Portrait of René Descartes (1596-1650) by Fran’s Hals 1649. Statens Museum for Kunst, Coppenhagen
No one comes close to the ingenuity of the man who changed our fundamental understanding of nature (and ourselves) like the legendary French philosopher, scientist and mathematician Rene Descartes. He was not an inventor like Graham Bell or Galileo but he did something iconic. At a time in history when curiosity was suppressed in the name of conformity to the authority of religion and prevailing philosophy, he was the first among (the other was Francis Bacon) to assert that: “There is need of a method for finding out the truth.” As one of the history’s most intriguing minds, Descartes laid the foundation to reason and critical thinking.
There is need of a method for finding out the truth – René Descartes
What happens when a random flash of insight is coupled with an incredible capacity to comprehend and expand upon it? Rene Descartes life is filled with such impactful epiphanies. After determining that the typical path to a standard career wasn’t for him, Rene Descartes made a huge (and uncharacteristic) leap of faith by moving to Holland to join the military. Quickly realizing that he wasn’t necessarily cut out to be a soldier, Descartes made his mark as an engineer, relying on his keen mathematical sense rather than his physicality.
Years of intense education convinced him of only one thing – he could learn more by way of his own philosophy and studying science alone, without the distraction of textbooks and the authority of teachers. He was right. One seemingly ordinary day, as Descartes lay in bed daydreaming, he idly watched a fly buzz about his room. He came to a realization at that instance – the position of the fly at any time could be represented by three numbers – providing a distance from the three walls that met in the corner. We know these today as the Cartesian co-ordinates. In school, we learned that any point on a graph is represented by two numbers, corresponding to the distance along the x axis and up the y axis.
What did this mean? It meant that any shape could be represented with just a set of numbers related to one another by mathematical equation. The discovery, once published, transformed mathematics from its roots. This discovery made geometry able to be analyzed using algebra – the consequence of which went on to inspire both the theory of relativity and quantum theory in the twentieth century.
You might also remember using the beginning of the alphabet (a, b, c) to represent known quantities, and letters at the end of the alphabet (especially x, y, z) to represent the unknown quantities. It was Descartes’ who inscribed this language into mathematics.
René Descartes, L’homme…. These drawings show the influence of Descartes’ knowledge of mathematics and geometry on his perception of how the body works.
At the age of 24, Descartes left the military in 1620 and sold his estate he’d inherited from his mother, using the proceeds to finance his continued dedication to independent studies. From 1629 to 1633, Descartes worked tirelessly on his treatise Le Monde ou Traité de la lumière, which detailed his ideas on physics. Unfortunately, in a seemingly knee-jerk reaction, Descartes stopped publication immediately upon hearing news of Galileo’s trial for heresy as he was convicted for Copernican beliefs. Luckily Descartes was later able to recycle much of his work in different projects.
René Descartes, L’homme…. “…I desire you to consider, I say, that these functions imitate those of a real man as perfectly as possible and that they follow naturally in this machine entirely from the disposition of the organs-no more nor less than do the movements of a clock or other automaton, from the arrangement of its counterweights and wheels.”
René Descartes, de Homine figuris. In this work Descartes posited that much human behavior can be explained by mechanical responses rather than the actions of the soul. Through a better knowledge of the mechanics of the body, he hoped to cure and prevent disease, and even to slow aging.
His first publication after retracting his original treatise was The Method, published in 1637, which covered meteorology, optics and geometry. Perhaps most profound about this particular work was that it was one of the first essays that attempted to explain meteorology with science and not with the tales of higher beings. While a man of God, Descartes showed us that life and the world around us can be understood through science – all the Earth’s inhabitants obeying laws of which can be determined through experimentation and keen observation. These observations, along with the thoughts and studies of Francis Bacon, laid the groundwork for the scientific method we know today.
