Why 1729 is a special number? — –The Magic of Hardy Ramanujan
Srinivasa Ramanujan was a person who really knew Infinity or knew more than infinity. He contributed theorems and independently compiled 3,900 results (mostly identities and equations). However, inquisitive minds and those dabbling in mathematical science would also know him for the Hardy-Ramanujan number.
| Full Name: | Srinivasa Aiyangar Ramanujan |
| Known For: | Prolific mathematician |
| Parents’ Names: | K. Srinivasa Aiyangar, Komalatammal |
| Born: | December 22, 1887 in Erode, India |
| Died: | April 26, 1920 at age 32 in Kumbakonam, India |
| Interesting Fact: | Ramanujan’s life is depicted in a book published in 1991 and a 2015 biographical film, both titled “The Man Who Knew Infinity.” |
Srinivasa Ramanujan (Biography):
The man who knew Infinity, Srinivasa Ramanujan knew more than infinity. He contributed theorems and independently compiled 3900 results. However, to inquisitive minds and those dabbling in mathematical science would also know him for the Hardy-Ramanujan number.
The Hardy-Ramanujan number is named such after an anecdote of the British mathematician G.H. Hardy who had gone to visit S. Ramanujan in hospital. The anecdote is a part of Ramanujan’s biography ‘The Man Who Knew Infinity’ by Robert Knaigel.
Why 1729 is a Special Number? / কেন 1729 একটি বিশেষ সংখ্যা?
Mr. Hardy quipped that he came in a taxi with the number ‘1729’ which seemed a fairly ordinary number. Ramanujan said that it was not. 1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways.
1729 is the sum of the cubes of 10 and 9 – cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.
1729 is also the sum of the cubes of 12 and 1- cube of 12 is 1728 and cube of 1 is 1; adding the two results in 1729.
While, the Ramanujan number is not his greatest combination, it is certainly a fascinating discovery that is easiest to remember among all of his discoveries.
The Magic of Hardy Ramanujan / হার্ডি রামানুজনের ম্যাজিক:
Hardy quipped that he came in a taxi with the number ‘1729’ which seemed a fairly ordinary number. Ramanujan said that it was not. “He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, ‘rather a dull number,’ adding that he hoped that wasn’t a bad omen. ‘No, Hardy,’ said Ramanujan, ‘it is a very interesting number. It is the smallest number expressible as the sum of two [positive] cubes in two different ways’ “.
1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways.
1729 is the sum of the cubes of 10 and 9 – a cube of 10 is 1000 and a cube of 9 is 729; adding the two numbers results in 1729.
1729 is also the sum of the cubes of 12 and 1- a cube of 12 is 1728 and a cube of 1 is 1; adding the two results in 1729.
However, similarly, there are more fascinating discoveries about it. Here positive numbers are taken as the smallest number considering negative cubes also will be-
91 is the sum of the cubes of 6 and -5 i.e. the cube of 6 is 216 and the cube of -5 is 125; adding the two numbers results in 91.
91 is also the sum of the cubes of 4 and 3 i.e. the cube of 4 is 64 and the cube of 3 is 27; adding the two numbers results in 91.
Ramanujan was fascinated with numbers and made striking contributions to a branch of mathematics partitio numerorum, the study of partitions of numbers.
Srinivasa Ramanujan’s birthday, December 22, was declared as the National mathematics Day in 2012 by the then Prime Minister Dr. Manmohan Singh. Coupled with this and a movie based on his life, he has grabbed the attention of the non-mathematical population as well.
