Ramanujan’s story is as inspiring as it is tragic. Born in 1887 in a small village around 400 km from Madras (now Chennai), Ramanujan developed a passion for mathematics at a young age, but had to pursue it mostly alone and in poverty. Until, in 1913, he decided to write a letter to the famous Cambridge number theorist G.H. Hardy. Accustomed to this early form of spam, Hardy might have been forgiven for dispatching the highly unorthodox letter straight to the bin. But he didn’t. Recognising the author’s genius, Hardy invited Ramanujan to Cambridge, where he arrived in 1914. Over the following years, Ramanujan more than repaid Hardy’s faith in his talent, but suffered ill health due, in part, to the grizzly English climate and food. Ramanujan returned to India in 1919, still feeble, and died the following year, aged only 32. Hardy later described his collaboration with Ramanujan as “the one romantic incident in my life”.
The taxi-cab number
The romanticism rubbed off on the number 1729, which plays a central role in the Hardy-Ramanujan story. “I remember once going to see [Ramanujan] when he was ill at Putney,” Hardy wrote later. “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.'” What Ramanujan meant is that…