John Forbes Nash Jr. was born June 13, 1928 in Bluefield, West Virginia. Mr. Nash Jr. is an American mathematician who won the 1994 Nobel Prize for his works in the late 1980’s on game theory. Game theory is the study of strategic decision making or more formally known as the mathematical models of conflict and cooperation between intelligent and rational decision makers. Game theory is mainly used in economics, political science, and psychology, as well as logic and biology. Mr. Nash Jr. as also contributed numerous publications involving differential geometry, and partial differential equation (PDE). Differential geometry is a mathematical discipline that uses differential calculus and integral calculus, linear algebra and multi linear algebra to study geometry problems. Partial differential equation is a differential equation that contains unknown multivariable functions and their partial derivatives. These are used to formulate problems involving functions of several variables. Mr. Nash Jr. used all of these skills and is known for developing the Nash embedding theorem.
The Nash embedding theorem stated that every Riemannian manifold ( a real smooth manifold equipped with an inner product on each tangent space that varies smoothly from point to point) can be isometrically embedded into some Euclidean space ( a three dimensional space of Euclidean geometry, distinguishes these spaces from the curved spaces of Non-Euclidean geometry). An example used on Wikipedia is the bending of a piece of paper with out stretching or tearing the paper gives it an isometric embedding of the page into Euclidean space because curves drawn on the page retain the same arclenth however the page is bent.
John Nash Jr. also made significant contributions tp parabolic partial differential equations and to singularity theory. While working on an elliptic partial differential equation in 1956, Mr. Nash Jr. suffered sever disappointment when he learned of another mathematician, Ennio de Giorgi, who had published a proof a couple of months before Nash. Both mathematicians arrived at their conclusions using two separate routes. It has been speculated that if only one of them had reached the solution he would have won the Fields Medal.
In 1978, Mr. Nash was awarded with the John von Neumann Theory Prize and was also awarded the Leroy P. Steele Prize in 1999 for his discovery of non-cooperative equilibria, called Nash equilibria. In 2011, the National Security Agency declassified letters Mr. Nash had written in the 1950’s, in which he proposed a new encryption-decryption machine. These letters show how Mr. Nash Jr. had anticipated many concepts of modern cryptography, which are based on computational hardness. Mr. Nash accomplished all of these feats while battling paranoid schizophrenia for the majority of his adult life. Mr. Nash Jr. ’s life has been the subject of the Hollywood movie A Beautiful Mind. Mr. Nash Jr. has stated that the movie incorrectly portayed that he was currently taking the apshycotic medication, the he instead gradually intellectually rejected the delusions. Mr. Nash now resides in a Township in New Jersey where his recent works involve advanced game theory, and has been a prolific guest speaker at numerous world class events, such as the Warwick Economics Summit in 2005.