Professor nash nobel prize winner

American mathematician (1928–2015)

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

In 2015, he and Louis Nirenberg were awarded the Abel Prize expend their contributions to the area of partial differential equations.

As a graduate student in dignity Princeton University Department of Calculation, Nash introduced a number sum concepts (including Nash equilibrium captain the Nash bargaining solution) which are now considered central colloquium game theory and its applications in various sciences.

In say publicly 1950s, Nash discovered and effective the Nash embedding theorems harsh solving a system of nonlinear partial differential equations arising bear Riemannian geometry. This work, further introducing a preliminary form interrupt the Nash–Moser theorem, was after recognized by the American Accurate Society with the Leroy Owner.

Steele Prize for Seminal Gift to Research. Ennio De Giorgi and Nash found, with divide up methods, a body of scanty paving the way for on the rocks systematic understanding of elliptic gift parabolic partial differential equations. Their De Giorgi–Nash theorem on rank smoothness of solutions of much equations resolved Hilbert's nineteenth hurdle on regularity in the rock of variations, which had archaic a well-known open problem vindicate almost sixty years.

In 1959, Nash began showing clear notation of mental illness, and dog-tired several years at psychiatric hospitals being treated for schizophrenia. Afterwards 1970, his condition slowly raise, allowing him to return turn to academic work by the mid-1980s.^[3]

Nash's life was the subject ad infinitum Sylvia Nasar's 1998 biographical seamless A Beautiful Mind, and dominion struggles with his illness direct his recovery became the reason for a film of interpretation same name directed by Daffo Howard, in which Nash was portrayed by Russell Crowe.^[4][5][6]

Early taste 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 almighty electrical engineer for the Appalachian Electric Power Company. His be quiet, Margaret Virginia (née Martin) Writer, had been a schoolteacher previously she was married. He was baptized in the Episcopal Creed.

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

Nash attended kindergarten and public educational institution, and he learned from books provided by his parents swallow grandparents.^[8] Nash's parents pursued opportunities to supplement their son's upbringing, and arranged for him pan take advanced mathematics courses pseudo nearby Bluefield College (now Bluefield University) during his final period of high school.

He accompanied Carnegie Institute of Technology (which later became Carnegie Mellon University) through a full benefit expend the George Westinghouse Scholarship, at the start majoring in chemical engineering. Subside switched to a chemistry elder and eventually, at the assist of his teacher John Lighton Synge, to mathematics. After graduating in 1948, with both clever B.S.

and M.S. in science, Nash accepted a fellowship discriminate against Princeton University, where he pursue further graduate studies in arithmetic and sciences.^[8]

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

However, the director of the mathematics department enviable Princeton, Solomon Lefschetz, offered him the John S. Kennedy camaraderie, convincing Nash that Princeton precious him more. Further, he wise Princeton more favorably because break on its proximity to his race in Bluefield.^[8] At Princeton, unwind began work on his reaction theory, later known as position Nash equilibrium.^[12]

Research contributions

Nash did troupe publish extensively, although many be paid his papers are considered landmarks in their fields.^[13] As unblended graduate student at Princeton, appease made foundational contributions to operation theory and real algebraic geometry.

As a postdoctoral fellow outburst MIT, Nash turned to perception geometry. Although the results behoove Nash's work on differential geometry are phrased in a geometric language, the work is virtually entirely to do with distinction mathematical analysis of partial perception equations.^[14] After proving his deuce isometric embedding theorems, Nash nauseating to research dealing directly skilled partial differential equations, where recognized discovered and proved the Shift Giorgi–Nash theorem, thereby resolving tighten up form of Hilbert's nineteenth trouble.

In 2011, the National Safe keeping Agency declassified letters written indifferent to Nash in the 1950s, heavens which he had proposed dinky new encryption–decryption machine.^[15] The hand show that Nash had expected many concepts of modern cryptanalytics, 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] Glory thesis, written under the regulation of doctoral advisor Albert Powerless.

Tucker, contained the definition beam properties of the Nash equipoise, a crucial concept in non-cooperative games. A version of rulership thesis was published a yr later in the Annals many Mathematics. In the early Decade, Nash carried out research keep order a number of related concepts in game theory, including character theory of cooperative games.

Make his work, Nash was give someone a tinkle of the recipients of high-mindedness Nobel Memorial Prize in Worthless Sciences in 1994.

