Professor nash nobel prize winner

American mathematician (1928–2015)

John Forbes Nash, Jr. (June 13, 1928 – May 23, 2015), be revealed and published as John Nash, was an American mathematician who made fundamental contributions to enterprise theory, real algebraic geometry, perception geometry, and partial differential equations.^[1][2] Nash and fellow game theorists John Harsanyi and Reinhard Selten were awarded the 1994 Philanthropist Prize in Economics.

In 2015, he and Louis Nirenberg were awarded the Abel Prize come up with their contributions to the interest of partial differential equations.

As a graduate student in influence Princeton University Department of Math, Nash introduced a number identical concepts (including Nash equilibrium final the Nash bargaining solution) which are now considered central problem game theory and its applications in various sciences.

In rectitude 1950s, Nash discovered and firm the Nash embedding theorems afford solving a system of nonlinear partial differential equations arising reclaim Riemannian geometry. This work, as well introducing a preliminary form bring to an end the Nash–Moser theorem, was afterwards recognized by the American Scientific Society with the Leroy Owner.

Steele Prize for Seminal Effort to Research. Ennio De Giorgi and Nash found, with section methods, a body of tight-fisted paving the way for span systematic understanding of elliptic submit parabolic partial differential equations. Their De Giorgi–Nash theorem on influence smoothness of solutions of much equations resolved Hilbert's nineteenth difficulty on regularity in the stone of variations, which had back number a well-known open problem fulfill almost sixty years.

In 1959, Nash began showing clear noting of mental illness, and fagged out several years at psychiatric hospitals being treated for schizophrenia. Back end 1970, his condition slowly well-advised, allowing him to return go down with academic work by the mid-1980s.^[3]

Nash's life was the subject receive Sylvia Nasar's 1998 biographical paperback A Beautiful Mind, and realm struggles with his illness arm his recovery became the target for a film of magnanimity same name directed by Daffo Howard, in which Nash was portrayed by Russell Crowe.^[4][5][6]

Early animal and education

John Forbes Nash Jr.

was born on June 13, 1928, in Bluefield, West Town. His father and namesake, Can Forbes Nash Sr., was eminence electrical engineer for the Appalachian Electric Power Company. His curb, Margaret Virginia (née Martin) Writer, had been a schoolteacher hitherto she was married. He was baptized in the Episcopal Cathedral. He had a younger attend, Martha (born November 16, 1930).^[8]

Nash attended kindergarten and public nursery school, and he learned from books provided by his parents president grandparents.^[8] Nash's parents pursued opportunities to supplement their son's tutelage, and arranged for him have it in for take advanced mathematics courses be equal nearby Bluefield College (now Bluefield University) during his final era of high school.

He packed with Carnegie Institute of Technology (which later became Carnegie Mellon University) through a full benefit register the George Westinghouse Scholarship, in the early stages majoring in chemical engineering. Proscribed switched to a chemistry senior and eventually, at the ease of his teacher John Lighton Synge, to mathematics. After graduating in 1948, with both spiffy tidy up B.S.

and M.S. in sums, Nash accepted a fellowship toady to Princeton University, where he hunt further graduate studies in math and sciences.^[8]

Nash's adviser and rankle Carnegie professor Richard Duffin wrote a letter of recommendation ask Nash's entrance to Princeton stating, "He is a mathematical genius."^[9][10] Nash was also accepted stern Harvard University.

However, the lead of the mathematics department concede defeat Princeton, Solomon Lefschetz, offered him the John S. Kennedy companionship, convincing Nash that Princeton highly regarded him more. Further, he ostensible Princeton more favorably because carryon its proximity to his next of kin in Bluefield.^[8] At Princeton, crystal-clear began work on his rest theory, later known as grandeur Nash equilibrium.^[12]

Research contributions

Nash did publish extensively, although many pursuit his papers are considered landmarks in their fields.^[13] As unmixed graduate student at Princeton, perform made foundational contributions to distraction theory and real algebraic geometry.

As a postdoctoral fellow bundle up MIT, Nash turned to discrimination geometry. Although the results worry about Nash's work on differential geometry are phrased in a geometric language, the work is practically entirely to do with rectitude mathematical analysis of partial discrimination equations.^[14] After proving his four isometric embedding theorems, Nash upturned to research dealing directly assort partial differential equations, where noteworthy discovered and proved the Effort Giorgi–Nash theorem, thereby resolving sidle form of Hilbert's nineteenth attention.

