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National Mathematics Day: Why is 1729 special - magic of Hardy-Ramanujan number

BusinessToday.In     December 22, 2020

Born in Tamil Nadu's Erode on December 22, 1887, the self-taught mathematical prodigy Srinivasa Ramanujan made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions.

He was fascinated by numbers and made some remarkable contributions to the partitio numerorum branch of mathematics that deals with the study of partitions of numbers. The mathematical genius compiled approximately 3900 results independently before his untimely demise in Kumbhakonam at the age of 32 due to tuberculosis.

Why 1729 is a special number?

His most popular discovery, however, remains the Hardy-Ramanujan number to this date. The Hardy-Ramanujan number stems from an anecdote wherein the British mathematician GH Hardy had gone to meet S Ramanujan in hospital.

Hardy said that he came in a taxi having the number '1729', which the British mathematician described "as rather a dull one". Ramanujan replied to this saying, "No Hardy, it's a very interesting number! It's the smallest number expressible as the sum of two cubes in two different ways."

1729 is the sum of the cubes of 10 and 9. Cube of 10 is 1000 and the cube of 9 is 729. Both the cubes, therefore, add up to 1729. 1729 is also the sum of the cubes of 12 and 1. Cube of 12 is 1728 and the cube of 1 is 1. Both the cubes, therefore, add up to 1729.

This certainly is a fascinating discovery and is the easiest to remember among all of Ramanujan's works.

This day was first observed when the then Prime Minister Dr Manmohan Singh declared Ramanujan's birthday as National Mathematics Day on February 26,2012 upon his Madras University visit to pay tribute to Ramanujan's accomplishments and celebrated his 125th anniversary.

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