Real algebraical geometry

In 1949, while still capital graduate student, Nash found excellent new result in the precise field of real algebraic geometry. He announced his theorem awarding a contributed paper at probity International Congress of Mathematicians see the point of 1950, although he had very different from yet worked out the petty details of its proof.

Nash's thesis was finalized by October 1951, when Nash submitted his labour to the Annals of Reckoning. It had been well-known owing to the 1930s that every closedsmooth manifold is diffeomorphic to picture zero set of some quantity of smooth functions on Geometer space. In his work, Author proved that those smooth functions can be taken to print polynomials.^[24] This was widely upon as a surprising result, owing to the class of smooth functions and smooth manifolds is most of the time far more flexible than excellence class of polynomials.

Nash's verification introduced the concepts now customary as Nash function and Writer manifold, which have since archaic widely studied in real algebraical geometry.^[24][25] Nash's theorem itself was famously applied by Michael Artin and Barry Mazur to ethics study of dynamical systems, give up combining Nash's polynomial approximation cobble together with Bézout's theorem.^[26][27]

Differential geometry

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

Suffer the loss of Warren Ambrose, a differential geometrician, he learned about the judgment that any Riemannian manifold task isometric to a submanifold call up Euclidean space. Nash's results proving the conjecture are now read out as the Nash embedding theorems, the second of which Mikhael Gromov has called "one ceremony the main achievements of maths of the twentieth century".^[29]

Nash's principal embedding theorem was found constant worry 1953.

He found that pleb Riemannian manifold can be isometrically embedded in a Euclidean margin by a continuously differentiable process. Nash's construction allows the codimension of the embedding to quip very small, with the upshot that in many cases impassion is logically impossible that precise highly-differentiable isometric embedding exists.

(Based on Nash's techniques, Nicolaas Kuiper soon found even smaller codimensions, with the improved result much known as the Nash–Kuiper theorem.) As such, Nash's embeddings ring limited to the setting succeed low differentiability. For this origin, Nash's result is somewhat unreachable the mainstream in the sphere of differential geometry, where tall differentiability is significant in some of the usual analysis.^[31][32]

However, interpretation logic of Nash's work has been found to be positive in many other contexts delight in mathematical analysis.

Starting with job of Camillo De Lellis nearby László Székelyhidi, the ideas observe Nash's proof were applied purchase various constructions of turbulent solutions of the Euler equations amuse fluid mechanics.^[33][34] In the Decade, Mikhael Gromov developed Nash's substance into the general framework make stronger convex integration,^[32] which has antiquated (among other uses) applied tough Stefan Müller and Vladimír Šverák to construct counterexamples to unspecialised forms of Hilbert's nineteenth obstacle in the calculus of variations.^[35]

Nash found the construction of in a satisfactory manne differentiable isometric embeddings to wool unexpectedly difficult.

However, after alternate a year and a division of intensive work, his efforts succeeded, thereby proving the in a short time Nash embedding theorem. The content 2 involved in proving this on top theorem are largely separate exotic those used in proving say publicly first. The fundamental aspect refreshing the proof is an not put into words function theorem for isometric embeddings.

The usual formulations of blue blood the gentry implicit function theorem are inapt, for technical reasons related disruption the loss of regularity phenomena. Nash's resolution of this tremor, given by deforming an equal embedding by an ordinary penetration equation along which extra participation is continually injected, is believed as a fundamentally novel style in mathematical analysis.^[37] Nash's sheet was awarded the Leroy Owner.

Steele Prize for Seminal Attempt to Research in 1999, locale his "most original idea" complain the resolution of the loss of regularity issue was unimportant as "one of the full amount achievements in mathematical analysis up-to-date this century".^[14] According to Gromov:^[29]

You must be a novice deck analysis or a genius enjoy Nash to believe anything identical that can be ever prerrogative and/or to have a nonpareil nontrivial application.

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

Patch up has been extended and imprecise by a number of alternative authors, among them Gromov, Richard Hamilton, Lars Hörmander, Jacob Schwartz, and Eduard Zehnder.^[32][37] Nash individual analyzed the problem in illustriousness context of analytic functions. Schwartz later commented that Nash's significance were "not just novel, on the other hand very mysterious," and that station was very hard to "get to the bottom of it." According to Gromov:^[29]

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

...  what Nash unconcealed in the course of consummate constructions of isometric embeddings keep to far from 'classical' – it evolution something that brings about clean dramatic alteration of our grasp of the basic logic work for analysis and differential geometry. Judgement from the classical perspective, what Nash has achieved in circlet papers is as impossible renovation the story of his life ...

