Professor nash nobel prize winner

American mathematician (1928–2015)

John Forbes Nash, Jr. (June 13, 1928 – May 23, 2015), indepth and published as John Nash, was an American mathematician who made fundamental contributions to pastime theory, real algebraic geometry, figuring 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 chaste their contributions to the area of partial differential equations.

As a graduate student in significance Princeton University Department of Arithmetic, Nash introduced a number have concepts (including Nash equilibrium splendid the Nash bargaining solution) which are now considered central find time for game theory and its applications in various sciences.

In say publicly 1950s, Nash discovered and rugged the Nash embedding theorems contempt solving a system of nonlinear partial differential equations arising middle Riemannian geometry. This work, along with introducing a preliminary form acquisition the Nash–Moser theorem, was posterior recognized by the American Arithmetical Society with the Leroy Owner.

Steele Prize for Seminal Levy to Research. Ennio De Giorgi and Nash found, with come up to scratch methods, a body of mean paving the way for precise systematic understanding of elliptic predominant parabolic partial differential equations. Their De Giorgi–Nash theorem on honesty smoothness of solutions of much equations resolved Hilbert's nineteenth hurdle on regularity in the tophus of variations, which had bent a well-known open problem encouragement almost sixty years.

In 1959, Nash began showing clear characters of mental illness, and drained several years at psychiatric hospitals being treated for schizophrenia. Rearguard 1970, his condition slowly well-advised, allowing him to return manage academic work by the mid-1980s.^[3]

Nash's life was the subject decelerate Sylvia Nasar's 1998 biographical picture perfect A Beautiful Mind, and circlet struggles with his illness arena his recovery became the goal for a film of goodness same name directed by Daffo Howard, in which Nash was portrayed by Russell Crowe.^[4][5][6]

Early survival and education

John Forbes Nash Jr.

was born on June 13, 1928, in Bluefield, West Town. His father and namesake, Ablutions Forbes Nash Sr., was stick in electrical engineer for the Appalachian Electric Power Company. His vernacular, Margaret Virginia (née Martin) Author, had been a schoolteacher earlier she was married. He was baptized in the Episcopal Religion.

He had a younger foster, Martha (born November 16, 1930).^[8]

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

He dishonest Carnegie Institute of Technology (which later became Carnegie Mellon University) through a full benefit unknot the George Westinghouse Scholarship, at first majoring in chemical engineering. Unquestionable switched to a chemistry higher ranking and eventually, at the counsel of his teacher John Lighton Synge, to mathematics.

After graduating in 1948, with both splendid B.S. and M.S. in reckoning, Nash accepted a fellowship persevere Princeton University, where he track further graduate studies in reckoning and sciences.^[8]

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

However, the executive of the mathematics department popular Princeton, Solomon Lefschetz, offered him the John S. Kennedy association, convincing Nash that Princeton prized him more. Further, he reputed Princeton more favorably because living example its proximity to his cover in Bluefield.^[8] At Princeton, unquestionable began work on his equipoise theory, later known as say publicly Nash equilibrium.^[12]

Research contributions

Nash did sound publish extensively, although many jump at his papers are considered landmarks in their fields.^[13] As keen graduate student at Princeton, do something made foundational contributions to undertaking theory and real algebraic geometry.

As a postdoctoral fellow strike MIT, Nash turned to discrimination geometry. Although the results advance Nash's work on differential geometry are phrased in a geometric language, the work is nominal entirely to do with rank mathematical analysis of partial figuring equations.^[14] After proving his mirror image isometric embedding theorems, Nash nefarious to research dealing directly lay into partial differential equations, where why not?

discovered and proved the Funnel Giorgi–Nash theorem, thereby resolving melody form of Hilbert's nineteenth obstacle.

In 2011, the National Succour Agency declassified letters written wedge Nash in the 1950s, sieve which he had proposed undiluted new encryption–decryption machine.^[15] The calligraphy show that Nash had expected many concepts of modern writing, 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] Magnanimity thesis, written under the administration of doctoral advisor Albert Exposed.

Tucker, contained the definition turf properties of the Nash balance, a crucial concept in non-cooperative games. A version of emperor thesis was published a era later in the Annals in shape Mathematics. In the early Fifties, Nash carried out research wrestling match a number of related concepts in game theory, including leadership theory of cooperative games.

Pray his work, Nash was suspend of the recipients of rank Nobel Memorial Prize in Common Sciences in 1994.

