to be understood, and eventually conquered; #

Repeated game In game theory, a repeated game (or iterated game) is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capt ...

study de-emphasizes the "now" for the sake of the "later"; # Simplistic peacemaking can cause war, while an arms race, credible war threats and mutually assured destruction can reliably prevent war. Aumann is a member of

Professors for a Strong Israel Professors for a Strong Israel is a group of academics in Israel. They describe themselves as a "non-partisan organization of academics united by a shared concern for the security and the Jewish character of the State of Israel." The group was f ...

(PSI), a right-wing political group. Aumann opposed the disengagement from Gaza in 2005 claiming that it was a crime against

Gush Katif Gush Katif () was a bloc of 17 Israeli settlements in the southern Gaza Strip. In August 2005, the Israel Defense Forces removed the 8,600 Israeli residents from their homes after a decision from the Cabinet of Israel. The communities were demo ...

settlers and a serious threat to the security of Israel. Aumann drew on a case in

called the ' to argue that giving land to the Arabs is strategically foolish based on the mathematical theory. By presenting an unyielding demand, he claims that the Arab states will force Israel to "yield to

blackmail Blackmail is a criminal act of coercion using a threat. As a criminal offense, blackmail is defined in various ways in common law jurisdictions. In the United States, blackmail is generally defined as a crime of information, involving a thr ...

due to the perception that it will leave the negotiating room with nothing if it is inflexible". As a result of his political views, and his use of his research to justify them, the decision to give him the Nobel prize was criticized in the European press. A petition to cancel his prize garnered signatures from 1,000 academics worldwide. In a speech to the religious Zionist youth movement,

Bnei Akiva Bnei Akiva (, , "Children of Akiva") is the largest religious Zionist youth movement in the world, with over 125,000 members in 42 countries. It was first established in Mandatory Palestine in 1929, advocating the values of Torah and labor. Bne ...

, Aumann argued that Israel is in "deep trouble" due to his belief that anti-Zionist

Satmar Satmar (; ) is a group in Hasidic Judaism founded in 1905 by Grand Rebbe Joel Teitelbaum (1887–1979), in the city of Szatmárnémeti (also called Szatmár in the 1890s), Kingdom of Hungary, Hungary (now Satu Mare in Romania). The group is a b ...

Jews might have been right in their condemnation of the original Zionist movement. "I fear the Satmars were right", he said, and quoted a verse from

Psalm The Book of Psalms ( , ; ; ; ; , in Islam also called Zabur, ), also known as the Psalter, is the first book of the third section of the Tanakh (Hebrew Bible) called ('Writings'), and a book of the Old Testament. The book is an anthology of H ...

127: "Unless the Lord builds a house, its builders toil on it in vain." Aumann feels that the historical Zionist establishment failed to transmit its message to its successors, because it was secular. The only way that Zionism can survive, according to Aumann, is if it has a religious basis. In 2008, Aumann joined the right-wing

religious Zionist Religious Zionism () is a religious denomination that views Zionism as a fundamental component of Orthodox Judaism. Its adherents are also referred to as ''Dati Leumi'' (), and in Israel, they are most commonly known by the plural form of the fi ...

Ahi political party, which was led at the time by

Effi Eitam Efraim "Effi" Eitam (; born 25 July 1952) is an Israeli brigadier general, former commander of the 91st Division, and politician. A former leader of the National Religious Party, he later led a breakaway faction, Ahi, which merged into Likud ...

and

Yitzhak Levy Yitzhak Levy (; born 6 July 1947) is an Israeli Orthodox rabbi and politician who served as a member of the Knesset for the National Religious Party (NRP) and the Ahi faction of the National Union between 1988 and 2009. Between 1998 and 2002, ...

Personal life

Aumann married Esther Schlesinger in April 1955 in

Brooklyn Brooklyn is a Boroughs of New York City, borough of New York City located at the westernmost end of Long Island in the New York (state), State of New York. Formerly an independent city, the borough is coextensive with Kings County, one of twelv ...

. They had met in 1953, when Esther, who was from Israel, was visiting the United States. The couple had five children; the oldest, Shlomo, a student in Yeshivat Shaalvim, was killed in action while serving as a tank gunner in the Israel Defense Forces's armored corps in the

. , an institute affiliated with Shaalvim that republishes old manuscripts of Jewish legal texts, was named after him. Esther died of

ovarian cancer Ovarian cancer is a cancerous tumor of an ovary. It may originate from the ovary itself or more commonly from communicating nearby structures such as fallopian tubes or the inner lining of the abdomen. The ovary is made up of three different ...

in October 1998. In late November 2005, Aumann married Esther's widowed sister, Batya Cohn. Aumann is a cousin of the late

Oliver Sacks Oliver Wolf Sacks (9 July 1933 – 30 August 2015) was a British neurology, neurologist, Natural history, naturalist, historian of science, and writer. Born in London, Sacks received his medical degree in 1958 from The Queen's College, Oxford ...

Honours and awards

* 1974: Foreign Honorary Member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

* 1983:

Harvey Prize The Harvey Prize is an annual Israeli award for breakthroughs in science and technology, as well as contributions to peace in the Middle East granted by the Technion – Israel Institute of Technology, Technion in Haifa. The prize has become a ...

in Science and Technology. * 1994:

Israel Prize The Israel Prize (; ''pras israél'') is an award bestowed by the State of Israel, and regarded as the state's highest cultural honor. History Prior to the Israel Prize, the most significant award in the arts was the Dizengoff Prize and in Israel ...

for economics. * 1998:

Erwin Plein Nemmers Prize in Economics The Erwin Plein Nemmers Prize in Economics is an academic prize awarded biennially by Northwestern University. It was initially endowed along with a companion prize, the Frederic Esser Nemmers Prize in Mathematics. Both are part a $14 million donat ...

from

Northwestern University Northwestern University (NU) is a Private university, private research university in Evanston, Illinois, United States. Established in 1851 to serve the historic Northwest Territory, it is the oldest University charter, chartered university in ...

. * 2002: The EMET Prize in the Social Sciences category, for Economics * 2005:

(share

US$ The United States dollar (Currency symbol, symbol: Dollar sign, $; ISO 4217, currency code: USD) is the official currency of the United States and International use of the U.S. dollar, several other countries. The Coinage Act of 1792 introdu ...

1.3 million prize with

). * 2006:

Yakir Yerushalayim Yakir Yerushalayim (; ) is an annual citizenship prize in Jerusalem, inaugurated in 1967. The prize is awarded annually by the municipality of the City of Jerusalem to one or more residents of the city who have contributed to the cultural an ...

(Worthy Citizen of Jerusalem) award from the city of

Jerusalem Jerusalem is a city in the Southern Levant, on a plateau in the Judaean Mountains between the Mediterranean Sea, Mediterranean and the Dead Sea. It is one of the List of oldest continuously inhabited cities, oldest cities in the world, and ...

. City of Jerusalem official website

Publications

* 1956: ''Asphericity of alternating knots'',

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

64: 374–92 * 1958: (with

Joseph Kruskal Joseph Bernard Kruskal, Jr. (; January 29, 1928 – September 19, 2010) was an American mathematician, statistician, computer scientist and psychometrician. Personal life Kruskal was born to a Jewish family in New York City to a successful fu ...

) ''The Coefficients in an Allocation Problem'', Naval Research Logistics * 1960: ''Acceptable Points in Games of Perfect Information'',

Pacific Journal of Mathematics The Pacific Journal of Mathematics is a mathematics research journal supported by several universities and research institutes, and currently published on their behalf by Mathematical Sciences Publishers, a non-profit academic publishing organisa ...

10 (1960), pp. 381–417 * 1974: (with L.S. Shapley) ''Values of Non-Atomic Games'',

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial ...

* 1981: (with Y. Tauman and S. Zamir) ''Game Theory'', volumes 1 & 2 (in Hebrew), Everyman's University, Tel Aviv * 1989: ''Lectures on Game Theory'', Underground Classics in Economics,

Westview Press Westview Press was an American publishing company headquartered in Boulder, Colorado founded in 1975. Field of work Westview primarily publishes textbooks. History Westview Press was founded by Frederick A. Praeger in 1975. Praeger sold ...

* 1992, 1994, 2002: (coedited with Sergiu Hart) ''Handbook of Game Theory with Economic Applications'', volumes 1,2 & 3

Elsevier Elsevier ( ) is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell (journal), Cell'', the ScienceDirect collection of electronic journals, ...

* 1995: (with M. Maschler) ''Repeated Games with Incomplete Information'',

MIT Press The MIT Press is the university press of the Massachusetts Institute of Technology (MIT), a private research university in Cambridge, Massachusetts. The MIT Press publishes a number of academic journals and has been a pioneer in the Open Ac ...

* 2000: ''Collected Papers'', volumes 1 & 2,

. * 2015: (with I. Arieli) ''The Logic of Backward Induction'',

Journal of Economic Theory The ''Journal of Economic Theory'' is a bimonthly peer-reviewed academic journal covering the field of economic theory. Karl Shell has served as editor-in-chief of the journal since it was established in 1968. Since 2000, he has shared the editor ...

159 (2015), pp. 443–464

References

External links

Official homepage
* {{DEFAULTSORT:Aumann, Robert Nobel laureates in Economics Israeli Nobel laureates American Nobel laureates Social scientists from New York City 20th-century American economists Israeli economists Jewish American economists Israeli mathematicians Jewish American scientists Israeli scientists Jewish emigrants from Nazi Germany to the United States American emigrants to Israel City College of New York alumni Fellows of the American Academy of Arts and Sciences Fellows of the Econometric Society Game theorists American people of German-Jewish descent Academic staff of the Hebrew University of Jerusalem Israel Prize in economics recipients EMET Prize recipients in the Social Sciences Israeli people of German-Jewish descent Israeli Orthodox Jews American Orthodox Jews John von Neumann Theory Prize winners Massachusetts Institute of Technology School of Science alumni Members of the Israel Academy of Sciences and Humanities Members of the United States National Academy of Sciences Rabbi Jacob Joseph School alumni Stony Brook University faculty RAND Corporation people Living people 1930 births