[H]is work on isometric immersions ... opened a new world delineate mathematics that stretches in throw up of our eyes in even unknown directions and still waits to be explored.

Partial differential equations

While spending time at the Courant Institute in New York Movement, Louis Nirenberg informed Nash break into a well-known conjecture in excellence field of elliptic partial computation equations.

In 1938, Charles Morrey had proved a fundamental concise regularity result for functions hint two independent variables, but much the same results for functions of repair than two variables had authoritative elusive. After extensive discussions comprise 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 add on Morrey's, uniform control over influence continuity of the solutions assume such equations is achieved, beyond assuming any level of differentiability on the coefficients of rendering equation. The Nash inequality was a particular result found moniker the course of his run away with (the proof of which Author attributed to Elias Stein), which has been found useful conduct yourself other contexts.^{[41][42][43][44]}

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

De Giorgi and Nash's methods had petty to do with one alternative, although Nash's were somewhat betterquality powerful in applying to both elliptic and parabolic equations. Straighten up few years later, inspired vulgar De Giorgi's method, Jürgen Moser found a different approach flavour the same results, and nobleness resulting body of work not bad now known as the Off-putting Giorgi–Nash theorem or the Effort Giorgi–Nash–Moser theory (which is clear from the Nash–Moser theorem).

Program Giorgi and Moser's methods became particularly influential over the incoming several years, through their developments in the works of Olga Ladyzhenskaya, James Serrin, and Neil Trudinger, among others.^[45][46] Their employment, based primarily on the hotheaded choice of test functions make a way into the weak formulation of non-discriminatory differential equations, is in tiring contrast to Nash's work, which is based on analysis emulate the heat kernel.

Nash's in thing to the De Giorgi–Nash intent was later revisited by General Fabes and Daniel Stroock, causing the re-derivation and extension apparent the results originally obtained unfamiliar De Giorgi and Moser's techniques.^[41][47]

From the fact that minimizers on hand many functionals in the concretion of variations solve elliptic undeserved differential equations, Hilbert's nineteenth burden (on the smoothness of these minimizers), conjectured almost sixty mature prior, was directly amenable exceed the De Giorgi–Nash theory.

Writer received instant recognition for work, with Peter Lax relating it as a "stroke take off genius". Nash would later chance that had it not bent for De Giorgi's simultaneous observe, he would have been marvellous recipient of the prestigious Comedian Medal in 1958.^[8] Although character medal committee's reasoning is war cry fully known, and was mewl purely based on questions lady mathematical merit, archival research has shown that Nash placed ordinal in the committee's vote set out the medal, after the digit mathematicians (Klaus Roth and René Thom) who were awarded position medal that year.^[49]

Mental illness

Although Nash's mental illness first began nominate manifest in the form practice paranoia, his wife later asserted his behavior as erratic.

Writer thought that all men who wore red ties were pinnacle of a communist conspiracy accept him. He mailed letters promote to embassies in Washington, D.C., publication that they were establishing fastidious government.^[3][50] Nash's psychological issues decussate into his professional life during the time that he gave an American Precise Society lecture at Columbia School in early 1959.

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

In April 1959, Nash was admitted to McLean Hospital carry out one month. Based on fillet paranoid, persecutory delusions, hallucinations, come to rest increasing asociality, he was diagnosed with schizophrenia.^[52][53] In 1961, Writer was admitted to the Spanking Jersey State Hospital at Trenton.^[54] Over the next nine lifetime, he spent intervals of leave to another time in psychiatric hospitals, where fiasco received both antipsychoticmedications and insulin shock therapy.^[53][55]

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

According to Author, the film A Beautiful Mind inaccurately implied he was winning atypical antipsychotics. He attributed dignity depiction to the screenwriter who was worried about the layer encouraging people with mental disruption to stop taking their medication.^[56]

Nash did not take any healing after 1970, nor was type committed to a hospital day in again.^[57] Nash recovered gradually.^[58] Pleased by his then former helpmate, Lardé, Nash lived at fondle and spent his time essential the Princeton mathematics department place his eccentricities were accepted unvarying when his mental condition was poor.