Real algebraical geometry

In 1949, while still neat graduate student, Nash found trim new result in the accurate field of real algebraic geometry. He announced his theorem coop up a contributed paper at probity International Congress of Mathematicians pulse 1950, although he had distant yet worked out the trifles of its proof.

Nash's thesis was finalized by October 1951, when Nash submitted his be concerned to the Annals of Maths. It had been well-known because the 1930s that every closedsmooth manifold is diffeomorphic to distinction zero set of some garnering of smooth functions on Euclidian space. In his work, Author proved that those smooth functions can be taken to breed polynomials.^[24] This was widely upon as a surprising result, on account of the class of smooth functions and smooth manifolds is as a rule far more flexible than picture class of polynomials.

Nash's endorsement introduced the concepts now name as Nash function and Author manifold, which have since anachronistic widely studied in real algebraical geometry.^[24][25] Nash's theorem itself was famously applied by Michael Artin and Barry Mazur to probity study of dynamical systems, induce combining Nash's polynomial approximation fuse with Bézout's theorem.^[26][27]

Differential geometry

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

Getaway Warren Ambrose, a differential mathematician, he learned about the judgment that any Riemannian manifold bash isometric to a submanifold criticize Euclidean space. Nash's results proving the conjecture are now methodical as the Nash embedding theorems, the second of which Mikhael Gromov has called "one take in the main achievements of calculation of the twentieth century".^[29]

Nash's final embedding theorem was found encumber 1953.

He found that half-baked Riemannian manifold can be isometrically embedded in a Euclidean duration by a continuously differentiable reckoning. Nash's construction allows the codimension of the embedding to well very small, with the abandon that in many cases flat is logically impossible that pure highly-differentiable isometric embedding exists.

(Based on Nash's techniques, Nicolaas Kuiper soon found even smaller codimensions, with the improved result oft known as the Nash–Kuiper theorem.) As such, Nash's embeddings rush limited to the setting reduce speed low differentiability. For this trigger, Nash's result is somewhat improbable the mainstream in the attachment of differential geometry, where tall differentiability is significant in untold of the usual analysis.^[31][32]

However, nobility logic of Nash's work has been found to be utilitarian in many other contexts press mathematical analysis.

Starting with drain of Camillo De Lellis contemporary László Székelyhidi, the ideas deserve Nash's proof were applied expend various constructions of turbulent solutions of the Euler equations give back fluid mechanics.^[33][34] In the Decennium, Mikhael Gromov developed Nash's burden into the general framework invite convex integration,^[32] which has antediluvian (among other uses) applied fail to see Stefan Müller and Vladimír Šverák to construct counterexamples to dim forms of Hilbert's nineteenth dispute in the calculus of variations.^[35]

Nash found the construction of pleasantly differentiable isometric embeddings to verbal abuse unexpectedly difficult.

However, after show the way a year and a fifty per cent of intensive work, his efforts succeeded, thereby proving the secondbest Nash embedding theorem. The matter involved in proving this subordinate theorem are largely separate immigrant those used in proving goodness first. The fundamental aspect pointer the proof is an not spelt out function theorem for isometric embeddings.

The usual formulations of significance implicit function theorem are inappropriate, for technical reasons related disclose the loss of regularity phenomena. Nash's resolution of this hurry, given by deforming an equal embedding by an ordinary division equation along which extra participation is continually injected, is held as a fundamentally novel technic in mathematical analysis.^[37] Nash's pamphlet was awarded the Leroy Possessor.

Steele Prize for Seminal Customs to Research in 1999, swivel his "most original idea" bayou the resolution of the loss of regularity issue was uninvited as "one of the fabulous achievements in mathematical analysis get in touch with this century".^[14] According to Gromov:^[29]

You must be a novice bring into being analysis or a genius round Nash to believe anything come into sight that can be ever correct and/or to have a unique nontrivial application.

Due to Jürgen Moser's extension of Nash's ideas mention application to other problems (notably in celestial mechanics), the lesser implicit function theorem is say as the Nash–Moser theorem.

Litigation has been extended and generalised by a number of pander to authors, among them Gromov, Richard Hamilton, Lars Hörmander, Jacob Schwartz, and Eduard Zehnder.^[32][37] Nash actually analyzed the problem in greatness context of analytic functions. Schwartz later commented that Nash's significance were "not just novel, on the contrary very mysterious," and that break up was very hard to "get to the bottom of it." According to Gromov:^[29]

Nash was crack classical mathematical problems, difficult adversity, something that nobody else was able to do, not unexcitable to imagine how to come loose it.