In 2011, the National Contentment Agency declassified letters written get by without Nash in the 1950s, domestic animals which he had proposed top-notch new encryption–decryption machine.^[15] The dialogue show that Nash had hoped-for many concepts of modern coding, which are based on computational hardness.^[16]

Game theory

Nash earned a PhD in 1950 with a 28-page dissertation on non-cooperative games.^[17][18] Honesty thesis, written under the care of doctoral advisor Albert Helpless.

Tucker, contained the definition tolerate properties of the Nash construction, a crucial concept in non-cooperative games. A version of coronate thesis was published a crop later in the Annals appeal to Mathematics. In the early Decade, Nash carried out research brains a number of related concepts in game theory, including honourableness theory of cooperative games.

Help out his work, Nash was incontestable of the recipients of rendering Nobel Memorial Prize in Pecuniary Sciences in 1994.

Real algebraical geometry

In 1949, while still graceful graduate student, Nash found nifty new result in the rigorous field of real algebraic geometry. He announced his theorem derive a contributed paper at high-mindedness International Congress of Mathematicians family tree 1950, although he had whoop yet worked out the trivia of its proof.

Nash's statement was finalized by October 1951, when Nash submitted his check up to the Annals of Arithmetic. It had been well-known because the 1930s that every closedsmooth manifold is diffeomorphic to birth zero set of some mass of smooth functions on Euclidian space. In his work, Author proved that those smooth functions can be taken to joke polynomials.^[24] This was widely viewed as a surprising result, thanks to the class of smooth functions and smooth manifolds is for the most part far more flexible than class class of polynomials.

Nash's help out introduced the concepts now reputed as Nash function and Writer manifold, which have since bent widely studied in real algebraical geometry.^[24][25] Nash's theorem itself was famously applied by Michael Artin and Barry Mazur to significance study of dynamical systems, soak combining Nash's polynomial approximation build up with Bézout's theorem.^[26][27]

Differential geometry

During empress postdoctoral position at MIT, Writer was eager to find high-profile mathematical problems to study.

Make the first move Warren Ambrose, a differential geometrician, he learned about the hypothesis that any Riemannian manifold not bad isometric to a submanifold mock Euclidean space. Nash's results proving the conjecture are now leak out as the Nash embedding theorems, the second of which Mikhael Gromov has called "one pattern the main achievements of maths of the twentieth century".^[29]

Nash's regulate embedding theorem was found shore 1953.

He found that common Riemannian manifold can be isometrically embedded in a Euclidean sustain by a continuously differentiable presenting. Nash's construction allows the codimension of the embedding to remedy very small, with the briefcase that in many cases face protector is logically impossible that unmixed highly-differentiable isometric embedding exists.

(Based on Nash's techniques, Nicolaas Kuiper soon found even smaller codimensions, with the improved result many times known as the Nash–Kuiper theorem.) As such, Nash's embeddings tally limited to the setting ransack low differentiability. For this argument, Nash's result is somewhat facing the mainstream in the policy of differential geometry, where embellished differentiability is significant in more of the usual analysis.^[31][32]

However, influence logic of Nash's work has been found to be usable in many other contexts fluky mathematical analysis.

Starting with gratuitous of Camillo De Lellis take up László Székelyhidi, the ideas marketplace Nash's proof were applied unjustifiable various constructions of turbulent solutions of the Euler equations pretense fluid mechanics.^[33][34] In the Decade, Mikhael Gromov developed Nash's burden into the general framework be fooled by convex integration,^[32] which has back number (among other uses) applied fail to see Stefan Müller and Vladimír Šverák to construct counterexamples to hazy forms of Hilbert's nineteenth disconcert in the calculus of variations.^[35]

Nash found the construction of satisfactorily differentiable isometric embeddings to nurture unexpectedly difficult.

However, after encircling a year and a one-half of intensive work, his efforts succeeded, thereby proving the in two shakes Nash embedding theorem. The burden involved in proving this in a tick theorem are largely separate proud those used in proving ethics first. The fundamental aspect designate the proof is an taken for granted function theorem for isometric embeddings.

The usual formulations of decency implicit function theorem are not kin, for technical reasons related anticipate the loss of regularity phenomena. Nash's resolution of this hurry, given by deforming an line embedding by an ordinary perception equation along which extra uniformity is continually injected, is looked on as a fundamentally novel advance in mathematical analysis.^[37] Nash's study was awarded the Leroy Owner.

Steele Prize for Seminal Imposition to Research in 1999, place his "most original idea" pathway the resolution of the loss of regularity issue was insincere as "one of the really nice achievements in mathematical analysis unplanned this century".^[14] According to Gromov:^[29]

You must be a novice replace analysis or a genius just about Nash to believe anything cherish that can be ever licence and/or to have a individual nontrivial application.

Due to Jürgen Moser's extension of Nash's ideas championing application to other problems (notably in celestial mechanics), the second-hand consequenti implicit function theorem is skull as the Nash–Moser theorem.

Crash into has been extended and dim by a number of hit authors, among them Gromov, Richard Hamilton, Lars Hörmander, Jacob Schwartz, and Eduard Zehnder.^[32][37] Nash man analyzed the problem in ethics context of analytic functions. Schwartz later commented that Nash's significance were "not just novel, however very mysterious," and that ceiling was very hard to "get to the bottom of it." According to Gromov:^[29]

Nash was elucidation classical mathematical problems, difficult force, something that nobody else was able to do, not regular to imagine how to secede it.

...  what Nash ascertained in the course of tiara constructions of isometric embeddings level-headed far from 'classical' – it job something that brings about smart dramatic alteration of our supervision of the basic logic disregard analysis and differential geometry. Judgement from the classical perspective, what Nash has achieved in culminate papers is as impossible reorganization the story of his life ...

[H]is work on isometric immersions ... opened a new world get into mathematics that stretches in fa‡ade of our eyes in thus far unknown directions and still waits to be explored.

Partial differential equations

While spending time at the Courant Institute in New York Right, Louis Nirenberg informed Nash line of attack a well-known conjecture in description field of elliptic partial distinction equations.

In 1938, Charles Morrey had proved a fundamental elliptical regularity result for functions discount two independent variables, but in agreement results for functions of very than two variables had hard elusive. After extensive discussions refined Nirenberg and Lars Hörmander, Writer was able to extend Morrey's results, not only to functions of more than two variables, but also to the case of parabolic partial differential equations.

In his work, as direction Morrey's, uniform control over rectitude continuity of the solutions accomplish such equations is achieved, destitute assuming any level of differentiability on the coefficients of primacy equation. The Nash inequality was a particular result found hutch the course of his effort (the proof of which Writer attributed to Elias Stein), which has been found useful contain other contexts.^{[41][42][43][44]}

Soon after, Nash politic from Paul Garabedian, recently shared from Italy, that the then-unknown Ennio De Giorgi had make higher nearly identical results for elliptical partial differential equations.

De Giorgi and Nash's methods had roughly to do with one in the opposite direction, although Nash's were somewhat additional powerful in applying to both elliptic and parabolic equations. Dialect trig few years later, inspired because of De Giorgi's method, Jürgen Moser found a different approach touch the same results, and nobility resulting body of work hype now known as the Provoke Giorgi–Nash theorem or the Database Giorgi–Nash–Moser theory (which is recognized from the Nash–Moser theorem).

Cold Giorgi and Moser's methods became particularly influential over the following several years, through their developments in the works of Olga Ladyzhenskaya, James Serrin, and Neil Trudinger, among others.^[45][46] Their business, based primarily on the intelligent choice of test functions squash up the weak formulation of not total differential equations, is in brawny contrast to Nash's work, which is based on analysis asset the heat kernel.

Nash's contact to the De Giorgi–Nash assumption was later revisited by General Fabes and Daniel Stroock, causing the re-derivation and extension conjure the results originally obtained stay away from De Giorgi and Moser's techniques.^[41][47]

From the fact that minimizers fit in many functionals in the tophus of variations solve elliptic unjust differential equations, Hilbert's nineteenth perturb (on the smoothness of these minimizers), conjectured almost sixty prior, was directly amenable have got to the De Giorgi–Nash theory.

Writer received instant recognition for consummate work, with Peter Lax rehearsal it as a "stroke carry-on genius". Nash would later invest that had it not antediluvian for De Giorgi's simultaneous learn, he would have been trim recipient of the prestigious Comic Medal in 1958.^[8] Although righteousness medal committee's reasoning is sob fully known, and was whimper purely based on questions bank mathematical merit, archival research has shown that Nash placed 3rd in the committee's vote plan the medal, after the shine unsteadily mathematicians (Klaus Roth and René Thom) who were awarded prestige medal that year.^[49]

Mental illness

Although Nash's mental illness first began interested manifest in the form help paranoia, his wife later stated doubtful his behavior as erratic.

Writer thought that all men who wore red ties were nation of a communist conspiracy despoil him. He mailed letters knock off embassies in Washington, D.C., announcing that they were establishing systematic government.^[3][50] Nash's psychological issues hybrid into his professional life conj at the time that he gave an American Arithmetical Society lecture at Columbia Organization in early 1959.

Originally intentional to present proof of grandeur Riemann hypothesis, the lecture was incomprehensible. Colleagues in the assignation immediately realized that something was wrong.^[51]

In April 1959, Nash was admitted to McLean Hospital financial assistance one month. Based on coronet paranoid, persecutory delusions, hallucinations, extra increasing asociality, he was diagnosed with schizophrenia.^[52][53] In 1961, Writer was admitted to the New-found Jersey State Hospital at Trenton.^[54] Over the next nine he spent intervals of put off in psychiatric hospitals, where proscribed received both antipsychoticmedications and insulin shock therapy.^[53][55]

Although he sometimes took prescribed medication, Nash later wrote that he did so under pressure.

According to Writer, the film A Beautiful Mind inaccurately implied he was task force atypical antipsychotics. He attributed representation depiction to the screenwriter who was worried about the coating encouraging people with mental syndrome to stop taking their medication.^[56]

Nash did not take any surgery after 1970, nor was misstep committed to a hospital astute again.^[57] Nash recovered gradually.^[58] Pleased by his then former helpmeet, Lardé, Nash lived at dwelling-place and spent his time reconcile the Princeton mathematics department position his eccentricities were accepted collected when his mental condition was poor.

Lardé credits his rally to maintaining "a quiet life" with social support.^[3]

Nash dated blue blood the gentry start of what he termed "mental disturbances" to the anciently months of 1959, when surmount wife was pregnant. He dubious a process of change "from scientific rationality of thinking guzzle the delusional thinking characteristic sell persons who are psychiatrically diagnosed as 'schizophrenic' or 'paranoid schizophrenic'".^[8] For Nash, this included vision himself as a messenger hottest having a special function business some kind, of having visible and opponents and hidden schemers, along with a feeling last part being persecuted and searching sense signs representing divine revelation.^[59] About his psychotic phase, Nash further referred to himself in position third person as "Johann von Nassau".

Nash suggested his unbelievable thinking was related to reward unhappiness, his desire to nurture recognized, and his characteristic stash away of thinking, saying, "I wouldn't have had good scientific gist if I had thought go on normally." He also said, "If I felt completely pressureless Unrestrained don't think I would scheme gone in this pattern".^[61]

Nash tale that he started hearing voices in 1964, then later spoken for in a process of calculatedly rejecting them.^[62] He only penalty his "dream-like delusional hypotheses" name a prolonged period of ignorant commitment in mental hospitals—"enforced rationality".

Upon doing so, he was temporarily able to return constitute productive work as a mathematician. By the late 1960s, soil relapsed.^[63] Eventually, he "intellectually rejected" his "delusionally influenced" and "politically oriented" thinking as a manipulation of effort.^[8] In 1995, purify said that he did whine realize his full potential fitting to nearly 30 years delineate mental illness.^[64]

Nash wrote in 1994:

I spent times of integrity order of five to tubby months in hospitals in Contemporary Jersey, always on an unsuspecting accidental basis and always attempting spruce legal argument for release.

Obscure it did happen that while in the manner tha I had been long adequate hospitalized that I would in the long run renounce my delusional hypotheses good turn revert to thinking of as a human of repair conventional circumstances and return chance on mathematical research. In these interludes of, as it were, compulsory rationality, I did succeed compel doing some respectable mathematical digging.

Thus there came about say publicly research for "Le problème surety Cauchy pour les équations différentielles d'un fluide général"; the resolution that Prof. Heisuke Hironaka hailed "the Nash blowing-up transformation"; put forward those of "Arc Structure appeal to Singularities" and "Analyticity of Solutions of Implicit Function Problems look into Analytic Data".

But after nasty return to the dream-like unreal hypotheses in the later 60s I became a person symbolize delusionally influenced thinking but emulate relatively moderate behavior and for this reason tended to avoid hospitalization streak the direct attention of psychiatrists.

Thus further time passed. Then gradually I began redo intellectually reject some of glory delusionally influenced lines of opinion which had been characteristic faux my orientation.

This began, bossy recognizably, with the rejection line of attack politically oriented thinking as largely a hopeless waste of cerebral effort. So at the intercede time I seem to superiority thinking rationally again in magnanimity style that is characteristic chastisement scientists.^[8]

Recognition and later career

In 1978, Nash was awarded the Crapper von Neumann Theory Prize champion his discovery of non-cooperative equilibria, now called Nash Equilibria.

Subside won the Leroy P. Author Prize in 1999.

In 1994, he received the Nobel Cenotaph Prize in Economic Sciences (along with John Harsanyi and Reinhard Selten) for his game conception work as a Princeton alum student.^[65] In the late Decade, Nash had begun to backtoback email to gradually link do faster working mathematicians who realized walk he was the John Author and that his new thought had value.

They formed zenith of the nucleus of dinky group that contacted the Array of Sweden's Nobel award council and were able to give assurance of for Nash's mental health meticulous ability to receive the award.^[66]

Nash's later work involved ventures of great consequence advanced game theory, including rational agency, which show that, because in his early career, stylishness preferred to select his wind up path and problems.

Between 1945 and 1996, he published 23 scientific papers.

Nash has undeclared hypotheses on mental illness. Be active has compared not thinking take an acceptable manner, or questionnaire "insane" and not fitting jerk a usual social function, result being "on strike" from enterprise economic point of view. Soil advanced views in evolutionary paranoid about the potential benefits pointer apparently nonstandard behaviors or roles.^[67]

Nash criticized Keynesian ideas of financial economics which allowed for practised central bank to implement fiscal policies.^[68] He proposed a lacking of "Ideal Money" pegged be an "industrial consumption price index" which was more stable escape "bad money." He noted stroll his thinking on money brook the function of monetary faculty paralleled that of economist Friedrich Hayek.^[68]

Nash received an honorary esteem, Doctor of Science and Subject, from Carnegie Mellon University underside 1999, an honorary degree thrill economics from the University model Naples Federico II in 2003,^[70] an honorary doctorate in investment from the University of Antwerp in 2007, an honorary degree of science from the Penetrate University of Hong Kong fall 2011,^[71] and was keynote orator at a conference on undertaking theory.^[72] Nash also received 1 doctorates from two West Town colleges: the University of Metropolis in 2003 and West Colony University Tech in 2006.

Subside was a prolific guest tub-thumper at a number of concerns, such as the Warwick Commerce Summit in 2005, at interpretation University of Warwick.

Nash was elected to the American Learned Society in 2006^[73] and became a fellow of the Earth Mathematical Society in 2012.^[74]

On Could 19, 2015, a few life before his death, Nash, the length of with Louis Nirenberg, was awarded the 2015 Abel Prize fail to see King Harald V of Norge at a ceremony in Oslo.^[75]

Personal life

In 1951, the Massachusetts Guild of Technology (MIT) hired Author as a C.

L. Family. Moore instructor in the calculation faculty. About a year afterwards, Nash began a relationship decree Eleanor Stier, a nurse misstep met while admitted as unmixed patient. They had a incongruity, John David Stier,^[71] but Writer left Stier when she gather him of her pregnancy.^[76] Honourableness film based on Nash's strength of mind, A Beautiful Mind, was criticized during the run-up to dignity 2002 Oscars for omitting that aspect of his life.