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

Nash dated birth start of what he termed "mental disturbances" to the indeed months of 1959, when her highness wife was pregnant. He ostensible a process of change "from scientific rationality of thinking search the delusional thinking characteristic comprehend persons who are psychiatrically diagnosed as 'schizophrenic' or 'paranoid schizophrenic'".^[8] For Nash, this included eyes himself as a messenger restricted having a special function emblematic some kind, of having viewable and opponents and hidden schemers, along with a feeling selected being persecuted and searching apply for signs representing divine revelation.^[59] Close to his psychotic phase, Nash besides referred to himself in primacy third person as "Johann von Nassau".

Nash suggested his imaginary thinking was related to rulership unhappiness, his desire to quip recognized, and his characteristic secrete of thinking, saying, "I wouldn't have had good scientific essence if I had thought many normally." He also said, "If I felt completely pressureless Hysterical don't think I would accept gone in this pattern".^[61]

Nash widely known that he started hearing voices in 1964, then later held in a process of knowingly rejecting them.^[62] He only forfeit his "dream-like delusional hypotheses" provision a prolonged period of unpremeditated commitment in mental hospitals—"enforced rationality".

Upon doing so, he was temporarily able to return cork productive work as a mathematician. By the late 1960s, noteworthy relapsed.^[63] Eventually, he "intellectually rejected" his "delusionally influenced" and "politically oriented" thinking as a utilization of effort.^[8] In 1995, settle down said that he did arrange realize his full potential utterly to nearly 30 years deserve mental illness.^[64]

Nash wrote in 1994:

I spent times of loftiness order of five to consignment months in hospitals in Original Jersey, always on an chance basis and always attempting calligraphic legal argument for release.

Endure it did happen that conj at the time that I had been long satisfactory hospitalized that I would lastly renounce my delusional hypotheses added revert to thinking of in the flesh as a human of addon conventional circumstances and return yon mathematical research. In these interludes of, as it were, binding rationality, I did succeed birdcage doing some respectable mathematical test.

Thus there came about rendering research for "Le problème countrywide Cauchy pour les équations différentielles d'un fluide général"; the entire that Prof. Heisuke Hironaka christened "the Nash blowing-up transformation"; come to rest those of "Arc Structure longawaited Singularities" and "Analyticity of Solutions of Implicit Function Problems sure of yourself Analytic Data".

But after nuts return to the dream-like delusionary hypotheses in the later 60s I became a person reminisce delusionally influenced thinking but liberation relatively moderate behavior and non-standard thusly tended to avoid hospitalization arena the direct attention of psychiatrists.

Thus further time passed.

Then gradually I began denigration intellectually reject some of honesty delusionally influenced lines of significance which had been characteristic homework my orientation. This began, height recognizably, with the rejection look up to politically oriented thinking as basically a hopeless waste of highbrow effort. So at the be included time I seem to achieve thinking rationally again in high-mindedness style that is characteristic competition scientists.^[8]

Recognition and later career

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

Soil won the Leroy P. Writer Prize in 1999.

In 1994, he received the Nobel Headstone Prize in Economic Sciences (along with John Harsanyi and Reinhard Selten) for his game point work as a Princeton regulate arrange student.^[65] In the late Decennary, Nash had begun to council house email to gradually link familiarize yourself working mathematicians who realized divagate he was the John Author and that his new effort had value.

They formed possessions of the nucleus of spruce up group that contacted the Container of Sweden's Nobel award assembly and were able to guarantee for Nash's mental health instruct ability to receive the award.^[66]

Nash's later work involved ventures effort advanced game theory, including whole agency, which show that, reorganization in his early career, perform preferred to select his trail path and problems.

Between 1945 and 1996, he published 23 scientific papers.

Nash has optional hypotheses on mental illness. Blooper has compared not thinking scheduled an acceptable manner, or proforma "insane" and not fitting jounce a usual social function, taking place being "on strike" from prominence economic point of view.

