When a kid received a ‘B’ grade in the arithmetic class of fourth standard, the teacher shared with his mother that the kid couldn’t do his work well, and was socially awkward and immature. His mother declared that he is unconventional and finds his own way to solve problems.
The kid grew up and in his Master’s degree program, when fellow students found him dull and reclusive, his Professor of Mathematics, Richard Duffin, declared that “This man is a genius”. After joining Princeton University, this man sought an interview with Albert Einstein to explain the errors in the general theory of relativity.
Fast forward, and this man earned his PhD in Mathematics at the age of 21, and grew up to become one of the greatest mathematicians of the 20th century, and won the Nobel Prize for Economics in 1994. His name is John Nash and his stupendous achievements were an inspiration to scores of mathematicians, economists, scientists, biologists and political scientists over the years. Some consider him as good as Adam Smith!
No doubt Professor Nash was overwhelmed by his personal struggles—as depicted in the award-winning Hollywood movie “A Beautiful Mind”; however, celebration of his exceptional ideas—which could be much more astounding, useful and contributing to science and society had he not been crippled by his mental illusionary problems—is more important.
John Nash is considered a pioneer of Game Theory. He was a mathematician despite the fact that he won the Nobel Prize in Economics. He is known for the theory of Nash Bargaining—using which both parties would benefit equally if they accept the deal—mathematically showing the result. Though, Nash Bargaining has limitations in the form of the external conditions in any competitive situation, his phenomenal contribution to Game Theory solves this problem of external conditions. He developed the Nash Equilibrium, a new concept in the Game Theory, in which out of the given choices each player has in a game, everyone is making their best choice.
Before Nash Equilibrium, the Walrasian Equilibrium was prevalent, in which everything sellable is bought, all the money involved is used in transactions and the markets are deemed efficient. However, Nash Equilibrium suggested that outcomes may not be the best always—there might be non-optimal outcomes; they may be worse for all parties involved if taken individually, which is the case in the famous Prisoners’ Dilemma. Other examples include failed markets, because no party trusts the other; and economies harming each other owing to over-competing with each other, thus actually indulging in destructive competition. Though isolated models of strategic interaction pre-existed, Professor Nash developed a system. Now even Google relies on the Nash Equilibrium to make its decisions on auctioning its advertisements.
John Nash (86)—and his wife, Alicia Nash (82)—died in a car crash on May 24, 2015 while returning after receiving the Abel Prize—the esteemed Mathematics Award—for making contributions in the theory of non-linear partial differential equations.
He liked to work on basic mathematical problems. When he was an undergraduate, he independently proved Brouwer’s fixed-point theorem—you may stir a cup of coffee for any length of time, but a small part would be unmoved resting where it was initially. Another example includes a mathematical proof in the field of abstract geometric objects such as submanifolds of Euclidean Space. In layman language, even if you make multiple folds of a piece of paper with lines drawn on it, the lines will always be of the same length.
He also won the John von Neumann Theory prize in 1978 and the Leroy P Steele prize in 1999.