CLARKE R. REECE

MATHMATICS

PROF. KEVIN DENT

08/03/2012

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. has 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...

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