According to René Descartes (1596-1650), the universe operated as a continuously running machine which God had set in motion. Descartes argued that the universe was composed of a “subtle matter” he named “plenum,” which swirled in vortices like whirlpools and actually moved the planets by contact. Here, these vortices carry the planets around the Sun. The vortex theory did not require a gravitational force, so when Isaac Newton proposed a universal force of gravitation in 1687, many preferred Descartes’ explanation, because Newton’s force was not a mechanical force. However, Newton’s gravitational theory worked so well in explaining such matters as the tides, the shape of the earth, and the variation in pendulum clocks with changes in latitude, that cosmic vortices were in general dissipation by 1750, and Descartes’ swirling matter swirled itself into total and complete invisibility by the end of the century.
The Discourse on the Method (French: Discours de la méthode) is a philosophical and autobiographical treatise published by René Descartes in 1637. Its full name is Discourse on the Method of Rightly Conducting One’s Reason and of Seeking Truth in the Sciences. The Discourse on The Method is best known as the source of the famous quotation “Je pense, donc je suis” (“I think, therefore I am”), which occurs in Part IV of the work. (The similar statement in Latin, Cogito ergo sum, is found in Part I, §7 ofPrinciples of Philosophy.)
Steven Pressfield offers the most practical and remarkable advice to writers, young and old, in his Nobody Wants to Read Your Sh*t – guidance that applies to any creative endeavor, really:
Sometimes young writers acquire the idea from their school that the world is waiting to hear what they’ve written. They get this idea because their teachers had to read their essays or term papers or dissertations.
In the real world, no one is waiting to read what you’ve written.
Slightly unseen, they hate what you’ve written. Why? Because they might have to actually read it.
According to Pressfield, adopting this approach actually changes your mindset to produce better work. Antonio Damasio wrote in The Feeling of What Happens, “Sometimes we use our minds not to discover facts, but to hide them.” In a bold yet subtle way, Pressfield asserts:
It isn’t people are mean or cruel. They’re just busy. Nobody wants to read your shit.
What’s the answer?
Streamline your message. Focus it, and pare it down to its simplest, clearest, and easy to understand form.
Make its expression fun. Or sexy or interesting or scary or informative. Make it so interesting that a person would have to be crazy NOT to read it.
Apply that to all forms of writing or art or commerce.
The book becomes at once a tool of self-discovery as much as an instructional guide to better writing. He explains:
When you understand that nobody wants to read your shit, your mind becomes powerfully concentrated. You begin to understand that writing/reading is, above all, a transaction. The reader donates his time and attention, which are supremely valuable commodities. And in return you the writer must return something worthy of his gift to you.
The book is far from the typical ego-stroking run-of-the-mill how-to’s and serves as an essential companion for anyone laboring in the art of making something new.
When you understand that nobody wants to read your shit, you develop empathy.
With this, Pressfield brings life to the timeless wisdom of what makes an artist’s skill blossom and become cherished in the minds of audience.
You acquire the skill that is indispensable to all artists and entrepreneurs – the ability to switch back and forth in your imagination from your own point of view as a writer/painter/seller to the point of view of your reader/gallery-goer/customer. You learn to ask questions with every sentence and every phrase: Is this interesting? Is it fun or challenging or inventive? Am I giving the reader enough? Is she bored? She is following where I want to lead her?
Above all, this becomes not only a tool of accountability but a guide post to keep the artist or entrepreneur moving forward in the face of self-doubt and uncertainty.
Karma is a Sanskrit term, commonly translated to mean deed. What it really embodies is three processes – thinking, speaking and action, essentially encompassing nearly all human activity.
Dharma Comic by Leah Pearlman
The foundation of the belief in karma stems from one premise: As long as we look upon our individual lives as isolated, finite events beginning with the birth of the body and ending with its death, we will not find the explanation of our circumstances. Why is there injustice? Why is there misery? Suffering? However, when we connect our present lives with our past and our future, viewing our life as a looped continuum of eternal existence, we might find meaning in why all things happen in our life. Our present is the result of our past, and our future will be the result of our present.
This belief asserts that what we experience in this finite lifetime is only a blip in the continuum of the entire spectrum of our total existence. A simplified analogy was offered: Suppose our life began each morning and lasted for 24 hours. If we disconnect the life of today from that of yesterday and that of tomorrow and judge each day by its results, we would find poor compensation for our daily endeavors. Furthermore, it would seem terribly unjust to have our life falling on a gloomy, unpleasant day filled with tragedy, while another life fell on the following bright and shiny day filled with luck and bliss. We would not be able to justify the fragments of life.
On a more contemporary commentary in the same lines: “How we spend our days is, of course, how we spend our lives,” Annie Dillard wrote in her timeless The Writing Life.
Swami Vivekananda in Belgaum, India, 1892
Karma could also be viewed as a form of glorified rationalization amounting to, “You suffer because …” Obviously, this conviction cannot be scientifically proven – it is not a testable hypothesis. However, if we make a leap of faith in this assumption without restrictions, a great deal of existential confusion seems to suddenly make sense. Reckoning from this standpoint, we may find satisfactory reasons to some of the perplexing problems and complicated affairs of human life. We come to realize how our choices and actions shape who we become.
Every thought that we think, every deed that we do, after a certain time becomes fine, goes into seed form, so to speak, and lives in the fine body in a potential form and after a time it emerges again and bears its results. These results condition the life of man. Thus he molds his own life. Man is not bound by any other except that which he makes for himself. Our thoughts, our words, and deeds are the threads of the net which we throw around ourselves, for good or for evil. Once we set in motion a certain power, we have to take the full consequence of it. This is the law of karma.
The idea of karma is in accordance with the popular saying, “Heaven helps those who help themselves.” A person, therefore, is not to be judged by the sufferings he or she undergoes, but by his/her capacity to rise above – ultimately our attitude in the face of adversity.
“Karmic” is a painting by Horacio Cardozo. Its main concept depicts our past and present lives as a continuum of cosmic energy represented by the interconnected trees. They keep bound by a thin golden string that runs across ten pulleys hanging on both trees, which represent the tension of causes and effects throughout our lives.
To take this concept up a notch, karma comes down to one thing: Essentially the law of cause and effect pervades everything in the manifested world. Furthermore, understanding cause and effect entails recognizing the very philosophy of our lives, our belief in a super-natural being governing the fate of our lives and the role of freewill.
For those of us who are believers, it is the tug of war between the sovereignty of God and man’s freedom of action that result in our mundane conflict. If we relegate complete dominance of our lives to a supreme being, it makes God responsible for man’s vices and suffering – the all-powerful dictator. Such that, all that happens to us is predetermined by God; concluding that only some receive grace and others are doomed to live in everlasting misery.
The only way that sovereignty of a super-natural being and freedom of man come together is through a more unified understanding of our relationship with this Supreme Being – a non-duality approach. Non-duality means ‘not two’ and points to an understanding of the essential oneness, completeness and unity of life, a wholeness which exists here and now, void of any apparent separation.
Buddhist philosopher D. T. Suzuki says,
Where dualism holds good, this karma does not apply.
“A ZEN LIFE – D.T. Suzuki” is a documentary about Daisetz Teitaro Suzuki (1870-1966), credited with introducing Zen Buddhism to the West.
It is thus only through a non-dualistic view of the world that the idea of karma makes sense. As Madam Blavatsky, co-founder of the Theosophical Society in 1875 observed,
Karma is that unseen and unknown law which adjusts wisely, intelligently, and equitably each effect to its cause, tracing the latter back to its producer.
Albert Einstein, his wife Elsa and his stepdaughter Margot with Rabindranath Tagore, Pratima Devi, Tagore‘s daughter-in-law, and Professor and Mrs. Mahalanobis in Berlin, 1930
When the two scintillating geniuses of the East and West – Rabindranath Tagore and Albert Einstein – met in 1930, Dimitri Marianoff, a relative of Einstein, described the conversation “as though two planets were engaged in a chat.”
Rabindranath Tagore was a genius polymath of India. A prolific poet, play writer, and songwriter, he wrote 2,000 in his lifetime, one of which was adopted as the national anthem of India. He was also famously given a Nobel Prize for literature in 1913 for his collection of poems Gitanjali. In 1915, Tagore was knighted but he returned it after the Amritsar massacre in 1919.
Albert Einstein is the better known of the two to the world, who received Nobel Prize in 1921 not for his famous Theory of Relativity but for the lesser known theories on photoelectric effect. Einstein searched for universal truths that could be expressed through mathematical equations – an objective verification was required for him to ascertain truth. To him, every theory had to have mathematical simplicity, structure, and order. He not only wanted to understand the “mind of God” but to deduce it into a unified theory.
Rabindranath Tagore (7 May 1861 – 7 August 1941)
Tagore visited Einstein’s house in Caputh, near Berlin, on July 14, 1930. The discussion between the two great men was recorded and subsequently published in a 1931 issue of Modern Review. Einstein with his signature frizzy hair was 50; Tagore with long, flowing beard was 70.
Einstein 1921 by F Schmutzer
Interestingly, when they met, Tagore did not know German and Einstein’s English was too weak to converse. Hence they had to use interpreters for conversation.
Neither Tagore nor Einstein was happy with the recorded conversation, as the translations lost their charm. So, they themselves corrected their parts before making the conversation public.
When Albert Einstein and Rabindranath Tagore met in 1930
In the afternoon of July 14, 1930, Tagore went to meet Einstein at his house at Kaputh, near Postdam, Germany
Here is an excerpt of their conversation that started with the most fundamental existential question, “Nature of Reality,” the interplay of chance and predetermination. They went on to discuss the ordinary everyday events relating to family, the youth movement of Germany, and finally ended with discussing classical music.
EINSTEIN: Do you believe in the Divine as isolated from the world?
TAGORE: Not isolated. The infinite personality of Man comprehends the Universe. There cannot be anything that cannot be subsumed by the human personality, and this proves that the Truth of the Universe is human Truth.
I have taken a scientific fact to explain this — Matter is composed of protons and electrons, with gaps between them; but matter may seem to be solid. Similarly humanity is composed of individuals, yet they have their interconnection of human relationship, which gives living unity to man’s world. The entire universe is linked up with us in a similar manner, it is a human universe. I have pursued this thought through art, literature and the religious consciousness of man.
EINSTEIN: There are two different conceptions about the nature of the universe: (1) The world as a unity dependent on humanity. (2) The world as a reality independent of the human factor.
TAGORE: When our universe is in harmony with Man, the eternal, we know it as Truth, we feel it as beauty.
EINSTEIN: This is the purely human conception of the universe.
TAGORE: There can be no other conception. This world is a human world — the scientific view of it is also that of the scientific man. There is some standard of reason and enjoyment which gives it Truth, the standard of the Eternal Man whose experiences are through our experiences.
EINSTEIN: This is a realization of the human entity.
TAGORE: Yes, one eternal entity. We have to realize it through our emotions and activities. We realized the Supreme Man who has no individual limitations through our limitations. Science is concerned with that which is not confined to individuals; it is the impersonal human world of Truths. Religion realizes these Truths and links them up with our deeper needs; our individual consciousness of Truth gains universal significance. Religion applies values to Truth, and we know this Truth as good through our own harmony with it.
EINSTEIN: Truth, then, or Beauty is not independent of Man?
EINSTEIN: If there would be no human beings any more, the Apollo of Belvedere would no longer be beautiful.
EINSTEIN: I agree with regard to this conception of Beauty, but not with regard to Truth.
TAGORE: Why not? Truth is realized through man.
EINSTEIN: I cannot prove that my conception is right, but that is my religion.
TAGORE: Beauty is in the ideal of perfect harmony which is in the Universal Being; Truth the perfect comprehension of the Universal Mind. We individuals approach it through our own mistakes and blunders, through our accumulated experiences, through our illumined consciousness — how, otherwise, can we know Truth?
EINSTEIN: I cannot prove scientifically that Truth must be conceived as a Truth that is valid independent of humanity; but I believe it firmly. I believe, for instance, that the Pythagorean theorem in geometry states something that is approximately true, independent of the existence of man. Anyway, if there is a reality independent of man, there is also a Truth relative to this reality; and in the same way the negation of the first engenders a negation of the existence of the latter.
TAGORE: Truth, which is one with the Universal Being, must essentially be human, otherwise whatever we individuals realize as true can never be called truth – at least the Truth which is described as scientific and which only can be reached through the process of logic, in other words, by an organ of thoughts which is human. According to Indian Philosophy there is Brahman, the absolute Truth, which cannot be conceived by the isolation of the individual mind or described by words but can only be realized by completely merging the individual in its infinity. But such a Truth cannot belong to Science. The nature of Truth which we are discussing is an appearance – that is to say, what appears to be true to the human mind and therefore is human, and may be called maya or illusion.
EINSTEIN: So according to your conception, which may be the Indian conception, it is not the illusion of the individual, but of humanity as a whole.
TAGORE: The species also belongs to a unity, to humanity. Therefore the entire human mind realizes Truth; the Indian or the European mind meet in a common realization.
EINSTEIN: The word species is used in German for all human beings, as a matter of fact, even the apes and the frogs would belong to it.
TAGORE: In science we go through the discipline of eliminating the personal limitations of our individual minds and thus reach that comprehension of Truth which is in the mind of the Universal Man.
EINSTEIN: The problem begins whether Truth is independent of our consciousness.
TAGORE: What we call truth lies in the rational harmony between the subjective and objective aspects of reality, both of which belong to the super-personal man.
EINSTEIN: Even in our everyday life we feel compelled to ascribe a reality independent of man to the objects we use. We do this to connect the experiences of our senses in a reasonable way. For instance, if nobody is in this house, yet that table remains where it is.
TAGORE: Yes, it remains outside the individual mind, but not the universal mind. The table which I perceive is perceptible by the same kind of consciousness which I possess.
EINSTEIN: If nobody would be in the house the table would exist all the same — but this is already illegitimate from your point of view — because we cannot explain what it means that the table is there, independently of us.
Our natural point of view in regard to the existence of truth apart from humanity cannot be explained or proved, but it is a belief which nobody can lack — no primitive beings even. We attribute to Truth a super-human objectivity; it is indispensable for us, this reality which is independent of our existence and our experience and our mind — though we cannot say what it means.
TAGORE: Science has proved that the table as a solid object is an appearance and therefore that which the human mind perceives as a table would not exist if that mind were naught. At the same time it must be admitted that the fact, that the ultimate physical reality is nothing but a multitude of separate revolving centres of electric force, also belongs to the human mind.
In the apprehension of Truth there is an eternal conflict between the universal human mind and the same mind confined in the individual. The perpetual process of reconciliation is being carried on in our science, philosophy, in our ethics. In any case, if there be any Truth absolutely unrelated to humanity then for us it is absolutely non-existing.
It is not difficult to imagine a mind to which the sequence of things happens not in space but only in time like the sequence of notes in music. For such a mind such conception of reality is akin to the musical reality in which Pythagorean geometry can have no meaning. There is the reality of paper, infinitely different from the reality of literature. For the kind of mind possessed by the moth which eats that paper literature is absolutely non-existent, yet for Man’s mind literature has a greater value of Truth than the paper itself. In a similar manner if there be some Truth which has no sensuous or rational relation to the human mind, it will ever remain as nothing so long as we remain human beings.
EINSTEIN: Then I am more religious than you are!
TAGORE: My religion is in the reconciliation of the Super-personal Man, the universal human spirit, in my own individual being.
German philosopher Arthur Schopenhauer observed in his 1818 masterwork The World as Will and Representation: “Talent is like the marksman who hits a target which others cannot reach; genius is like the marksman who hits a target … which others cannot even see.”
Ramanujan commemorative postage stamp issued in India in 1962. This was his passport photo taken in 1919 on his way back to India. “He looks rather ill,” G. H. Hardy wrote when he first saw the photo in 1937, “but he looks all over the genius he was” – Master and Fellows of Trinity College, Cambridge
These are the individuals who dedicate their lives to passionate journeys doing whatever it is they love to do – treating the universe as an interesting playing field. Nothing more, nothing less. One such individual is little-known, self-taught mathematician Srinivasa Ramanujan, who in his short lifespan of merely 32 years, made some revolutionary and surprising discoveries.
