A BEAUTIFUL MIND

He was one of the towering intellects of the 20^th century; as well built and handsome as the Greek god Hercules. At age 20 he went into an argument with the aged Albert Einstein about his theory of relativity at the ornate Princeton Institute of Advanced Study. He was then a graduate student at the highly select Princeton Department of Mathematics, where he completed his doctorate at the unusual age of 22. In that debate with Einstein, the old sage gave the young man the fatherly counsel to go and “read a little more physics”.

Einstein’s advice was spot-on. The young man in question was rarely ever seen with a book. He did not believe in reading, taking the line that it would distort his thinking with the wrongheaded ideas of others. His approach was to think out mathematical theorems from scratch by himself. His entire life had been a massive thought experiment. He did not believe anyone had a right to deploy a mathematical formula without working it out by himself first as to how that formula came to be. He was a purist as far as mathematical proofs were concerned.

His was the lonely path of a genius. His name came to be associated with the Nash equilibrium which he invented. It is a form of non-cooperative game by two or more players in which either side is aware of the equilibrium strategies of the other and in which neither side could exploit an advantage against the other merely by changing their own optimal strategy. He thinks that I think that he thinks that….

John Nash made highly original contributions to game theory, partial differential equations and differential geometry. His work provided insights into decision theory and on the factors that shape chance and decision making in complex organisations in everyday business, with wide applications in computational science, economics, biology and artificial intelligence, public policy, politics and even military strategy.

John Forbes Nash Jr, born June 13 1923, died in an automobile accident in Princeton, New Jersey, together with his wife on May 23 2015, age 86. Sadly, neither he nor his wife were wearing a seat belt when the accident occurred. John Nash Jr grew up in a middle class Episcopalian family in the sleepy town of Bluefield in West Virginia.

He was not born a prodigy, if by that is meant a child who shows unusual intellectual or creative impulses. His grades in elementary and junior high school were those of an indifferent plodder. It was in the latter years of high school that he began to show the signs of super-normal intelligence. He won a scholarship to the Carnegie Institute of Technology intending to major in chemical engineering. Bored with the periodic table, he switched to his first love, mathematics.

One of the great attractions of American college education is the fact that a young man or woman is never bound by their stated major at point of entry. You always have the option of switching from neuroscience to English literature or from History to Astronomy. If John Nash had been educated in England he probably would have ended up as a frustrated provincial manager in a non-descript chemical factory. Thanks to the flexible American tradition, he was able to follow his heart, leading him to the epochal discoveries that have changed the structure of human thought, games theory, economics and the decision sciences.

Following a brilliant performance at Carnegie, he was among the small highly elite crop of graduate students that were carefully selected to do graduate work at Princeton. Princeton University at that time was the centre of the universe as far as mathematical cognoscenti were concerned. The nearby Institute of Advanced Study – not legally a part of the university – was the home of Albert Einstein and an impressive galaxy of stars such as John von Neumann, Oskar Morgenstern and Robert Oppenheimer. It was a mecca for such quantum giants as Niels Bohr and universal mathematical minds such as G. H. Hardy of Cambridge University.

At the Princeton Graduate School John Nash flowered and bloomed. Although all graduate math students were self-aware of themselves as highly gifted people, everybody seemed to agree that Nash was a step above everyone. He himself was a believer in his own innate genius. He soon won a reputation of being an eccentric and loner.

John Nash was appointed to a tenured professorship at the Massachusetts Institute of Technology (MIT) at the precocious age of 24. He dazzled students and faculty alike with his brilliance, originality and eccentricity. At MIT Nash met a bright graduate student from El Salvador, Alicia Lopex-Harrison de Larde, who was to become his wife. They were blessed with a son, who took his father’s name, John.

In 1959 he was diagnosed with paranoid schizophrenia. In the summer of that same year he went to give a seminar at Columbia University in New York, where he was ostensibly intending to give final proofs for the Riemann Hypothesis. His colleagues did not understand what he was mumbling. It soon became clear that something was grossly amiss. It was an illness that started mildly enough but was later to see him off to a mental asylum.

The equally formidable school of mathematics at Chicago, unaware that he had taken ill, wrote to offer him a highly prestigious professorship. Nash replied with profuse apologies that he could not take up their offer because he had just been appointed Emperor of Antarctica! He subsequently fled to Europe, ending up in a Paris that was going through the student upheavals of 1968. He unsuccessfully applied to become a citizen of the small Duchy of Luxembourg for reasons that we would probably never know.

For many academics and specialists in games theory, the name of John Nash towered so mightily across the firmament that they assumed he was an old man who died a long time ago. Few knew that he lived in the shadowlands of a mental asylum. He later made a remarkable recovery to the extent that he could do some research and even go on the lecture circuit. He was later to declare: “My quest has taken me through the physical, the metaphysical, the delusional -- and back”.

 In 1994 he shared the Nobel Prize in Economic Sciences with two other game theorists John Harsanyi and Reinhard Selten.

I have read the breath-taking biography written by Sylvia Nasar, A Beautiful Mind (Faber & Faber 1998). We all rushed to watch the film which was released by Hollywood bearing the same name. John Nash was a man who was endowed by the Almighty with an astonishingly beautiful mind. But, he was, sadly, a tortured soul. The demons that took possession of this great mind led him to the dungeons of unbelief where he imagined that he could live this life while totally denying his Creator.

There is nothing as frightening and as lonely as a genius who has to live with unbelief. It was a path that led the Japanese mathematical genius Yutaka Taniyama to suicide at the tender age of 31 in November 1958. The French prodigy Blaise Pascal gave his heart completely to the Almighty Creator and lived out his days with wisdom and grace.

John Nash once remarked: “I've always believed in numbers and the equations and logics that lead to reason. But after a lifetime of such pursuits, I ask, "What truly is logic? Who decides reason?" Perhaps he found an answer before he left our planet a month ago. Towards his last days he declared, “I have made the most important discovery of…my life: It is only in the mysterious equations of love that any logic or reasons can be found”.

Great mathematicians are wired differently from the rest of us mortals. I am wise enough to know that I shall never be a number cruncher of the Order of Euler, Gauss or Srinivasa Ramanujan. But I shall always be excited by the interesting happenings in probability and games theory. I shall always love numbers as the purest forms of truth in the sense understood by the philosopher Plato. I also know – and I know that I know that I know -- that  even if it were possible to live life outside the God of Abraham, Isaac and Jacob, such a life would not be worth living.