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1729: What is so special about the Hardy-Ramanujan number?
1729, the Hardy-Ramanujan number, exemplifies Srinivasa Ramanujan's genius. His birthday, December 22, is celebrated as National Mathematics Day.
Srinivasa Ramanujan's mathematical talent cannot be defined by just one of his many achievements during his short life. Known as "the man who knew infinity," he discovered his own theorems and independently compiled approximately 3,900 results.
The Hardy-Ramanujan number may not be his greatest contribution to mathematics, but it stands out as being particularly memorable. This was an anecdote mentioned in his biography 'The Man Who Knew Infinity" by Robert Knaigel.
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When British Mathematician GH Hardy visited a sick Ramanujan at the hospital, he travelled in a taxi cab with the number 1729. Hardy found it to be an ordinary number, but Ramanujan said it was not and explained that it is the smallest number that can be expressed as the sum of two cubes in two different ways.
1729 is the sum of cubes of one (1^3=1) and 12 (12^3=1728). It can also be expressed as the sum of cubes of nine and 10 (9^3=729, 10^3=1000).
The number 1729 is known to the world as the Hardy-Ramanujan number or the taxicab number.
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Srinivasa Ramanujan did not receive any formal training in pure mathematics but made impactful contributions to the field. His areas of work include infinite series, continued fractions, number theory and mathematical analysis.
He also made notable contributions like the hypergeometric series, the Riemann series, the elliptic integrals, the theory of divergent series, and the functional equations of the zeta function.
Ramanujan's birthday, December 22, is celebrated as National Mathematics Day in India. In 2012, then-Prime Minister Manmohan Singh declared this day to honour the great mathematician.
