Thanks to the pioneering efforts of Sylvia Nasar, Ron Howard
and Russell Crowe who epitomised the life and achievements of Nobel Memorial
Prize in Economics recipient John Forbes Nash Jr of Princeton University,
people across the World are aware of the phenomenal contributions of the
greatest Mathematician of our times. John Nash and his wife Alicia were killed
on May 23th when the cab they were riding lost control and hit the guard rail
at the New Jersey Turnpike. Sylvia Nasar, a German born American Journalist
authored a biography titled “A Beautiful Mind” of John Nash bringing into light
his personality, motivation and the stresses placed on his professional and
personal relationships due to his acute mental illness. The book was
subsequently made into a movie by Ron Howard under the same title with the lead
role played by Russell Crowe.
The Nashes were returning from Norway after receiving the
Abel Prize, instituted by the Government of Norway after the Norwegian Mathematician
Niels Henrick Abel in 2001. Described as Mathematician’s Nobel, John Nash was
awarded the prize for his work on “non linear partial differential equations
(he shared with Louis Nirenberg of New York University). John Nash made an
entry into the Annals of Global Geniuses as a recipient of the Nobel Prize in
Economics way back in 1994 for his work on Game Theory along with economists
John C Harsanyi of University of California at Berkeley and Reinhard Selten of
Friedrich-Wilhelms University of Bonn, Germany.
Game theory revolutionised the field of economics of
industrial organisation with its scope of applications. Just as the
demand-supply theory of yester years without which economics was considered
incomplete, game theory has taken the world astride with its implications in
theory of monetary policy and international trade. No student of economics can
aim to graduate without learning the rudimentary details of the Game theory.
Until the emergence of game theory economists assumed that firms could ignore
the effects of their behaviour on the actions of others. It might be true when
the markets are perfectly competitive and when monopolists hold the sway. But
this assumption might be wrong when few firms dominate the industry. A price
roll back or building of a new plant by a firm can affect how rivals behave.
Besides the industrial policy it has implications in international trade, where
some countries may impose trade sanctions on others in an attempt to prise open
protected markets. Similarly even a football coach plans his attacks taking
into account the response of the defenders. Game theory is nowadays very
popular among the political scientists, evolutionary biology and government
regulators who use it as an intellectual tool to organise thoughts
systematically, apply them in consistent way by ruling out errors.
Game theory is the branch of Mathematics fathered by John Von
Neumann in 1944 and honed by economist Oskar Morgenstern who initially
concentrated on “Zero-Sum” games where one player’s gain is another’s loss. But
real life interactions are more complicated. Nash lifted these constraints and
unleashed the game theory potential. In early 1950 he developed compelling
equations contained in his 27-page doctoral thesis, he wrote when he was 21 provided an analysis of how each player can
maximise his benefits assuming that players would act to maximize their
self-interests. A Nash Equilibrium occurs when no player wants to change their
strategy even after having full knowledge of strategies of other players. In
spite of the insights provided by the game theory, economists of wary of it
partly because it is full of tricky mathematics. Game theory helps in
understanding the intricate underlying strategic interdependencies and
producing ever more refined concepts of equilibrium but less adept at giving
advices to governments and firms.
While elucidating the life and accomplishments of John Nash,
Mathematician Sylvian Chappell of New York University enunciated that every
generation offers a small group of geniuses who commit themselves to pushing
the boundaries of what is illuminated by knowledge into the darkness of what is
yet-to-be-known. There are three types of people working on the boundaries. One
is the scientist who mines the edges finding nuggets, polishing them into
proofs with little care towards their application and hands them over to second
group of innovators who finds ingenious ways to use them. The third group are
described as “paratroopers”, who descend behind the boundaries in the darkness
and fight their way back into the light and then share the learning. Nash is
one such courageous geniuses “fearless and willing to risk everything to hurl
himself into the unknown in search of elegant new discoveries”.
Nash is rare combination of genius and hard work. Besides his
phenomenal work in understanding the game theory his equations developed in pure
maths are indispensable to analyse the abstract geometric objects such as “sub
manifolds of Euclidean Space”. Engineers can’t imagine to work without these
equations which help in understanding how fluids flow, chemical react and
gravity pulls. But as his career continued to flourish, he was bogged down for
his erratic behaviour following his relationship with several men. As a result
the illustrious Putnam Competition and Field’s Medal eluded him. His brilliance
soon turned into scourge as he was diagnosed with paranoid schizophrenia in
1959. By then his wife Alicia Nash married for two years and pregnant supported
him. But following a rough ride, they divorced in 1963. Even then his wife
continued to support. Post 1959 till 1970 Nash didn’t hold any post. With
growing popularity of Game theory, Nash’s work was cited more frequently than
ever. By 1990 Nobel Committee started contemplating on recognising his work.
But his illness acted as a deterrent later by the persistent persuasions of
Nobel Committee by his colleagues like Dr. Kuhn Nash was considered for the
prestigious prize. Later as the spectacular accomplishments of Nash became
public after the release of his biography “A Beautiful Mind” followed by his
biopic the mathematical genius received a new lease for life. Fondly referred
to as Phantom of Fine Hall in Princeton University, with his untimely death the
world has lost “a man with a long history of achievements and the one who waged
an incredible battle with mental illness”.
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