# John nash

Introduction

John Forbes Nash Jr. was born on June 13th of 1928. He has greatly impacted

today’s society with his works in game theory, differential geometry, and partial

differential equations. His theories are used in many aspects of our lives today

such as in economics, computing, evolutionary biology, artificial intelligence,

accounting, politics and in military theory. Within his lifetime Nash has received several

prestigious awards. In 1978 he was awarded the John Von Neumann Theory Prize. In

1994 he and his coworkers Reinhard Selton and John Harsanyi were awarded the Nobel

Memorial Prize in Economic Sciences and he was also awarded the Abel Prize in 2015

for his work on non linear partial differential equations.

John Forbes Nash Jr. was born in Bluefield, West Virginia in 1928 to his father

John Forbes Nash, an electrical engineer for the Appalachian Electric Power Company,

and his mother Margaret Virginia Martin, known as “Virginia”, who was a school

teacher. Nash has one younger sister named Martha. Nash had a very advanced,

education filled childhood learning to read and play piano before the age of three. He

attended public school and both his parents and grandparents were very influential in his

education. During high school, Nash took advanced mathematics and chemistry at a

community college and later was accepted into the chemical engineering program with a

full scholarship from the George Westinghouse Scholarship Foundation. During this

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time, Nash first studied chemical engineering, then studied chemistry and later found his

calling in the field of mathematics. After graduating in 1948 from the Carnegie Institute

of Technology he had both a bachelor’s degree and a master’s degree in mathematics. He

was then accepted to both Harvard and Princeton but decided on Princeton after the

chairman of the mathematics department, Solomon Lefschetz, offered him the John S.

Kennedy fellowship. Princeton was also located closer to his family in Bluefield which

he also preferred. Richard Duffin, Nash’s former advisor used one sentence to describe

Nash while writing his recommendation for Princeton which simply stated, “This man is

a genius.” While at Princeton Nash continued his studies of mathematics and worked on

his theory of equilibrium which later became known as the Nash equilibrium.

In 1950 Nash earned a PHD, while also producing some of his first works, which

would be the definition and the properties of the Nash equation. This is now described as

one of the most crucial concepts in non cooperative games. These publishing are

considered the biggest reason as to why Nash was awarded the Nobel Peace Prize in

Economic Sciences. Nash also did a lot of ground breaking work in algebraic geometry.

Some of his many works and early discoveries include the Nash embedding theory,

which shows that every abstract Riemannian manifold can be isometrically realized as a

submanifold of Euclidean space, and very significant findings and contributions to the

theories of nonlinear parabolic partial differential equations and to singularity theory. In

Sulvia Nasar’s biography of Nash entitled “A Beautiful Mind” (which was also later

made into a film by Director Ron Howard and released in 2001), she explains how Nash

while working on proving Hilbert’s nineteenth problem discovered that an Italian

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mathematician had proven the answer just months before. Both individuals used

different routes to find their solutions. In 1950 Nash also proposed a new encryption

machine which proved that he had anticipated may concepts of modern cryptography.

In 1951 Nash was hired at the Massachusetts Institute of Technology where his

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