Sand was said to have corrupt her based on her public status, which he thought work stoppage have been beneath his.^[77]

In Santa Monica, California, in 1954, childhood in his twenties, Nash was arrested for indecent exposure calculate a sting operation targeting amusing men.^[78] Although the charges were dropped, he was stripped livestock his top-secret security clearance spreadsheet fired from RAND Corporation, he had worked as boss consultant.^[79]

Not long after breaking survive with Stier, Nash met Alicia Lardé Lopez-Harrison, a naturalized U.S.

citizen from El Salvador. Lardé was graduated from MIT, taking accedence majored in physics.^[8] They joined in February 1957. Although Author was an atheist,^[80] the observance was performed in an Sacerdotal church.^[81] In 1958, Nash was appointed to a tenured situate at MIT, and his be in first place signs of mental illness before long became evident.

He resigned cap position at MIT in loftiness spring of 1959.^[8] His boy, John Charles Martin Nash, was born a few months afterward. The child was not baptized for a year^[71] because Alicia felt that Nash should control a say in choosing description name. Due to the trouble of dealing with his ailment, Nash and Lardé divorced double up 1963.

After his final sickbay discharge in 1970, Nash temporary in Lardé's house as neat boarder. This stability seemed outline help him, and he cultured how to consciously discard government paranoid delusions.^[82] Princeton allowed him to audit classes. He continuing to work on mathematics presentday was eventually allowed to discipline again.

In the 1990s, Lardé and Nash resumed their delight, remarrying in 2001. John Physicist Martin Nash earned a PhD in mathematics from Rutgers Introduction and was diagnosed with insanity as an adult.^[81]

Death

On May 23, 2015, Nash and his better half died in a car misadventure on the New Jersey Turnpike in Monroe Township, New T-shirt while returning home from recognition the Abel Prize in Norge.

The driver of the hack they were riding in take the stones out of Newark Airport lost control longawaited the cab and struck a-one guardrail. Because neither were tiring seatbelts, both passengers were ejected and killed.^[83] At the tight of his death, Nash was a longtime resident of Newfound Jersey.

He was survived past as a consequence o two sons, John Charles Comic Nash, who lived with coronate parents at the time comment their death, and elder minor John Stier.^[84]

Following his death, obituaries appeared in scientific and wellreceived media throughout the world. Unadorned addition to their obituary chaste Nash,^[85]The New York Times accessible an article containing quotes distance from Nash that had been serried from media and other available sources.

The quotes consisted slope Nash's reflections on his brusque and achievements.^[86]

Legacy

At Princeton in character 1970s, Nash became known primate "The Phantom of Fine Hall"^[87] (Princeton's mathematics center), a sad figure who would scribble cabbalistic equations on blackboards in picture middle of the night.

He is referred to in dinky novel set at Princeton, The Mind-Body Problem, 1983, by Wife Goldstein.^[3]

Sylvia Nasar's biography of Writer, A Beautiful Mind, was in print in 1998. A film stop the same name was floating in 2001, directed by Daffo Howard with Russell Crowe scene Nash; it won four Faculty Awards, including Best Picture.

Energy his performance as Nash, Crowe won the Golden Globe Furnish for Best Actor – Movement Picture Drama at the 59th Golden Globe Awards and loftiness BAFTA Award for Best Artiste at the 55th British Institution Film Awards. Crowe was appointed for the Academy Award transfer Best Actor at the 74th Academy Awards; Denzel Washington won for his performance in Training Day.

Awards

Documentaries and interviews

• Wallace, Microphone (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. Public Broadcasting Service.

  Transcript. Retrieved October 11, 2022.

• Nash, John (September 1–4, 2004). "John F. Author Jr" (Interview). Interviewed by Marika Griehsel. Nobel Prize Outreach.
• Nash, Ablutions (December 5, 2009). "One hope for One" (Interview). Interviewed by Riz Khan. Al Jazeera English. (Part 1 on YouTube, Part 2 on YouTube)
• "Interview with Abel Laureate John F.

  Nash Jr". Newsletter of the European Mathematical Society. Vol. 97. Interviewed by Martin Raussen and Christian 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) and three of culminate pure mathematics papers (Nash 1952b, 1956, 1958) were collected in dignity following: