American mathematician (1928-2015) who made fundamental contributions to game theory, differential geometry, and the study of partial differential equations, and was awarded the 1994 Nobel Memorial Prize in Economic Sciences; his struggles with paranoid schizophrenia were chronicled in the Oscar-winning film A Beautiful Mind, adapted from Sylvia Nasar's biography of the same name. Scientific journal entitled "Proceedings of the American Mathematical Society," Volume 10, Number 2, published in April 1959, 334 pages, 6 x 9.5, signed at the top of the front cover in green fountain pen with his ownership signature, "J. Nash." It is noteworthy that the signature is in green—Nash would always carry green, red, blue, purple, and black pens, and used multicolored chalk in his classes so as to differentiate various mathematical problems. Loosely laid in is a postcard addressed to Nash at MIT, inviting him to Arnold Shapiro's seminars on "Symplectic Manifolds" at Brandeis University, beginning on June 2, 1959. In very good to fine condition, with irregular toning to the covers and a fairly strong musty odor; interior pages are generally clean and fine.
This journal dates to a most significant time in John F. Nash, Jr.'s life and career. In February 1959, he was expected to present a highly anticipated proof of the Riemann hypothesis during a meeting of the American Mathematical Society at Columbia University. His condition manifested itself as the lecture descended into incomprehensibility, and it became clear to his colleagues and the audience that something was wrong. Nash was committed to the renowned McLean Hospital in April 1959—the very month of this publication—where he was diagnosed with paranoid schizophrenia. Nash remained at McLean through May, and upon discharge—still afflicted by debilitating paranoia—he resigned from his professorship at MIT. He was hospitalized for several periods throughout the ensuing decade, and was discharged for the final time in 1970. His condition slowly improved thereafter, allowing him to return to academic work.
Nash’s invitation to Shapiro's seminars on "Symplectic Manifolds" is especially relevant, as the topic pertains to one of Nash’s widely recognized areas of mathematical expertise: one part of his work proved embedding of Riemannian manifolds in Euclidean space. Of Nash’s work in this area, Mikhail Leonidovich Gromov observed: ‘What Nash discovered in the course of his constructions of isometric embeddings is far from ‘classical’—it is something that brings about a dramatic alteration of our understanding of the basic logic of analysis and differential geometry.’
In addition to these fundamental contributions to pure mathematics, Nash earned fame for his practical work in game theory. His thesis on non-cooperative games contained the definition and properties of the Nash equilibrium, which earned him the Nobel Memorial Prize in Economic Sciences in 1994.
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