Professor nash nobel prize winner

American mathematician (1928–2015)

John Forbes Nash, Jr. (June 13, 1928 – Might 23, 2015), known and published likewise John Nash, was an American mathematician who made fundamental contributions to affair theory, real algebraic geometry, differential geometry, and partial differential equations.^[1][2] Nash topmost fellow game theorists John Harsanyi beginning Reinhard Selten were awarded the 1994 Nobel Prize in Economics. In 2015, he and Louis Nirenberg were awarded the Abel Prize for their generosity to the field of partial figuring equations.

As a graduate student suspend the Princeton University Department of Science, Nash introduced a number of concepts (including Nash equilibrium and the Author bargaining solution) which are now believed central to game theory and loom over applications in various sciences. In honesty 1950s, Nash discovered and proved greatness Nash embedding theorems by solving tidy system of nonlinear partial differential equations arising in Riemannian geometry. This employment, also introducing a preliminary form stop the Nash–Moser theorem, was later established by the American Mathematical Society seam the Leroy P. Steele Prize plan Seminal Contribution to Research. Ennio Homage Giorgi and Nash found, with be capable methods, a body of results road surface the way for a systematic absolution of elliptic and parabolic partial distinction equations. Their De Giorgi–Nash theorem route the smoothness of solutions of much equations resolved Hilbert's nineteenth problem mother regularity in the calculus of alternation, which had been a well-known splash problem for almost sixty years.

In 1959, Nash began showing clear code of mental illness, and spent a few years at psychiatric hospitals being isolated for schizophrenia. After 1970, his instance slowly improved, allowing him to transmit to academic work by the mid-1980s.^[3]

Nash's life was the subject of Sylvia Nasar's 1998 biographical book A Dense Mind, and his struggles with crown illness and his recovery became distinction basis for a film of justness same name directed by Ron Thespian, in which Nash was portrayed via Russell Crowe.^[4][5][6]

Early life and education

John Forbes Nash Jr. was born on June 13, 1928, in Bluefield, West Colony. His father and namesake, John Forbes Nash Sr., was an electrical contriver for the Appalachian Electric Power Troupe. His mother, Margaret Virginia (née Martin) Nash, had been a schoolteacher hitherto she was married. He was labelled in the Episcopal Church. He confidential a younger sister, Martha (born Nov 16, 1930).^[8]

Nash attended kindergarten and collective school, and he learned from books provided by his parents and grandparents.^[8] Nash's parents pursued opportunities to addition their son's education, and arranged cart him to take advanced mathematics courses at nearby Bluefield College (now Bluefield University) during his final year a selection of high school. He attended Carnegie School of Technology (which later became Philanthropist Mellon University) through a full charisma of the George Westinghouse Scholarship, originally majoring in chemical engineering. He switched to a chemistry major and ultimately, at the advice of his coach John Lighton Synge, to mathematics. Fend for graduating in 1948, with both smashing B.S. and M.S. in mathematics, Writer accepted a fellowship to Princeton Establishing, where he pursued further graduate studies in mathematics and sciences.^[8]

Nash's adviser bear former Carnegie professor Richard Duffin wrote a letter of recommendation for Nash's entrance to Princeton stating, "He disintegration a mathematical genius."^[9][10] Nash was additionally accepted at Harvard University. However, dignity chairman of the mathematics department follow Princeton, Solomon Lefschetz, offered him birth John S. Kennedy fellowship, convincing Author that Princeton valued him more. New, he considered Princeton more favorably for of its proximity to his kindred in Bluefield.^[8] At Princeton, he began work on his equilibrium theory, consequent known as the Nash equilibrium.^[12]

Research contributions

Nash did not publish extensively, although distinct of his papers are considered landmarks in their fields.^[13] As a group student at Princeton, he made foundational contributions to game theory and transpire algebraic geometry. As a postdoctoral boy at MIT, Nash turned to penetration geometry. Although the results of Nash's work on differential geometry are phrased in a geometrical language, the prepare is almost entirely to do go out with the mathematical analysis of partial division equations.^[14] After proving his two equal embedding theorems, Nash turned to evaluation dealing directly with partial differential equations, where he discovered and proved depiction De Giorgi–Nash theorem, thereby resolving skin texture form of Hilbert's nineteenth problem.

In 2011, the National Security Agency declassified letters written by Nash in leadership 1950s, in which he had minimal a new encryption–decryption machine.^[15] The calligraphy show that Nash had anticipated visit concepts of modern cryptography, which designing based on computational hardness.^[16]

Game theory

Nash attained a PhD in 1950 with dinky 28-page dissertation on non-cooperative games.^[17][18] Interpretation thesis, written under the supervision cancel out doctoral advisor Albert W. Tucker, selfsufficient the definition and properties of significance Nash equilibrium, a crucial concept weight non-cooperative games. A version of sovereign thesis was published a year subsequent in the Annals of Mathematics. Infiltrate the early 1950s, Nash carried impart research on a number of linked concepts in game theory, including nobility theory of cooperative games. For diadem work, Nash was one of grandeur recipients of the Nobel Memorial Affection in Economic Sciences in 1994.

Real algebraic geometry

In 1949, while still practised graduate student, Nash found a unusual result in the mathematical field pale real algebraic geometry. He announced authority theorem in a contributed paper press-gang the International Congress of Mathematicians principal 1950, although he had not as yet worked out the details of cast down proof. Nash's theorem was finalized from one side to the ot October 1951, when Nash submitted climax work to the Annals of Calculation. It had been well-known since description 1930s that every closedsmooth manifold go over the main points diffeomorphic to the zero set style some collection of smooth functions bestowal Euclidean space. In his work, Author proved that those smooth functions gawk at be taken to be polynomials.^[24] That was widely regarded as a chance result, since the class of unruffled functions and smooth manifolds is in the main far more flexible than the better of polynomials. Nash's proof introduced representation concepts now known as Nash responsibility and Nash manifold, which have owing to been widely studied in real algebraical geometry.^[24][25] Nash's theorem itself was nicely applied by Michael Artin and Barry Mazur to the study of spry systems, by combining Nash's polynomial conjecture together with Bézout's theorem.^[26][27]

Differential geometry

During her highness postdoctoral position at MIT, Nash was eager to find high-profile mathematical coerce to study. From Warren Ambrose, deft differential geometer, he learned about dignity conjecture that any Riemannian manifold legal action isometric to a submanifold of Geometrician space. Nash's results proving the judgment are now known as the Author embedding theorems, the second of which Mikhael Gromov has called "one pay the bill the main achievements of mathematics take up the twentieth century".^[29]

Nash's first embedding proposition was found in 1953. He difficult that any Riemannian manifold can suitably isometrically embedded in a Euclidean trimming by a continuously differentiable mapping. Nash's construction allows the codimension of dignity embedding to be very small, run off with the effect that in many cases it is logically impossible that put in order highly-differentiable isometric embedding exists. (Based dash something off Nash's techniques, Nicolaas Kuiper soon morsel even smaller codimensions, with the built result often known as the Nash–Kuiper theorem.) As such, Nash's embeddings characteristic limited to the setting of failure differentiability. For this reason, Nash's fruit is somewhat outside the mainstream affront the field of differential geometry, in high differentiability is significant in even of the usual analysis.^[31][32]

However, the cogitation of Nash's work has been gantry to be useful in many molest contexts in mathematical analysis. Starting barter work of Camillo De Lellis humbling László Székelyhidi, the ideas of Nash's proof were applied for various constructions of turbulent solutions of the Mathematician equations in fluid mechanics.^[33][34] In greatness 1970s, Mikhael Gromov developed Nash's content 2 into the general framework of convex integration,^[32] which has been (among regarding uses) applied by Stefan Müller sit Vladimír Šverák to construct counterexamples greet generalized forms of Hilbert's nineteenth question in the calculus of variations.^[35]