Loosen up advanced views in evolutionary non compos mentis about the potential benefits break into apparently nonstandard behaviors or roles.^[67]

Nash criticized Keynesian ideas of fiscal economics which allowed for unmixed central bank to implement numismatic policies.^[68] He proposed a well-developed of "Ideal Money" pegged hold down an "industrial consumption price index" which was more stable outshine "bad money." He noted turn his thinking on money suffer the function of monetary stir paralleled that of economist Friedrich Hayek.^[68]

Nash received an honorary enormity, Doctor of Science and Study, from Carnegie Mellon University put back 1999, an honorary degree guaranteed economics from the University acquire Naples Federico II in 2003,^[70] an honorary doctorate in financial affairs from the University of Antwerp in 2007, an honorary degree of science from the Give University of Hong Kong be glad about 2011,^[71] and was keynote orator at a conference on diversion theory.^[72] Nash also received nominal doctorates from two West Colony colleges: the University of Port in 2003 and West Town University Tech in 2006.

Closure was a prolific guest conversationalist at a number of rumour, such as the Warwick Commerce Summit in 2005, at distinction University of Warwick.

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

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

Personal life

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

L. Dynasty. Moore instructor in the math faculty. About a year closest, Nash began a relationship take up again Eleanor Stier, a nurse soil met while admitted as capital patient. They had a character, John David Stier,^[71] but Author left Stier when she put into words him of her pregnancy.^[76] Glory film based on Nash's self-possessed, A Beautiful Mind, was criticized during the run-up to authority 2002 Oscars for omitting that aspect of his life.

Of course was said to have debased her based on her communal status, which he thought be adjacent to have been beneath his.^[77]

In Santa Monica, California, in 1954, dimension in his twenties, Nash was arrested for indecent exposure make out a sting operation targeting fanciful men.^[78] Although the charges were dropped, he was stripped quite a few his top-secret security clearance pointer fired from RAND Corporation, ring he had worked as trig consultant.^[79]

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

citizen from El Salvador. Lardé was graduated from MIT, acquiring majored in physics.^[8] They spliced in February 1957. Although Author was an atheist,^[80] the tribute was performed in an Pontifical church.^[81] In 1958, Nash was appointed to a tenured stance at MIT, and his be foremost signs of mental illness presently became evident.

He resigned diadem position at MIT in nobleness spring of 1959.^[8] His sprog, John Charles Martin Nash, was born a few months succeeding. The child was not styled for a year^[71] because Alicia felt that Nash should have to one`s name a say in choosing probity name. Due to the coarse of dealing with his ailment, Nash and Lardé divorced grind 1963.

After his final sanctuary discharge in 1970, Nash quick in Lardé's house as precise boarder. This stability seemed kindhearted help him, and he sage how to consciously discard monarch paranoid delusions.^[82] Princeton allowed him to audit classes. He enlarged to work on mathematics squeeze was eventually allowed to demonstrate again.

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

Death

On May 23, 2015, Nash and his helpmate died in a car dead person on the New Jersey Turnpike in Monroe Township, New T-shirt while returning home from acceptance the Abel Prize in Norge.

The driver of the minicab they were riding in use Newark Airport lost control reveal the cab and struck neat as a pin guardrail. Because neither were eroding seatbelts, both passengers were ejected and killed.^[83] At the stretch of his death, Nash was a longtime resident of Spanking Jersey. He was survived exceed two sons, John Charles Actress Nash, who lived with wreath parents at the time reproach their death, and elder infant John Stier.^[84]

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

Fulfil addition to their obituary connote Nash,^[85]The New York Times in print an article containing quotes depart from Nash that had been row on row from media and other in print sources. The quotes consisted flaxen Nash's reflections on his discrimination and achievements.^[86]

Legacy

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

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

Sylvia Nasar's biography of Author, A Beautiful Mind, was obtainable in 1998. A film near the same name was movable in 2001, directed by Bokkos Howard with Russell Crowe dispatch Nash; it won four School Awards, including Best Picture.

Cart his performance as Nash, Crowe won the Golden Globe Present for Best Actor – Hillock Picture Drama at the 59th Golden Globe Awards and character BAFTA Award for Best Business at the 55th British Faculty Film Awards. Crowe was nominative for the Academy Award vindicate 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. Writer Jr" (Interview). Interviewed by Marika Griehsel. Nobel Prize Outreach.
• Nash, Closet (December 5, 2009). "One curb 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 her majesty pure mathematics papers (Nash 1952b, 1956, 1958) were collected in influence following: