Troubled Genius

“No great mind has ever existed without a touch of madness.”
Aristotle

I love reading memoirs because they take me inside the life of someone in a different place and age. Last year I read “The man who knew infinity” by Robert Kanigel. It’s a biography of Srinivas Ramanujan – the mystical mathematical genius. Then earlier this year I read “A beautiful mind” by Sylvia Nasser – a biography of mathematician and Nobel laureate John Nash.

There have been famous movies made on both these books and though they only scratch at the surface, they did a decent job at popularizing two geniuses whose work is mostly abstract and difficult to comprehend for laymen.

Ramanujan’s story begins in a remote South Indian village where despite poverty he discovers surprising joy in mathematics. He scribbles equations in a slate suspended in some kind of a meditation. He has trouble with school authorities where there is no one to understand his precocious talents.

Often he skips the details and jumps straight to the answer and when asked how he got it, he is unable to write down the steps for the “proof”. He tries to explain that his answer is correct, he just knows it, in fact “it came to him”. South India of the mid 1900s was no place for such an eccentric genius.

The only person who believes in him is his doting mother. Ramanujan is discouraged, mocked and often ridiculed by the establishment because they have never seen someone like him. They are unable to comprehend his incredible talents. Eventually he sends his hastily written theorems to GH Hardy the famed English mathematician.

At first Hardy just throws the envelope aside not taking it seriously. The odds seem staggering – an unknown man from India with no degrees or credentials to his name writing to the pre-eminent mathematician of the age at Cambridge and claiming that these are all theorems he has discovered.

When Hardy finally starts pouring over Ramanujan’s work, he is simply astounded. Ramanujan in his characteristic style has offered no rigorous proofs but the symmetry and beauty of the work is unmistakable. Hardy later said he knew it was all true, the equations were of such spell binding beauty that no one could have just manufactured them. They had to be true!

Hardy begins a series of now famous correspondence with Ramanujan asking questions, looking for more material and it goes back and forth till he asks Ramanujan to join him in Cambridge. Despite the odds, Ramanujan makes the perilous journey across the seas and begins one of the most remarkable partnerships in the history of mathematics,

Hardy is vindicated as Ramanujan routinely turns in work of the highest caliber. He is even awarded a doctorate though his work surpasses all realms of degrees handed by institutions. This is when tragedy strikes, the English weather and poor diet has a terrible impact on Ramanujan’s health.

Deeply religious and having lived most of his life in tropical lands, he is unable to come to terms with the infamous English chill. The lack of vegetarian food, family and the depressing weather have a compounding effect on him. His few friends and Hardy try their best to get him treatment but nothing works.

By the time Ramanujan returns to India he is in extremely poor health and suffering from tuberculosis. Despite his rapidly falling health he continues to churn out brilliant work, scribbling equations and theorems to the end of his days. In a heartbreaking finale, Ramanujan passes away in his early thirties having accomplished what most gifted mathematicians would not even in multiple lifetimes.

Such is the legacy of his work that today there are “Ramanujan Scholars” who are still grappling with the enormous task of proving his theorems. Ramanujan’s life very much reads like a greek tragedy. Hardy had this to say in his famous ‘A mathematician’s apology’ – “I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, ‘Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.”

John Nash burst onto popular consciousness after “A beautiful mind” starring Russel Crowe was released in 2001 and received critical acclaim. Nash had been awarded the Nobel prize in 1994 for his seminal work in Game theory.

The movie was loosely based on Sylvia Nasser’s book by the same name. John grew up in West Virginia and displayed precocious mathematical ability. He had a rebellious anti establishment streak in him and was obsessed with originality.

By the time he was a student at MIT and later at Princeton, he had morphed into a kind of abrasive, arrogant personality with wild mood swings. By this time he had already established himself as a genius in the eyes of his professors and peers. Nash’s recommendation letter for Princeton simply read – “He’s a mathematical genius”.

However all wasn’t well within the confines of his turbulent mind. After he had done his now famous work on game theory which later found applications in economics and stock markets and led to the Nobel prize, he slowly receded into devastating mental illness. He was diagnosed to be suffering from Schizophrenia.

The character that viewers saw Russel Crowe playing in the movie was heavily romantized true to Hollywood conventions. The movie did succeed in showing his struggles against mental illness and then using his will to overpower them but it left so many details from his real life unexplored.

John Nash wasn’t an easy person to live with. He had an affair with a nurse named Eleanor with whom he had a love child. He was extremely mean to both of them and denied fatherhood. Later he married Alicia who was one of his students at Princeton.

Alicia stood by John even though she had divorced him briefly. However they later remarried and John after years of mental trauma was able to surmount schizophrenia. Towards his later life he reunited with his elder son and famously  became a Nobel laureate.

Compared to Ramanujan, his life came around and despite his struggles he eventually had a good life and family. As his character says in the memorable last scene in his Nobel acceptance speech – “~ I’ve made the most important discovery of my life. It’s only in the mysterious equations of love that any logical reasons can be found. I’m only here tonight because of you. You’re the only reason I am…you’re all my reasons.~”

History is replete with geniuses who had a very difficult life or for whom life was mercilessly cut short. Alan Turing probably one of the greatest minds ever and widely considered the father of modern computer science committed suicide by eating a cyanide laced apple. He was also young and in his thirties.

The unforgiving conservative world of the 1940s and 50s didn’t take kindly of his sexual deviations and he was put to trial and extremely vilified in what would be possibly considered as violation of every human right today.

I often wonder why the fate of such great geniuses who contributed so much in such short time was so brutal. They suffered so much either due to illness or by being castigated by powers that be.

But despite that, their exceptional genius glittered and mesmerized the world in the short time that they were here.

 

Knowledge

“True knowledge exists in knowing that you know nothing” – Socrates

Like most people of my generation, I grew up confusing education with the relentless march of examinations and grades. As a student I was diligent and hard working not particularly bright. I had some bad academic years in middle school but eventually performed quite well in the examinations that ‘mattered’.

By the time I made it to College, I found that I had become numb to things like exams, tutorials, grades – the stuff of academic life. I always loved learning new things but the way they were presented in textbooks and  the unwavering drone of professors made me feel completely inadequate.

Despite my good grades, I never felt I truly understood something from the basic principles. Mostly all I remembered after years of schooling and four years of engineering education were disjoint facts and big names and even those I started to forget as I began my professional life.

For some reason this always bothered me, it made me look at myself as a fake and I wanted to do something about it. One of the books I fortunately chanced upon early were the Feynman Lectures in Physics. Of course I have only read parts of it but it opened up a new way of seeing things.

For the first time I figured out what does it mean to say something is true within a framework where we have to first assume that certain fundamental truths hold good.Feynman’s engaging style and his complete abhorrence for big words reignited the joy of learning for knowledge’s sake.

One of his childhood anecdotes where his friend asks him the name of a bird and when Feynman is unable to answer, his friend haughtily says ” Your father doesn’t teach you anything!”. Feynman goes on to say that his father taught him the difference between knowing the name of something and knowing something. Its not important to know the name of the bird as long as you know what it eats, what kind of nests it builds, where does it migrate from..

I have tried to apply this principle to my own learning and found that though it is extremely time consuming and hard work but it is hugely rewarding and the kick you get in truly knowing something is unparalleled.

To cite an example of how fragile the bookish knowledge can be, I was looking over quadratic equations in my son’s high school textbook, and right there on the first page was this big, terrifying formulae to derive the 2 roots of a quadratic equation. I had never thought about where this formula comes from, though like any other student I must have solved hundreds of these quadratic equations.

So I searched online for a real math textbook and to my pleasant surprise found the famed Hall & Knight algebra series still in circulation. I had used these books during my engineering entrance days. I decided to buy a bunch of these classics – Higher Algebra, School Geometry,  SL Loney’s Coordinate Geometry and Trigonometry. The Indian editions of these timeless books are priced cheaper than a cup of Cappuccino.

And so I eagerly flipped to the chapter on quadratics and found that before that chapter there was a whole chapter dedicated to the method of solving quadratic equations by completing squares and then they just extended this method and came up with the familiar quadratic roots formula. It was not only rythmic and logical but the understanding felt deep and permanent. In fact while researching this I chanced upon another beautiful proof that an equation of nth degree will have n roots.

This is certainly not the way I had learned in school. My school textbook just magically thew up this formula followed by several types of problems. No one told me to step back and think and understand why this formula worked.

Knowledge is not grades or passing of routine examinations though those are inevitable. It is something that we owe to ourselves. Quoting Feynman again “The first principle is that you must not fool yourself and you are the easiest person to fool.”.