The Mystery of Ramanujan's Dreams

#4 in a series on dreams

One of my favorite dreamers in history, Srinavasa Ramanujan, was born December 22, 1887, in the small, Southern city of Erode, India. His father was a petty clerk in a cloth merchant’s shop, his mother devoutly religious. From an early age, Ramanujan was drawn to mathematics. He was that kid and then some, showing such an unusual aptitude for math that in grade school his teachers turned to him to ask if what they were doing was correct. He received a scholarship, but flunked out, because by then he refused to study any subject but math. At age 16, too poor to afford paper, often hiding under a cot because his parents disapproved of his math monomania, he taught himself number theory by working through every problem in a borrowed textbook on a slate board he wiped clean with an elbow, to make it last longer. And as if that wasn’t astonishing enough, he expanded his efforts from this textbook to both rediscover entire branches of pure mathematics—otherwise unknown to him because dude had just one book—while simultaneously producing hundreds of wholly original discoveries, many of which came to him in dreams.

By 1913, at the age of 23, Ramanujan was barely scraping by as an obscure clerk when he wrote a letter to an eminent mathematician at Cambridge, G. H. Hardy, to ask for help with getting his work published. Hardy took a peek at the 120+ theorems he’d tucked inside, and, like the previous two luminaries to whom Ramanujan had sent cold letters, assumed he was nuts. But as Hardy looked more closely, he realized that portions of the work were so advanced as to exceed his ability to evaluate them. The rest is history—Hardy invited Ramanujan to Cambridge, secured a funded position for him, championed his work, and they collaborated. Later in life, a colleague asked Hardy to identify his greatest achievement, and he said without hesitation that it was discovering Ramanujan.

Though Ramanujan’s career was tragically cut short by tuberculosis at age 32, he had already produced hundreds, if not thousands of original discoveries in elliptic functions, infinite series, modular forms, hypergeometric series, and continued fractions, to name just a few, and had given birth to probabilistic number theory and mock theta functions, both entirely new branches of math. Many mathematicians following in his footsteps have devoted entire decades of their careers to proving his conjectures, and hundreds more still elude proof. A century after his death, his influence only grows, while so much about his work remains outside our understanding that the full scope of his contributions cannot yet be known.

Ramanujan’s creative process was unique among mathematicians. Even today, the intuitive methods by which he was able to arrive at deep results in mathematics remain a total mystery. “The enigma of Ramanujan’s creative process is still covered by a curtain that has barely been drawn,” remarked the mathematician Bruce Berndt, after working with his notebooks full-time for years. Outside of his published papers, Ramanujan had little interest in producing conventional mathematical proofs, and preferred to simply write his conjectures as formulas. Hardy famously stated that if you were to score mathematical ability on a scale of 100, with 100 being the most capacity possible—then Hardy would rate a 25, Littlewood 30, Hilbert 80, and Ramanujan 100.

Ramanujan told a friend that these extraordinary mathematical abilities began, in part, with a dream. According to friends, he paid careful attention to his dreams and was adept at their interpretation. Throughout his career, “scrolls of the most complicated mathematics” would unfold before him in dreams, so fluidly and profusely that he could scarcely write them all down upon waking. Here’s my beef: Nobody—especially his math peers at Cambridge, who were obviously lacking points on the math aptitude scale and stood to benefit most—showed the slightest interest in bothering to find out what in the actual fuck was going on with his dreams.

In fact, the opposite occurred.

Ramanujan had no conventional qualifications. He was about as far from the inner sanctum of math society as you could get. While Hardy and the Royal Society at Cambridge rightly recognized his genius, they perceived him through their own biased conceptual framework, and in both subtle and not-so-subtle ways omitted, suppressed, or just plain ignored facets of his character that didn’t fit their worldview.

In their remarks, English mathematicians were careful to stress that Ramanujan was rational and rigorous—characteristics that were worthy, in their eyes, of conventional respect, while Ramanujan’s devout practice as a Hindu was glossed over, as if this were merely a set of odd behavioral codes he happened to scrupulously observe. His first biographer received complaints about having included in the biography various remarks from Ramanujan’s childhood friends which detailed his great passion for occult and religious subjects, because any association with such matters apparently contaminated his mathly reputation. And these distortions persist to this day: His most popular biographer avoids the topic of his dreams, merely including a few as incidental, offhand notes. Personally, I think if you’re a 25, or sub-5, or even an 80 on the mathalete scale, it would be prudent to cultivate a healthy, open-minded curiosity about someone operating at a 100. What did Ramanujan know about mathematics that we don’t?

Across his biographical material, so far I’ve found only 6 specific dreams mentioned. One he credited with the inception of his mathematical abilities; in another the goddess Namagiri bestowed him with the gift of precociousness by writing on his tongue; during a difficult period, his abdomen appeared to him as an appendage of “indefinable mathematical surges”; a reassuring premonitory dream guided him to the right time for the publication of his work; another premonitory dream anticipated the death of a neighbor’s child; and the last is the only dream report in which we see his mathematical work in action. This last dream floats, excerpted, through the interwebs in endless chaff SEO-optimized blog posts, but these mentions have stripped away the dream’s context, which is particularly fascinating.

In 1911, Ramanujan was very much undiscovered, unemployed and couch-surfing. One evening, he stopped by a friend’s place and asked to spend the night. The main house was full, but his friend offered a bed in a little outhouse, where a monk was also staying. The next morning Ramanujan said to his friend:

He is such a powerful soul. I am glad I had the opportunity to share the room with him. His presence stimulated me a good deal. While asleep I had an unusual experience. There was a red screen formed by flowing blood as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of results in elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing.

I’ve never read a dream report where the specific presence of another soul in the room prompted an unusual experience for a dreamer, and this detail alone suggests an uncommon receptivity on the part of Ramanujan. The physical setting of the dreamer, on the other hand, has a long tradition of importance. For many thousands of years, across cultures in the East and Near East, it was a common practice to induce special revelatory dreams by sleeping over at a temple or sacred space, and this outhouse-monk setup reads like an unplanned, impromptu dream inducement, gesturing toward a merging of the everyday and sacred. He mentions that the monk’s presence provoked this unusual dream experience, yet later anecdotes from his friends indicate that he had many blood-scroll math dreams—could this have been the first, and thus especially significant? No one seems to have ever asked such simple questions.

I’m struck by many facets of this dream report, but what stands out foremost is the dreamer’s attention. Under circumstances that might freak out lesser dreamers (flowing blood screen?), Ramanujan is attentively observing, then **all** attention, then he’s become a kind of attention-magnet to which results have stuck. A dream responds to the dreamer—and in this case, the unspoken qualities of Ramanujan’s attention and its rapt escalation call forth a corresponding screen, mysterious hand, and effortless results in elliptic integrals. In both our waking lives and our dreams, quality of attention is a profound skill, in many ways the foundation of all others. And he was, by this point, clearly a master.

Ramanujan and his family were ardent devotees of Narasimha—the lion-faced incarnation, or avatara, of god, and consort of the goddess Namagiri—and for them, seeing drops of blood in a dream was considered a sign of Narasimha’s grace. It is also worth noting that roughly around this time, while in the midst of explaining a mathematical relation to a friend, Ramanujan paused for a moment, then turned to his listener and out of nowhere said, “An equation has no meaning for me unless it expresses a thought of GOD.” Might these details suggest that within Ramanujan’s interior network of dream-meaning—stimulated by the presence of a monk—a mysterious hand wrote thoughts of god on a screen of god’s grace? It is remarkable that this dream unfolds in a seamless flow of blood, grace, attention, writing, and math, and perhaps for Ramanujan they were inseparable. You do not achieve a dream like that by accident.

After reading first-hand descriptions of Ramanujan from his friends and colleagues, the one word mentioned over and over again is devotion. Perched on a step outside his parent’s house or hiding underneath a cot, he worked on his slate board day and night for years. His work was certainly not all intuitive flights—his notebooks were filled with a strange mixture of finished results seemingly plucked from the ether, and unrelated pages of relentless numerical calculation, in which he got to know each positive integer as a “personal friend.” As the scholar B. M. Wilson put it, Ramanujan’s research into number theory was often “preceded by a table of numerical results, carried usually to a length from which most of us would shirk.” Outside of math, in his smallest acts he scrupulously observed his family’s religious customs, regularly invoking the goddess Namagiri and basing his actions on what he took to be her will. For purely religious reasons, he refused Hardy’s initial, life-changing offer to math it up in England, and only relented after Namagiri blessed the invitation in one of his mother’s dreams. Traditions he could not observe due to social pressure at Cambridge, such as the tuft of hair customarily worn by Hindu men, caused him genuine pain.

He was deeply religious, but mystification is not an explanation for Ramanujan’s outrageous capacities. Worshiping the goddess Namagiri probably won’t make you India’s all-time-best math whiz. You could sit on your butt and wait for a dream where god reveals elliptic integrals just for you, but at that rate, you might as well wait for your cats to type out Hamlet too. Ramanujan’s dreams and religious beliefs were not magical shortcuts—instead, they were elements of an original, highly advanced method of creative inquiry. Awake and asleep, he worked fluidly with emotion, intellect, and extraordinarily deep levels of intuition, all of which he honed over the course of years through sincere devotion to his craft. His practice of mathematics was considered quite old-fashioned at the time—he generated conjectures as formulas when rigor and proofs were all the rage—but after a century we have only begun to appreciate how forward-looking and innovative his discoveries truly were. And in time, the fullness of his creative process will be seen in the same light, at once inseparable from the ancient religious traditions of a humble Southern town, and utterly radical in his implementation.

These days it’s common to stumble across self-help articles lauding obsession as a precondition for success. But this is a thoroughly secular and sanitized concept that only became fashionable in the late 20^th century. Obsession suggests compulsivity in a single-minded pursuit; it flirts with the pathological. Somewhere we lost the depth we sought in older religious forms. Devotion is desire transmuted across time into love. It is an elevation of attention; a singleness of purpose, but in service to something greater than ourselves. Ramanujan’s pure devotion to god and to math seem indistinguishable, in both the hints and anecdotes that remain as a record of his life, and especially in his dreams.

Preview image: 1986-01-05 OGB w Epsilon by Ian Regan