Biography hardy ramanujan number

This story about the number 1729 goes back to 1918 when G. H. Hardy paid a visit to Indian Mathematician Srinivasa Ramanujan when he was suffering from tuberculosis and was admitted to a hospital near London. Hardy had arrived in a taxi having the number 1729 and considered it as a dull number but Ramanujan replied by saying “no Hardy this is quite an interesting number!” That’s how this story started.

Born in the state of Tamil Nadu, India known as the man who knew infinity was born on 22nd December 1887 Srinivasa Ramanujan has made extraordinary contributions in the fields of number theory, continued fractions, mathematical analysis.

Ramanujan was a self-taught mathematical prodigy and at a very early age, he started to work on his mathematics and discoveries as he was fascinated by numbers. He also contributed to the branch of mathematics which had all the works related to ‘partitions of numbers’.

Here’s why the number 1729 is known as the Hardy-Ramanujan Number:
So Hardy was asked a question about Ramanujan “if Ramanujan’s methods differed in any way than that of other mathematicians, and whether in his mode of thinking was there anything abnormal.”

Incidentally while answering this question Hardy shared the story about the number 1729, and Hardy answered by saying “Ramanujan’s thinking skills, memory and power of calculation cannot be reasonably called ‘abnormal’ as his skills were very extraordinary and unusual.” Hardy also added that he believed that all mathematicians think at the bottom similarly that ‘Ramanujan was no exception’.

Interesting Mathematical story : The most exceptional number that is divisible all the digits from 1 to 10

To illustrate his point Hardy then shared the story about the number 1729 and said that how Ramanujan told him that “this is not an ordinary number it’s the smallest number which can be described as the sum of two cubes in two different ways.”

1729 is the total sum of cubes of 10 and 9. Cube of 10 is 1

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.

Also read: National Mathematics Day 2024: Essential role of maths in shaping future innovators

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.

Also read: Brain teaser: If you crack this tricky maths puzzle, you’ll earn the crown of ultimate genius

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.

Also read: National Mathematics Day 2024: Date, history, significance of the day and interesting facts about Srinivasa Ramanujan

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 hon

Natural number

Natural number

1729 is the natural number following 1728 and preceding 1730. It is the first nontrivial taxicab number, expressed as the sum of two cubic numbers in two different ways. It is known as the Ramanujan number or Hardy–Ramanujan number after G. H. Hardy and Srinivasa Ramanujan.

As a natural number

1729 is composite, the squarefree product of three prime numbers 7 × 13 × 19. It has as factors 1, 7, 13, 19, 91, 133, 247, and 1729. It is the third Carmichael number, and the first Chernick–Carmichael number. Furthermore, it is the first in the family of absolute Euler pseudoprimes, a subset of Carmichael numbers. 1729 is divisible by 19, the sum of its digits, making it a harshad number in base 10.

1729 is the dimension of the Fourier transform on which the fastest known algorithm for multiplying two numbers is based. This is an example of a galactic algorithm.

1729 can be expressed as the quadratic form. Investigating pairs of its distinct integer-valued that represent every integer the same number of times, Schiemann found that such quadratic forms must be in four or more variables, and the least possible discriminant of a four-variable pair is 1729.

Visually, 1729 can be found in other figurate numbers. It is the tenth centered cube number (a number that counts the points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points), the nineteenth dodecagon

Indian mathematician (1887–1920)

"Ramanujan" redirects here. For other uses, see Ramanujan (disambiguation).

In this Indian name, the name Srinivasa is a patronymic, and the person should be referred to by the given name, Ramanujan.

Srinivasa Ramanujan Aiyangar (22 December 1887 – 26 April 1920) was an Indian mathematician. Often regarded as one of the greatest mathematicians of all time, though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable.

Ramanujan initially developed his own mathematical research in isolation. According to Hans Eysenck, "he tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered". Seeking mathematicians who could better understand his work, in 1913 he began a mail correspondence with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognising Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Hardy commented that Ramanujan