Ramanujan & My Four-Year Journey to Answer a 100-Year Old Question

In 2016, I watched The Man Who Knew Infinity, starring Dev Patel and Jeremy Irons, and it had a profound impact on my life.

The movie chronicles a critical period in the short life of Srinivasa Ramanujan, one of the greatest--yet least known--mathematicians of all time. I recently polled by LinkedIn connections and only 40% indicated they know of him.

Born in 1887, Ramanujan grew up in British ruled India with practically no formal education. Yet he was able to develop thousands of mathematical identities and equations, including some of the most groundbreaking concepts in the history of pure mathematics as well as solutions to mathematical problems considered unsolvable at the time. Ramanujan was able to solve complex mathematical problems quickly and documented his work in a series of notebooks, the last of which he worked on until his death at the early age 32 in 1920 (100 years ago).

Based on samples of his work, Ramanujan was invited to work at Trinity College, Cambridge with G.H. Hardy, one of the most prominent mathematicians of the first half of the 20th century, which he did from 1914 to 1919, becoming both a Fellow of the Royal Society and a Fellow of Trinity College. Years later, Hardy created a rating scale of natural mathematical ability from zero to 100, on which he assigned himself 25 and Ramanujan the highest possible score of 100.

Unlike others with exceptionally rare intellectual abilities whose work is generally attributed simply to being ‘geniuses’--Albert Einstein naturally comes to mind--there remains an important outstanding question about how Ramanujan was able to develop such an extensive body of unprecedented and remarkable work. This question was a primary focus in The Man Who Knew Infinity and results primarily from the fact that much of Ramanujan’s work was not accompanied by traditional mathematical proofs of how it was derived or substantiated, leading to a conclusion that in some extraordinary way, Ramanujan’s mind did not work like everyone else’s. According to Hardy: “All his results...had been arrived at by a process of mingled argument, intuition and induction, of which he was entirely unable to give any coherent account.”

The question also arises based on Ramanujan’s own statements that his mathematical insights had a divine origin, and that he saw mathematical formulas unfold before his eyes in dreams and visions from the goddess Namagiri Thayar, a form of the Hindu goddess Lakshmi. In fact, Ramanujan is known to have said "An equation for me has no meaning, unless it expresses a thought of God."

During the four years since I watched The Man Who Knew Infinity, I’ve spent countless days (and nights) searching for an answer to the question of how Ramanujan was able to do what he did. What was the source of Ramanujan’s profound knowledge of mathematics that reaches so far that it even relates to structures of the universe--like black holes--unknown at his time?

Since Ramanujan is not alive for us to speak with or examine, we likely will never fully know exactly how his mind worked. Highly respected mathematicians and others have over the years referred to Ramanujan as having “intuition,” “natural and pure talent” and the like but the prevailing thinking is that there simply is no satisfactory answer to how he was able to develop such exceptionally complex mathematical insights with such apparent ease. George E. Andrews, Professor of Mathematics at Pennsylvania State University, who in 1976 rediscovered Ramanujan’s lost notebook, the whereabouts of which were unknown for decades, was quoted in a 2011 article by Scientific American as saying about Ramanujan: "He was a magical genius, and the rest of us wish we knew how he was able to see so deeply."

My quest to understand the mystery of the source of Ramanujan’s abilities has taken me in directions well beyond mathematics into areas as diverse as cognitive neuroscience, fractal geometry, quantum biology, religion and astrophysics and exploring concepts such as the Golden Ratio and Newcomb–Benford Law. While I’m certainly not an expert in any of these areas, based on everything I have studied and learned along the way, I have concluded that Ramanujan had an extremely rare type of mind that exists at an unusual intersection of synesthesia and savant syndrome, which explains the abilities he exhibited and work he created, all in a manner that’s entirely consistent with the way in which he described it’s source.

Synesthesia occurs when distinct regions of the brain that typically function independently instead interact through atypical neural connections, generally causing crossover among different sensory systems, such as perceiving sound concurrently as color. Savant syndrome is a condition where brain disorders disrupt typical brain functions, creating spectacular intellectual abilities--such as superior autobiographical memory (videographic memory) and the ability to perform calendrical calculations--although it is usually accompanied by extreme mental disabilities. Savant syndrome, which was popularized in the 1988 movie, Rain Man, is extremely rare--much more so than synesthesia, which is thought to occur in 4% of the population.

At an unconscious (what many generally refer to day-to-day as “subconscious”) level, of which we do not have any awareness, humans consume and process vast quantities of information that are obtained in a wide variety of ways and through a range of bodily senses, including the five basic senses of touch, sight, hearing, smell and taste. The results are generally processed within respective regions of the brain and simplified into conscious awareness that allows us to interpret and understand the world in a way that’s suited to going about our everyday lives. At the intersection of synesthesia and savantism lies a condition where the structures and functioning of the brain allow for the conscious perception of information--and the processing of that information--that otherwise only exists at an unconscious level. Simply put, this condition opens a unilateral communication channel from the unconscious mind to the conscious mind (and possibly a bilateral channel), and is unlike traditional forms of synesthesia, which primarily cross the senses, and is also unlike traditional forms of savant syndrome in that the resulting superior abilities specifically relate to access to the unconscious mind versus any number of other extraordinary abilities relating only to the conscious mind.

The universe is intrinsically mathematical in nature, and unconscious information processing innately utilizes this mathematics in every aspect of human existence--just maneuvering your hand to move an object, for example, requires exceptionally complex calculations. I believe Ramanujan’s mind--at the intersection of synesthesia and savant syndrome: (1) gave him involuntary conscious access to and an understanding of the complex calculations his brain was performing unconsciously, likely in an inherent visual context in which it is processed unconsciously, and (2) enabled him to use that information and understanding to both consciously translate mental images into the mathematics native to the universe as well as to rapidly solve many extremely challenging mathematical problems presented to him. This ability to passively conceive mental images can be tantamount to the sort of divine visions that Ramanujan referenced. In a 1987 interview for a UK documentary called The Indian Clerk, Béla Bollobás, a Fellow of Trinity College, Cambridge, for example, described how Ramanujan had nightmares in which he would mathematically quantify relative areas of abdominal pain he experienced during a period of significant illness that ultimately claimed his life.

There are important examples of individuals--both throughout history and alive today--that have some form of synesthesia or savant syndrome and at least one case that appears very similar to that of Ramanujan. For example, many of Jackson Pollock's paintings, which appear random, actually contain mathematical forms called fractals, which occur in nature. Similarly, Vincent van Gogh’s The Starry Night, which is one of the most widely known paintings in Western culture and that he painted while having mental health issues and staying at an asylum, depicts turbulence so accurately that it compares to descriptions by physicists and mathematicians. And likewise, Beethoven's Moonlight Sonata, which he composed as he was going deaf, has underlying mathematical structures--pitch frequencies of different notes that form a geometric series which can be represented as equations--and Beethoven is said to have referenced mental images in composing music. Nikola Tesla is yet another example--he was able to vividly visualize solutions to mathematical problems, including in the form of what appeared to him as actual objects.

Another example is Daniel Tammet, who is documented as having synesthesia and sees numbers in various forms composed of colors, shapes, sizes and textures. In a number of interviews, Tammet describes the ability to multiply any two numbers simply by interpreting the space between the visual representations of those two numbers in his mind, without having to perform any conscious calculations. Although Ramanujan and Tammet appear to have entirely different capabilities--with Tammet’s possibly more inclined towards numerical (grapheme–color and ordinal personification) rather than mathematical--Tammet’s spontaneous ability to manipulate numbers is not dissimilar to an example contained in an anecdote Hardy tells of an exchange he had with Ramanujan:

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

While these examples seem instructive and helpful, they far from fully explain the wondrous capabilities and unprecedented results Ramanujan achieved. One individual, however, appears to be much closer to supporting the thesis that Ramanujan had a rare combination of synesthesia and savant syndrome--Washington State resident, Jason Padgett.

Padgett’s story is well documented, including in his 2014 book Struck by Genius: How a Brain Injury Made Me a Mathematical Marvel and I have been fortunate to have had many conversations with Jason to understand him and his thinking first hand. His current abilities were the result of a 2002 traumatic brain injury that altered his brain structure and therefore the way in which he perceives reality. Following the brain injury, Padgett started to see the world in pixelated, serial frames that form visual representations that can be reduced to mathematical formulas. Based on my conversations with him, he states that our brains observe reality in Planck length at steady, discrete time intervals overlaid onto a grid-like structure, allowing us to process mathematical formulas in geometric forms. In the closest example of Ramanujan, Padgett has similarly been able to derive mathematical identities and equations.

This year--2020--is the 100th anniversary of Ramanujan’s death, and I am excited to share my thoughts on Ramanujan for four reasons. Specifically, I believe these thoughts are: 

1. Important to further the understanding of Ramanujan’s work,
2. An opportunity to bring greater awareness to Ramanujan, who has simply not received the requisite credit and recognition for his contributions to humanity, 
3. Helpful to thinking about the human mind’s potential to reveal the true nature of reality beyond that which we readily perceive--including through and beyond mathematics--and, more importantly, to actually reveal that true nature of reality, and
4. Critical to fully understanding the vast implications of human brain-computer interfaces and the resulting potential access to vast quantities of information and processing power.

In a 1987 interview for the UK documentary, The Indian Clerk, Ramanujan’s widow, Janaki Ammal said “On his deathbed, he told me that his name would live for 100 years.” I feel truly privileged to have this opportunity to help keep Ramanujan’s name alive on the 100-year anniversary of his untimely passing.

Anil D. Aggarwal