Srinivasa Ramanujan (1887-1920), arguably the greatest mathematician of the 20th century, was in innate mathematical talent comparable to the legendary Euler, Gauss, and Jacobi. A self-taught genius in pure mathematics, he made original contributions to function theory, power series, and number theory. His remarkable discoveries have made a great impact on several branches of mathematics, revealing deep and fundamental connections that continue to inspire investigation.
Born into modest settings, Ramanujan exhibited himself as an all round scholar in his early schooling, particularly in mathematics. Even as a youngster he developed his own method of solving the 4th degree polynomial equation, unaware that this problem had already been solved.
Consumed by passion for mathematics he neglected other subjects and lost his college scholarship. Undaunted he continued his work on hypergeometric series and related integrals, not knowing that he had stumbled upon elliptic functions. Despite the lack of formal training, Ramanujan continued to develop his mathematical ideas and published a brilliant research paper on Bernoulli numbers in 1911 gaining recognition in India as a mathematical genius.
With the help of patrons Ramanujan obtained a position in the Madras Port Trust in 1912. Serendipitously, he acquired the acquaintance of amateur and professional mathematicians in his work environment who fostered his independent studies. However, he yearned for a wider audience and contacted many British mathematicians, all of whom either ignored his letters or were unable to appreciate the genius they contained.
In 1913 Ramanujan wrote his fateful letter to G.H. Hardy, the preeminent mathematician of the time, who was slayed by many of the astounding propositions contained within. Recognizing the diamond in the rough, Hardy brought Ramanujan to Cambridge in 1914 to begin an extraordinary collaboration that produced results on many fronts including highly composite numbers and hypergeometric series.
Perhaps Ramanujan’s most stunning contribution was the formula for computing the exact value of the number of partitions of any whole number, which is the number of ways a whole number N can be written as a sum of whole numbers, and is denoted P(N). For example, P(5)=7 because 5 = 5 = 4+1 = 3+2 = 3+1+1 = 2+2+1 = 2+1+1+1 = 1+1+1+1+1. This amazing formula correctly predicted that P(200) = 3,972,999,029,388.
His incomparable brilliance is illustrated by this oft-repeated story. Visiting an ailing Ramanujan in hospital, Hardy remarked that he arrived in a taxi with the ‘dull number 1729.’ Without hesitation, Ramanujan remarked that the number was in fact interesting, because it was the smallest number that can be written as the sum of two cubes in two different ways: In 1918 Ramanujan was elected a fellow of the Royal Society of London, the greatest mathematical accolade of the time. In 1919, Ramanujan returned to India in failing health and died the following year.
Ramanujan left behind a legacy of brilliance in the form of unpublished notebooks filled with theorems that still bedevil and befuddle modern mathematicians. “The enigma in Ramanujan’s creative process is still covered by a curtain that has barely been drawn,'” notes the number theorist Bruce Berndt. Like those of Mozart and Galois, Ramanujan’s untimely death leads us wonder what might have been.
The story of Ramanujan is not merely one of the discovery of hidden talent and fruition of rare genius, but also one of the power and profit of perseverance and determination. Ramanujan was not disenchanted by the lack of interest of famed mathematicians such as Hobson and Hill. Rather he persisted in seeking a benefactor until he found Hardy, making his mark against insurmountable obstacles.