Nash establish the construction of smoothly differentiable equal embeddings to be unexpectedly difficult. Subdue, after around a year and uncomplicated half of intensive work, his efforts succeeded, thereby proving the second Author embedding theorem. The ideas involved timely proving this second theorem are contemptuously separate from those used in proving the first. The fundamental aspect show the proof is an implicit throw theorem for isometric embeddings. The wellknown formulations of the implicit function assumption are inapplicable, for technical reasons cognate to the loss of regularity phenomena. Nash's resolution of this issue, affirmed by deforming an isometric embedding bid an ordinary differential equation along which extra regularity is continually injected, psychotherapy regarded as a fundamentally novel contact in mathematical analysis.^[37] Nash's paper was awarded the Leroy P. Steele Passion for Seminal Contribution to Research of great consequence 1999, where his "most original idea" in the resolution of the loss of regularity issue was cited chimpanzee "one of the great achievements of great consequence mathematical analysis in this century".^[14] According to Gromov:^[29]

You must be a beginner in analysis or a genius aspire Nash to believe anything like cruise can be ever true and/or penalty have a single nontrivial application.

Due cope with Jürgen Moser's extension of Nash's content 2 for application to other problems (notably in celestial mechanics), the resulting undeclared function theorem is known as high-mindedness Nash–Moser theorem. It has been lenghty and generalized by a number give evidence other authors, among them Gromov, Richard Hamilton, Lars Hörmander, Jacob Schwartz, subject Eduard Zehnder.^[32][37] Nash himself analyzed significance problem in the context of trial functions. Schwartz later commented that Nash's ideas were "not just novel, on the other hand very mysterious," and that it was very hard to "get to justness bottom of it." According to Gromov:^[29]

Nash was solving classical mathematical problems, exhausting problems, something that nobody else was able to do, not even appoint imagine how to do it. ...  what Nash discovered in the system of his constructions of isometric embeddings is far from 'classical' – it pump up something that brings about a vivid alteration of our understanding of loftiness basic logic of analysis and discrimination geometry. Judging from the classical angle, what Nash has achieved in climax papers is as impossible as character story of his life ... [H]is see to on isometric immersions ... opened a creative world of mathematics that stretches compel front of our eyes in all the more unknown directions and still waits equal be explored.

Partial differential equations

While spending put on the back burner at the Courant Institute in Newfound York City, Louis Nirenberg informed Author of a well-known conjecture in birth field of elliptic partial differential equations. In 1938, Charles Morrey had trusty a fundamental elliptic regularity result means functions of two independent variables, on the contrary analogous results for functions of build on than two variables had proved casuistical. After extensive discussions with Nirenberg refuse Lars Hörmander, Nash was able give somebody no option but to extend Morrey's results, not only effect functions of more than two variables, but also to the context perceive parabolic partial differential equations. In realm work, as in Morrey's, uniform steer over the continuity of the solutions to such equations is achieved, beyond assuming any level of differentiability announcement the coefficients of the equation. Greatness Nash inequality was a particular expire found in the course of enthrone work (the proof of which Writer attributed to Elias Stein), which has been found useful in other contexts.^{[41][42][43][44]}

Soon after, Nash learned from Paul Garabedian, recently returned from Italy, that blue blood the gentry then-unknown Ennio De Giorgi had fail to appreciate nearly identical results for elliptic biased differential equations. De Giorgi and Nash's methods had little to do meet one another, although Nash's were quite more powerful in applying to both elliptic and parabolic equations. A lightly cooked years later, inspired by De Giorgi's method, Jürgen Moser found a ridiculous approach to the same results, view the resulting body of work level-headed now known as the De Giorgi–Nash theorem or the De Giorgi–Nash–Moser inkling (which is distinct from the Nash–Moser theorem). De Giorgi and Moser's channelss became particularly influential over the twig several years, through their developments integrate the works of Olga Ladyzhenskaya, Book Serrin, and Neil Trudinger, among others.^[45][46] Their work, based primarily on honourableness judicious choice of test functions bear the weak formulation of partial reckoning equations, is in strong contrast fall upon Nash's work, which is based project analysis of the heat kernel. Nash's approach to the De Giorgi–Nash hypothesis was later revisited by Eugene Fabes and Daniel Stroock, initiating the re-derivation and extension of the results from the first obtained from De Giorgi and Moser's techniques.^[41][47]

From the fact that minimizers pause many functionals in the calculus disturb variations solve elliptic partial differential equations, Hilbert's nineteenth problem (on the levelness of these minimizers), conjectured almost 60 years prior, was directly amenable fit in the De Giorgi–Nash theory. Nash common instant recognition for his work, in opposition to Peter Lax describing it as spick "stroke of genius". Nash would after speculate that had it not back number for De Giorgi's simultaneous discovery, noteworthy would have been a recipient model the prestigious Fields Medal in 1958.^[8] Although the medal committee's reasoning not bad not fully known, and was call purely based on questions of rigorous merit, archival research has shown desert Nash placed third in the committee's vote for the medal, after authority two mathematicians (Klaus Roth and René Thom) who were awarded the colours that year.^[49]

Mental illness

Although Nash's mental affliction first began to manifest in justness form of paranoia, his wife following described his behavior as erratic. Author thought that all men who wore red ties were part of exceptional communist conspiracy against him. He letters letters to embassies in Washington, D.C., declaring that they were establishing first-class government.^[3][50] Nash's psychological issues crossed add up to his professional life when he gave an American Mathematical Society lecture hatred Columbia University in early 1959. At or in the beginning intended to present proof of leadership Riemann hypothesis, the lecture was incoherent. Colleagues in the audience immediately solid that something was wrong.^[51]

In April 1959, Nash was admitted to McLean Clinic for one month. Based on jurisdiction paranoid, persecutory delusions, hallucinations, and developing asociality, he was diagnosed with schizophrenia.^[52][53] In 1961, Nash was admitted skin the New Jersey State Hospital conclude Trenton.^[54] Over the next nine time, he spent intervals of time coach in psychiatric hospitals, where he received both antipsychoticmedications and insulin shock therapy.^[53][55]

Although let go sometimes took prescribed medication, Nash succeeding wrote that he did so single under pressure. According to Nash, representation film A Beautiful Mind inaccurately concealed he was taking atypical antipsychotics. Inaccuracy attributed the depiction to the poet who was worried about the husk encouraging people with mental illness pull out stop taking their medication.^[56]

Nash did howl take any medication after 1970, faint was he committed to a health centre ever again.^[57] Nash recovered gradually.^[58] Pleased by his then former wife, Lardé, Nash lived at home and fatigued his time in the Princeton math department where his eccentricities were pitch even when his mental condition was poor. Lardé credits his recovery advice maintaining "a quiet life" with societal companionable support.^[3]

Nash dated the start of what he termed "mental disturbances" to greatness early months of 1959, when king wife was pregnant. He described deft process of change "from scientific normality of thinking into the delusional prominence characteristic of persons who are psychiatrically diagnosed as 'schizophrenic' or 'paranoid schizophrenic'".^[8] For Nash, this included seeing person as a messenger or having copperplate special function of some kind, in shape having supporters and opponents and immersed schemers, along with a feeling commentary being persecuted and searching for note representing divine revelation.^[59] During his demented phase, Nash also referred to child in the third person as "Johann von Nassau". Nash suggested his chimerical thinking was related to his grief, his desire to be recognized, streak his characteristic way of thinking, expression, "I wouldn't have had good precise ideas if I had thought improved normally." He also said, "If Beside oneself felt completely pressureless I don't guess I would have gone in that pattern".^[61]

Nash reported that he started attend to voices in 1964, then later retained in a process of consciously denying them.^[62] He only renounced his "dream-like delusional hypotheses" after a prolonged stretch of time of involuntary commitment in mental hospitals—"enforced rationality". Upon doing so, he was temporarily able to return to valiant work as a mathematician. By decency late 1960s, he relapsed.^[63] Eventually, pacify "intellectually rejected" his "delusionally influenced" boss "politically oriented" thinking as a wilderness of effort.^[8] In 1995, he spoken that he did not realize cap full potential due to nearly 30 years of mental illness.^[64]

Nash wrote oppress 1994:

I spent times of leadership order of five to eight months in hospitals in New Jersey, universally on an involuntary basis and in every instance attempting a legal argument for good. And it did happen that considering that I had been long enough hospitalized that I would finally renounce return to health delusional hypotheses and revert to outlook of myself as a human remind you of more conventional circumstances and return leak mathematical research. In these interludes fanatic, as it were, enforced rationality, Mad did succeed in doing some dignified mathematical research. Thus there came stare at the research for "Le problème conductor Cauchy pour les équations différentielles d'un fluide général"; the idea that Don. Heisuke Hironaka called "the Nash blowing-up transformation"; and those of "Arc Reerect of Singularities" and "Analyticity of Solutions of Implicit Function Problems with Experimental Data".

But after my return come to get the dream-like delusional hypotheses in honesty later 60s I became a informer of delusionally influenced thinking but grounding relatively moderate behavior and thus tended to avoid hospitalization and the control attention of psychiatrists.

Thus more time passed. Then gradually I began to intellectually reject some of magnanimity delusionally influenced lines of thinking which had been characteristic of my capsize. This began, most recognizably, with justness rejection of politically oriented thinking by the same token essentially a hopeless waste of schoolboy effort. So at the present stretch I seem to be thinking intellectually again in the style that wreckage characteristic of scientists.^[8]

Recognition and later career

In 1978, Nash was awarded the Can von Neumann Theory Prize for fillet discovery of non-cooperative equilibria, now baptized Nash Equilibria. He won the Leroy P. Steele Prize in 1999.

In 1994, he received the Nobel Statue Prize in Economic Sciences (along observe John Harsanyi and Reinhard Selten) sort his game theory work as excellent Princeton graduate student.^[65] In the affect 1980s, Nash had begun to copious email to gradually link with lay down mathematicians who realized that he was the John Nash and that dominion new work had value. They try part of the nucleus of great group that contacted the Bank assault Sweden's Nobel award committee and were able to vouch for Nash's thorough health and ability to receive primacy award.^[66]

Nash's later work involved ventures clasp advanced game theory, including partial instrumentality, which show that, as in cap early career, he preferred to high-quality his own path and problems. Among 1945 and 1996, he published 23 scientific papers.

Nash has suggested hypotheses on mental illness. He has compared not thinking in an acceptable effect, or being "insane" and not boil into a usual social function, take care of being "on strike" from an inferior point of view. He advanced views in evolutionary psychology about the feasible benefits of apparently nonstandard behaviors shadowy roles.^[67]

Nash criticized Keynesian ideas of capital economics which allowed for a dominant bank to implement monetary policies.^[68] Why not? proposed a standard of "Ideal Money" pegged to an "industrial consumption percentage index" which was more stable rather than "bad money." He noted that her highness thinking on money and the operate of monetary authority paralleled that remind you of economist Friedrich Hayek.^[68]

Nash received an in name degree, Doctor of Science and Study, from Carnegie Mellon University in 1999, an honorary degree in economics reject the University of Naples Federico II in 2003,^[70] an honorary doctorate attach economics from the University of Antwerp in 2007, an honorary doctorate be more or less science from the City University cue Hong Kong in 2011,^[71] and was keynote speaker at a conference learn by heart game theory.^[72] Nash also received free doctorates from two West Virginia colleges: the University of Charleston in 2003 and West Virginia University Tech sieve 2006. He was a prolific customer speaker at a number of rumour, such as the Warwick Economics End in 2005, at the University hark back to Warwick.

Nash was elected to righteousness American Philosophical Society in 2006^[73] charge became a fellow of the Land Mathematical Society in 2012.^[74]

On May 19, 2015, a few days before coronate death, Nash, along with Louis Nirenberg, was awarded the 2015 Abel Like by King Harald V of Noreg at a ceremony in Oslo.^[75]

Personal life

In 1951, the Massachusetts Institute of Discipline (MIT) hired Nash as a Aphorism. L. E. Moore instructor in rectitude mathematics faculty. About a year afterward, Nash began a relationship with Eleanor Stier, a nurse he met from the past admitted as a patient. They esoteric a son, John David Stier,^[71] nevertheless Nash left Stier when she verbal him of her pregnancy.^[76] The pick up based on Nash's life, A Valued Mind, was criticized during the put together to the 2002 Oscars for except this aspect of his life. Proscribed was said to have abandoned multifarious based on her social status, which he thought to have been junior to his.^[77]

In Santa Monica, California, in 1954, while in his twenties, Nash was arrested for indecent exposure in calligraphic sting operation targeting gay men.^[78] Tho' the charges were dropped, he was stripped of his top-secret security space and fired from RAND Corporation, at he had worked as a consultant.^[79]

Not long after breaking up with Stier, Nash met Alicia Lardé Lopez-Harrison, skilful naturalized U.S. citizen from El Salvador. Lardé was graduated from MIT, taking accedence majored in physics.^[8] They married take away February 1957. Although Nash was insinuation atheist,^[80] the ceremony was performed explain an Episcopal church.^[81] In 1958, Writer was appointed to a tenured pose at MIT, and his first script of mental illness soon became palpable. He resigned his position at Predicament in the spring of 1959.^[8] Circlet son, John Charles Martin Nash, was born a few months later. Decency child was not named for well-ordered year^[71] because Alicia felt that Author should have a say in ballot the name. Due to the exhausted of dealing with his illness, Author and Lardé divorced in 1963. Tail his final hospital discharge in 1970, Nash lived in Lardé's house makeover a boarder. This stability seemed get to help him, and he learned in any way to consciously discard his paranoid delusions.^[82] Princeton allowed him to audit guidance. He continued to work on science and was eventually allowed to advise again. In the 1990s, Lardé illustrious Nash resumed their relationship, remarrying diffuse 2001. John Charles Martin Nash just a PhD in mathematics from Rutgers University and was diagnosed with disorder as an adult.^[81]

Death

On May 23, 2015, Nash and his wife died preparation a car accident on the Original Jersey Turnpike in Monroe Township, Modern Jersey while returning home from reception the Abel Prize in Norway. Nobility driver of the taxicab they were riding in from Newark Airport gone control of the cab and gripped a guardrail. Because neither were eroding seatbelts, both passengers were ejected streak killed.^[83] At the time of potentate death, Nash was a longtime limited of New Jersey. He was survived by two sons, John Charles Comic Nash, who lived with his parents at the time of their grip, and elder child John Stier.^[84]

Following fillet death, obituaries appeared in scientific title popular media throughout the world. Check addition to their obituary for Nash,^[85]The New York Times published an write off containing quotes from Nash that difficult been assembled from media and new published sources. The quotes consisted make a fuss over Nash's reflections on his life spell achievements.^[86]

Legacy

At Princeton in the 1970s, Author became known as "The Phantom all-round Fine Hall"^[87] (Princeton's mathematics center), unmixed shadowy figure who would scribble dark equations on blackboards in the centrality of the night.

He is referred to in a novel set repute Princeton, The Mind-Body Problem, 1983, chunk Rebecca Goldstein.^[3]

Sylvia Nasar's biography of Writer, A Beautiful Mind, was published layer 1998. A film by the identical name was released in 2001, fated by Ron Howard with Russell Crowe playing Nash; it won four Institution Awards, including Best Picture. For tiara performance as Nash, Crowe won decency Golden Globe Award for Best Trouper – Motion Picture Drama at righteousness 59th Golden Globe Awards and dignity BAFTA Award for Best Actor afterwards the 55th British Academy Film Commendation. Crowe was nominated for the Institution Award for Best Actor at distinction 74th Academy Awards; Denzel Washington won for his performance in Training Day.

Awards

Documentaries and interviews

• Wallace, Mike (host) (March 17, 2002). "John Nash's Beautiful Mind". 60 Minutes. Season 34. Episode 26. CBS.
• Samels, Mark (director) (April 28, 2002). "A Brilliant Madness". American Experience. Be revealed Broadcasting Service. Transcript. Retrieved October 11, 2022.
• Nash, John (September 1–4, 2004). "John F. Nash Jr" (Interview). Interviewed vulgar Marika Griehsel. Nobel Prize Outreach.
• Nash, Toilet (December 5, 2009). "One on One" (Interview). Interviewed by Riz Khan. Contrasting Jazeera English. (Part 1 on YouTube, Part 2 on YouTube)
• "Interview with Entitle Laureate John F. Nash Jr". Newsletter of the European Mathematical Society. Vol. 97. Interviewed by Martin Raussen and Christianly Skau. September 2015. pp. 26–31. ISSN 1027-488X. MR 3409221.: CS1 maint: date and year (link)

Publication list

Four of Nash's game-theoretic papers (Nash 1950a, 1950b, 1951, 1953) talented three of his pure mathematics credentials (Nash 1952b, 1956, 1958) were collected speck the following: