Srinivasa Ramanujan Iyengar was a poor Hindu with only a basic mathematical education who, as a young man, made important mathematical discoveries. He impressed the great British mathematicial, G.H. Hardy, who invited him to join him at Cambridge University in England, where the two had a brilliant and fruitful collaboration, cut short when Ramanujan died young.
I read Robert Kanigel’s The Man Who Knew Infinity: A Life of the Genius Ramanujan after seeing the movie based on the book. The movie does justice to the spirit of the book and mostly conforms to fact, but cannot duplicate Kanigel’s richness of detail.
Both the movie and the book gave me food for thought on the nature and sources of genius. I once thought of mathematical discovery as a logical, step-by-step process, but I now realize it depends as much on inspiration as anything else.
Some of Ramanujan’s theorems came to him in dreams, sometimes on scrolls held by Hindu gods.
Since I do not believe in the Hindu gods myself, how do I explain the fact that Ramanujan’s visions of the gods have him true mathematical theorems and also good advice on major life decisions.
I have to believe that his visions were manifestations of his subconscious mind. Brain scientists tell us that most cognitive activity takes place below the level of consciousness. I believe that most inspiration and creative thought arises from subconscious sources, and that the conscious mind performs an executive function—deciding which intuitions have a basis in reality.
That executive function is important, because inspiration can be delusional. I think of intuition as like the engine of a car, and reason as like the steering wheel. You won’t get started without the first. You’ll likely wind up in a ditch without the second.
Ramanujan had a strong sense of intuition. He saw the truths of his theorems. So long as they worked, he saw little need for proof. That is what his mentor and collaborator G.H. Hardy insisted on.
Hardy was an atheist, who refused to believe in anything that couldn’t be proved. He provided the reality check that Ramanujan needed.
Yet Hardy’s devotion to mathematics, no less than Ramanujan’s, was akin to a spiritual quest. He never claimed that his pure mathematical studies had any practical use (although it turned out that they did did). He and Ramanujan were devoted to mathematics for its own sake—because of its austere beauty and logic.
Mathematical truth is not something tangible. You can’t see, hear or touch it. Yet it can be discovered through training and contemplation. In some ways the study of mathematics is like the spiritual discipline of a religion.
Mathematicians are different from religious seers in being able to prove their theorems, but only a tiny number of people are capable of understanding those proofs on the level of a Ramanujan or a Hardy.
And yet the rest of us are willing to support mathematicians and take their word for the truth of what they have discovered. Is this justified? I say “yes” and not just for the practical applications of mathematics, but I can’t articulate why.
Ramanujan had another quality of genius, which is obsessiveness. He was something like Ayn Rand’s Howard Roark character, in that he put his vision and his quest ahead of everything else, including career and wealth. He did fulfill minimal family responsibilities, but his heart was in his numbers.
Kanigel mentioned the many turning points in his life, which also were all possible failure points, in which he found the right patron or the right opportunity to continue his work. Ramanujan was more persistent than most people, and this paid off, but he still could easily have wound up a penniless and a seeming crank. How many geniuses wind up that way?