The elusive reality of the creative mind
More than 50 years ago, Jacques Hadamard sought to understand how mathematicians generate new ideas. In The Psychology of Invention in the Mathematical Field, he explored the creative processes of intellectual giants such as George Polya, Claude Lévi-Strauss and Albert Einstein. His findings strongly supported the role of unconscious mental activity in mathematical invention. Despite advances in research, the workings of creativity remain elusive. Even Einstein struggled to articulate precisely how his insights on gravitation took shape.
Harvard mathematician Oscar Zariski once wrote a letter to his wife, despairing over his inability to solve a particular problem. His experience underscores an essential truth: grappling with a problem through intense effort lays the groundwork for creative breakthroughs. Once this effort is in place, what follows in the journey towards discovery? Some aspects of this process remain largely unknown, while others are only partially understood. The difficulty of true originality lies in how seamlessly the subconscious interweaves memory with invention. Stanford mathematician Yitzhak Katznelson once found himself composing an entirely new proof for a theorem while drafting An Introduction to Harmonic Analysis. Later, he recalled that the same proof had been casually shared with him months earlier by the Swedish mathematician Lennart Carleson. A similar situation occurred in the world of music when George Harrison’s My Sweet Lord was found to resemble an earlier composition. The court ruled that the melody had been unconsciously borrowed rather than deliberately copied.
John Edensor Littlewood, the collaborator of Ramanujan and GH Hardy, observed that solutions often emerged unexpectedly after an intense period of work followed by rest. He believed the subconscious mind continued processing problems while the conscious mind stepped away. Creativity can also be unpredictable. Littlewood once recounted the story of a Cambridge scholar who claimed to receive profound insights in his dreams, only to forget them by morning. On Littlewood’s advice, he kept a notebook by his bedside and one night, determined to capture his midnight inspiration, scribbled it down on waking. In the morning, he read: “Higamus, hogamus, men are polygamous; hogamous, higamus, women are monogamous.”
The story of Samuel Taylor Coleridge’s Kubla Khan presents a more sobering example. As legend has it, Coleridge composed the poem in a trance-like state, effortlessly shaping its verses. His flow was abruptly broken by an unexpected visitor and he found himself unable to resume the composition. The result was a fragment of extraordinary beauty, never to be completed. One must also consider the role of experimentation in the creative process. Ramanujan, though often credited with an inexplicable intuitive gift, spent years compiling vast amounts of empirical data, both mentally and in writing. This systematic approach likely played a role in his formulation of ideas such as the Prime Number Theorem. The world beyond mathematics and science offers its own illustrations. Mahatma Gandhi’s decision to call for a nationwide strike, came to him in the quiet of an early morning in Chennai. The path to creative discovery blends effort, subconscious reflection, and experimentation. It demands an engagement that is both rigorous and fluid, requiring sustained labour and, at times, the willingness to step a way.