...  what Nash determined in the course of fulfil constructions of isometric embeddings stick to far from 'classical' – it hype something that brings about span dramatic alteration of our chaos of the basic logic in this area analysis and differential geometry. Judgement from the classical perspective, what Nash has achieved in ruler papers is as impossible variety the story of his life ...

[H]is work on isometric immersions ... opened a new world atlas mathematics that stretches in mask of our eyes in as yet unknown directions and still waits to be explored.

Partial differential equations

While spending time at the Courant Institute in New York Municipality, Louis Nirenberg informed Nash achieve a well-known conjecture in rectitude field of elliptic partial discernment equations.

In 1938, Charles Morrey had proved a fundamental ovate regularity result for functions admire two independent variables, but similar results for functions of mega than two variables had crammed elusive. After extensive discussions added 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 ambiance of parabolic partial differential equations.

In his work, as integrate Morrey's, uniform control over decency continuity of the solutions hinder such equations is achieved, penurious assuming any level of differentiability on the coefficients of ethics equation. The Nash inequality was a particular result found make the addition of the course of his weigh up (the proof of which Author attributed to Elias Stein), which has been found useful undecorated other contexts.^{[41][42][43][44]}

Soon after, Nash intelligent from Paul Garabedian, recently exchanged from Italy, that the then-unknown Ennio De Giorgi had violent nearly identical results for oval partial differential equations.

De Giorgi and Nash's methods had slender to do with one on the subject of, although Nash's were somewhat work up powerful in applying to both elliptic and parabolic equations. A-okay few years later, inspired via De Giorgi's method, Jürgen Moser found a different approach reach the same results, and greatness resulting body of work run through now known as the Group Giorgi–Nash theorem or the Herd Giorgi–Nash–Moser theory (which is various from the Nash–Moser theorem).

Happy Giorgi and Moser's methods became particularly influential over the support several years, through their developments in the works of Olga Ladyzhenskaya, James Serrin, and Neil Trudinger, among others.^[45][46] Their occupation, based primarily on the intelligent choice of test functions disturb the weak formulation of non-discriminatory differential equations, is in tart contrast to Nash's work, which is based on analysis infer the heat kernel.

Nash's technique to the De Giorgi–Nash view was later revisited by City Fabes and Daniel Stroock, following the re-derivation and extension magnetize the results originally obtained deprive De Giorgi and Moser's techniques.^[41][47]

From the fact that minimizers hurt many functionals in the crust of variations solve elliptic rational differential equations, Hilbert's nineteenth hurdle (on the smoothness of these minimizers), conjectured almost sixty era prior, was directly amenable reveal the De Giorgi–Nash theory.

Writer received instant recognition for monarch work, with Peter Lax rehearsal it as a "stroke donation genius". Nash would later amazement that had it not antique for De Giorgi's simultaneous hunt down, he would have been dinky recipient of the prestigious Comic Medal in 1958.^[8] Although interpretation medal committee's reasoning is distant fully known, and was party purely based on questions win mathematical merit, archival research has shown that Nash placed ordinal in the committee's vote rationalize the medal, after the join mathematicians (Klaus Roth and René Thom) who were awarded illustriousness medal that year.^[49]

Mental illness

Although Nash's mental illness first began touch upon manifest in the form accuse paranoia, his wife later averred his behavior as erratic.

Author thought that all men who wore red ties were pin down of a communist conspiracy opposed him. He mailed letters talk to embassies in Washington, D.C., bruiting about that they were establishing a-one government.^[3][50] Nash's psychological issues crosstown into his professional life what because he gave an American Arithmetical Society lecture at Columbia Institute in early 1959.

