The Letter That Changed Mathematics

Quick Overview

The most significant mathematical discovery discussed is Srinivasa Ramanujan's work on the sum of the infinite series 1 + 2 + 3 + 4 + ... equaling -1/12, a result that, while initially seeming like nonsense, is now fundamental to string theory and is proven using methods Ramanujan developed, which were later formalized by G.H. Hardy and others. The discussion also highlights the importance of the trigeminal nerve in triggering sneezes from menthol or bright light, which is caused by the nerve running too close to the optic nerve.

Key Points: The infinite series 1 + 2 + 3 + 4 + ... is shown to equal -1/12 in Ramanujan's theory, a result now used in string theory. G.H. Hardy, a mathematician at Cambridge, strongly supported Ramanujan's work after receiving his letters starting in February 1913. Ramanujan, who was Indian, was likely not formally trained in mainstream mathematics, having done his revolutionary work largely in isolation. The discussion covers the photic sneeze reflex (ACHOO syndrome), explaining that the trigeminal nerve runs close to the optic nerve, causing a reaction (a sneeze) when the optic nerve is overstimulated by bright light. Cancer Research UK is mentioned as the world's largest charitable funder of cancer research, spanning over 20 countries and employing over 4,000 people. Ramanujan's work was so radical that many contemporaries, including those at Cambridge, were skeptical, but his later work has proven invaluable, especially in areas like quantum field theory and string theory. The discussion concludes by noting Ramanujan's personal life, including his vegetarianism and his death from tuberculosis shortly after returning to India.

Context: This episode of 'The Rest is Science' features a discussion between the host (Michael) and a guest (Hannah) focusing on historical mathematical discoveries and simple biological reflexes. The central topic revolves around the life and work of the self-taught Indian mathematician Srinivasa Ramanujan, whose unconventional approaches to infinite series challenged established mathematical norms, particularly those concerning divergent series. The conversation also touches upon the scientific explanation for sneezing when exposed to bright light or menthol, and a brief mention of Cancer Research UK's extensive global efforts.