One day, the math teacher pointed out that any number divided by itself was one: Divide three fruits among three people, he was saying, each would get one…
So Ramanujan piped up: But is zero divided by zero also one? If no fruits are divided among no one, will each still get one?
This was Ramanujan’s question to his teacher when he was merely a the third grader. Robert Kanigel’s 1991 biography of Ramanujan, The Man Who Knew Infinity, from which the movie was later adapted, provides the most authentic account of Ramanujan’s early life.
Ramanujan performed his calculations as authentic as it gets — with chalk on slate, scrap paper, scribble on sand, whatever he could get his hands, or mind, on. His childhood best friend proclaimed him a genius the first time he walked in Ramanujan’s room, seeing all of the notes upon the walls. Unable to afford notebooks, he took to a large slate, using his own elbow as an eraser. “My elbow is making a genius of me,” Ramanujan would joke.
The Man Who Knew Infinity: A Life of the Genius Ramanujan. By Robert Kanigel
Being a genius of a certain order also comes with some penalties. Ramanujan’s unique obsession with mathematics made it especially difficult to fit in.
As Schopenhauer observed that individuals of extraordinary genius often fall victim to quite lonely course of life:
The common mortal, that manufacture of Nature which she produces by the thousand every day, is, as we have said, not capable, at least not continuously so, of observation that in every sense is wholly disinterested, as sensuous contemplation, strictly so called, is. He can turn his attention to things only so far as they have some relation to his will, however indirect it may be…
The man of genius, on the other hand, whose excessive power of knowledge frees it at times from the service of will, dwells on the consideration of life itself, strives to comprehend the Idea of each thing, not its relations to other things; and in doing this he often forgets to consider his own path in life, and therefore for the most part pursues it awkwardly enough.
By the time Ramanujan got to college, all he wanted to do was mathematics, failing all of his other classes. At one point, so frustrated with the seemingly arbitrary requirements of college, he ran away, causing his mother to send a missing-person letter to the newspaper:
‘A Missing Boy’, published in September, 1905 in a newspaper. It appeals for the public’s help in tracing “a Brahmin boy of the Vaishnava (Thengalai) sect, named Ramanujam, of fair complexion and aged about 18 years” who had “left his [Kumbakonam] home on some misunderstanding.”
As a college dropout from a poor family, Ramanujan’s future seemed bleak. He depended on the kindness of his friends and showcased his mathematical discovery-filled notebooks to patrons who just might support his work. When Ramanujan’s friends and acquaintances couldn’t land him a scholarship, Ramanujan started looking for jobs, working as an accounting clerk for the Port of Madras (now Chennai) in 1912.
Eventually, he wrote to mathematicians in Cambridge seeking validation of his work. Twice he wrote with no response; on the third try, he finally got an answer.
In 1913 a mathematician named G. H. Hardy in Cambridge, England received a package of papers with a cover letter that began:
I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras on a salary of only £20 per annum. I am now about 23 years of age….
and explained how he had made “startling” progress and solved the age-old problem of the distribution of prime numbers. Ramanujan concluded the letter with a heart-rending request:
Being poor, if you are convinced that there is anything of value I would like to have my theorems published…. Being inexperienced I would very highly value any advice you give me. Requesting to be excused for the trouble I give you.
Something about the 11 pages of technical formulas made Hardy take a second look, and show it to his collaborator J. E. Littlewood. Hardy wrote,
Some of the formulae defeated me completely. I have never seen anything in the least like them before. A single look at them is enough to show that they could only be written down by a mathematician of the highest class.
After a few hours, they concluded that the results “must be true because, if they were not true, no one would have had the imagination to invent them.”
Godfrey Harold “G. H.” Hardy (7 February 1877 – 1 December 1947). In an interview by Paul Erdős, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. He called their collaboration “the one romantic incident in my life.”
Hardy’s colleague, Bertrand Russell wrote that by the next day he “found Hardy and Littlewood in a state of wild excitement because they believe they have found a second Newton, a Hindu clerk in Madras making 20 pounds a year.”
In another letter to Hardy, Ramanujan confessed that he really just wanted someone to verify his results—so he’d be able to get a scholarship, since “I am already a half starving man. To preserve my brains I want food…”
Hardy wanted Ramanujan to come to England, which Ramanujan’s mother resisted as a matter of principle – high-caste Indians were not to travel to foreign lands. Luckily, she eventually agreed to let him go.
Ramanujan prepared for Europe with a new Western-inspired wardrobe, mastery of eating with knives and forks and learning how to tie a tie. He boarded a ship for England, sailing up through the Suez Canal, and arrived to London.
Although he tried his best to conform to the norms of the new society, his struggle to fit within the expectations of established academia seemed impossible. Ramanujan announced that he’d “changed [his] plan of publishing [his] results”. He said that since coming to England he had learned “their methods,” and was “trying to get new results by their methods so that I can easily publish these results without delay.”
The stark contrast between Hardy and Ramanujan is akin to that of many main-stream academicians and the true innovators who developed their own paths.
Hardy was no ordinary mathematician. He was credited with reforming British mathematics by bringing rigor into it. A man with natural affinity for numbers, Hardy’s papers were good examples of state-of-the-art mathematical craftsmanship. By 1910, Hardy had fell into a routine of normalcy as a Cambridge professor. He lived within the typical bounds of society while spending time practicing his mathematics.
Whereas, Ramanujan was a self-taught, poor Brahmin Indian with no formal education, who had a belief that fell far outside the bounds of organized study. He once told Hardy that, “A formula had no meaning unless it expressed a thought of God.”
While mathematicians in general were trained to systematically prove each of their theorems with extensive methodology, Ramanujan was a man of intuition. Once, Kaniglel writes, Ramanujan was asked about a new equation he had derived. His reply was that it was a Hindu goddess who had appeared in his dream and helped him solve that problem.
Here was a man who could work out modular equations, and theorems of complex multiplication, to orders unheard of, whose mastery of continued fractions was, on the formal side at any rate, beyond that of any mathematician in the world … It was impossible to ask such a man to submit to systematic instruction.
so I had to try to teach him, and in a measure I succeeded, though I obviously learnt from him much more than he learnt from me.
When Hardy saw Ramanujan’s “fast and loose” approach to the infinite limits and the like, his reaction was a need to “tame” Ramanujan and educate him in the structured European methodology.
Rigor in analysis defined Hardy’s work, while Ramanujan’s results were (as Hardy put it) “arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account.”
Pages from one of Ramanujan’s last letters.
As for his place in the world of Mathematics, Professor Bruce C. Berndt of the University of Illinois wrote:
Paul Erdos has passed on to us Hardy’s personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100, Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100.
Ramanujan couldn’t easily fit in the constraints of societal or academic expectations because his ideas were much bigger than the limitations imposed by convention.
Ramanujan (centre) with other graduates at Trinity College in March 1916.
Hardy-Ramanujan’s collaboration in England was mathematically productive. Cambridge granted Ramanujan a Bachelor of Science degree “by research” in 1916, and he was elected a Fellow of the Royal Society (the first Indian to be so honored) in 1918. His accomplishments were followed quickly by a stark decline in his health as a result of the English winter and the difficulties of adhering to strict dietary rules of his caste in the face of wartime shortages. In 1917 he was hospitalized and nearly died. By late 1918 his health had improved; he returned to India in 1919. But his health failed again, and he died the following year year.
Letter from Ramanujan to friend. Courtesy: Trinity College Cambridge.
In reply to the above letter, his friend wrote:
My dear Ramanujan,
I was exceedingly grieved to have your painful letter. Sorry to hear that the new cook is a failure as far as you are concerned. Now then, I will have to be a bit harsh with you. I am impressed with you being so particular about your palate. But you’ll have to choose between controlling your palate and killing yourself.
Surely some of the greatest minds like Isaac Newton and Albert Einstein lived through their 70’s and 80’s, but their best works were actually produced in their 20’s. These were the individuals who didn’t count their life by the number of years lived, but the contribution they made to the advancement of human progress.
DOCUMENTARY ON RAMANUJAN – Mathematical Genius
A formula had no meaning unless it expressed a thought of God