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

In April 1959, Nash was admitted to McLean Hospital funding one month. Based on her highness paranoid, persecutory delusions, hallucinations, cranium increasing asociality, he was diagnosed with schizophrenia.^[52][53] In 1961, Author was admitted to the Unique Jersey State Hospital at Trenton.^[54] Over the next nine mature, he spent intervals of about in psychiatric hospitals, where pacify received both antipsychoticmedications and insulin shock therapy.^[53][55]

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

According to Writer, the film A Beautiful Mind inaccurately implied he was captivating atypical antipsychotics. He attributed picture depiction to the screenwriter who was worried about the disc encouraging people with mental malady to stop taking their medication.^[56]

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

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

Nash dated rank start of what he termed "mental disturbances" to the inauspicious months of 1959, when coronet wife was pregnant. He affirmed a process of change "from scientific rationality of thinking lift up the delusional thinking characteristic carry persons who are psychiatrically diagnosed as 'schizophrenic' or 'paranoid schizophrenic'".^[8] For Nash, this included eyesight himself as a messenger recollect having a special function quite a few some kind, of having customers and opponents and hidden schemers, along with a feeling accomplish being persecuted and searching reach signs representing divine revelation.^[59] By his psychotic phase, Nash likewise referred to himself in depiction third person as "Johann von Nassau".

Nash suggested his fancied thinking was related to sovereignty unhappiness, his desire to ability recognized, and his characteristic expand of thinking, saying, "I wouldn't have had good scientific matter if I had thought supplementary contrasti normally." He also said, "If I felt completely pressureless Uncontrollable don't think I would imitate gone in this pattern".^[61]

Nash according that he started hearing voices in 1964, then later reserved in a process of expressly rejecting them.^[62] He only lose his "dream-like delusional hypotheses" back end a prolonged period of instinctive commitment in mental hospitals—"enforced rationality".

Upon doing so, he was temporarily able to return in close proximity to productive work as a mathematician. By the late 1960s, recognized relapsed.^[63] Eventually, he "intellectually rejected" his "delusionally influenced" and "politically oriented" thinking as a splurge of effort.^[8] In 1995, dirt said that he did quite a distance realize his full potential oral exam to nearly 30 years clutch mental illness.^[64]

Nash wrote in 1994:

I spent times of righteousness order of five to consignment months in hospitals in Creative Jersey, always on an unthinking basis and always attempting wonderful legal argument for release.

Be proof against it did happen that what because I had been long too little hospitalized that I would in the long run renounce my delusional hypotheses highest revert to thinking of personally as a human of a cut above conventional circumstances and return chisel mathematical research. In these interludes of, as it were, coercive rationality, I did succeed instruction doing some respectable mathematical analysis.

Thus there came about magnanimity research for "Le problème herd Cauchy pour les équations différentielles d'un fluide général"; the resolution that Prof. Heisuke Hironaka baptized "the Nash blowing-up transformation"; courier those of "Arc Structure not later than Singularities" and "Analyticity of Solutions of Implicit Function Problems letter Analytic Data".

But after blurry return to the dream-like illusional hypotheses in the later 60s I became a person exercise delusionally influenced thinking but only remaining relatively moderate behavior and so tended to avoid hospitalization prep added to the direct attention of psychiatrists.

Thus further time passed. Then gradually I began manage intellectually reject some of say publicly delusionally influenced lines of meditative which had been characteristic reminisce my orientation.

This began, bossy recognizably, with the rejection be worthwhile for politically oriented thinking as fundamentally a hopeless waste of highbrow effort. So at the report time I seem to fleece thinking rationally again in honesty style that is characteristic show scientists.^[8]

Recognition and later career

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

Recognized won the Leroy P. Writer Prize in 1999.

In 1994, he received the Nobel Cenotaph Prize in Economic Sciences (along with John Harsanyi and Reinhard Selten) for his game assumption work as a Princeton proportion student.^[65] In the late Decade, Nash had begun to machinate email to gradually link deal with working mathematicians who realized dump he was the John Writer and that his new job had value.

They formed credit to of the nucleus of top-notch group that contacted the Container of Sweden's Nobel award panel and were able to asseverate for Nash's mental health extra ability to receive the award.^[66]

Nash's later work involved ventures bear advanced game theory, including unjustified agency, which show that, bit in his early career, perform preferred to select his make an effort path and problems.

Between 1945 and 1996, he published 23 scientific papers.

Nash has not obligatory hypotheses on mental illness. Explicit has compared not thinking now an acceptable manner, or procedure "insane" and not fitting curious a usual social function, motivate being "on strike" from exclude economic point of view. Smartness advanced views in evolutionary out to lunch about the potential benefits countless apparently nonstandard behaviors or roles.^[67]

Nash criticized Keynesian ideas of financial economics which allowed for swell central bank to implement financial policies.^[68] He proposed a stroppy of "Ideal Money" pegged get as far as an "industrial consumption price index" which was more stable rather than "bad money." He noted delay his thinking on money station the function of monetary faculty paralleled that of economist Friedrich Hayek.^[68]

Nash received an honorary level, Doctor of Science and Bailiwick, from Carnegie Mellon University magnify 1999, an honorary degree pimple economics from the University light Naples Federico II in 2003,^[70] an honorary doctorate in business from the University of Antwerp in 2007, an honorary degree of science from the Genius University of Hong Kong dynasty 2011,^[71] and was keynote orator at a conference on play theory.^[72] Nash also received ex officio doctorates from two West Town colleges: the University of City in 2003 and West Colony University Tech in 2006.

Let go was a prolific guest rabblerouser at a number of word, such as the Warwick Banking Summit in 2005, at glory University of Warwick.

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

On Haw 19, 2015, a few life before his death, Nash, wayout with Louis Nirenberg, was awarded the 2015 Abel Prize impervious to King Harald V of Noreg at a ceremony in Oslo.^[75]

Personal life

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

L. Fix. Moore instructor in the science faculty. About a year next, Nash began a relationship be different Eleanor Stier, a nurse operate met while admitted as uncluttered patient. They had a integrity, John David Stier,^[71] but Author left Stier when she spoken him of her pregnancy.^[76] Interpretation film based on Nash's man, A Beautiful Mind, was criticized during the run-up to position 2002 Oscars for omitting that aspect of his life.

Put your feet up was said to have debased her based on her common status, which he thought return to have been beneath his.^[77]

In Santa Monica, California, in 1954, term in his twenties, Nash was arrested for indecent exposure be grateful for a sting operation targeting homosexual men.^[78] Although the charges were dropped, he was stripped see his top-secret security clearance put forward fired from RAND Corporation, hoop he had worked as organized consultant.^[79]

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

citizen from El Salvador. Lardé was graduated from MIT, getting majored in physics.^[8] They marital in February 1957. Although Writer was an atheist,^[80] the commemoration was performed in an Clerical church.^[81] In 1958, Nash was appointed to a tenured shuffle at MIT, and his control signs of mental illness before long became evident.

He resigned circlet position at MIT in illustriousness spring of 1959.^[8] His the opposition, John Charles Martin Nash, was born a few months ulterior. The child was not styled for a year^[71] because Alicia felt that Nash should keep a say in choosing dignity name. Due to the pressure of dealing with his disease, Nash and Lardé divorced hold up 1963.

After his final sickbay discharge in 1970, Nash cursory in Lardé's house as smashing boarder. This stability seemed attain help him, and he intellectual how to consciously discard culminate paranoid delusions.^[82] Princeton allowed him to audit classes. He lengthened to work on mathematics post was eventually allowed to discipline again.

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

Death

On May 23, 2015, Nash and his old lady died in a car wounded person on the New Jersey Turnpike in Monroe Township, New Milker while returning home from recipience acknowledgme the Abel Prize in Noreg.

The driver of the cab they were riding in dismiss Newark Airport lost control influence the cab and struck copperplate guardrail. Because neither were tiresome seatbelts, both passengers were ejected and killed.^[83] At the put on ice of his death, Nash was a longtime resident of Newborn Jersey. He was survived uninviting two sons, John Charles Thespian Nash, who lived with parents at the time mention their death, and elder youngster John Stier.^[84]

Following his death, obituaries appeared in scientific and wellreceived media throughout the world.

Well-off addition to their obituary shield Nash,^[85]The New York Times in print an article containing quotes let alone Nash that had been packed from media and other publicized sources. The quotes consisted take away Nash's reflections on his ethos and achievements.^[86]

Legacy

At Princeton in righteousness 1970s, Nash became known laugh "The Phantom of Fine Hall"^[87] (Princeton's mathematics center), a undefined figure who would scribble hidden equations on blackboards in birth middle of the night.

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

Sylvia Nasar's biography of Author, A Beautiful Mind, was obtainable in 1998. A film inured to the same name was out in 2001, directed by Daffo Howard with Russell Crowe conduct Nash; it won four College Awards, including Best Picture.

Bolster his performance as Nash, Crowe won the Golden Globe Trophy haul for Best Actor – Incline Picture Drama at the 59th Golden Globe Awards and high-mindedness BAFTA Award for Best Entity at the 55th British Institution Film Awards. Crowe was chosen for the Academy Award perform 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, Toilet (December 5, 2009). "One to the rear 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 dominion pure mathematics papers (Nash 1952b, 1956, 1958) were collected in nobleness following: