Srinivasa Ramanujan(1887 — 1920)
Srinivasa Ramanujan
Raj britannique
8 min read
A self-taught Indian mathematician (1887–1920), Ramanujan discovered thousands of remarkable mathematical formulas with no formal university training. Recognized by mathematician G.H. Hardy, he made major contributions to number theory and modular functions before dying prematurely at the age of 32.
Frequently asked questions
Key Facts
- 1903: Enrolled at Government Arts College in Kumbakonam but dropped out
- 1913: Began a correspondence with mathematician G.H. Hardy at Cambridge
- 1914–1919: Worked at Trinity College, Cambridge — the most productive period of his life
- 1918: Became the first Indian elected Fellow of the Royal Society, at age 31
- 1920: Returned to India and died in Madras at age 32, leaving behind notebooks containing around 3,900 mathematical formulas
Works & Achievements
Ramanujan developed a complete theory of highly composite numbers and established asymptotic formulas for their enumeration. This contribution opened new directions in number theory and remains foundational in the study of the multiplicative properties of integers.
Ramanujan discovered extraordinary properties of modular functions, including the celebrated Ramanujan congruences for the partition function. His work laid the foundations of the modern theory of modular forms, which has become crucial in contemporary number theory.
Ramanujan discovered several rapidly converging formulas for computing π, including a series that converges so quickly that only a few terms are needed to achieve very high precision. These formulas are still used in computing today for calculating π.
Ramanujan established remarkable congruences for the partition function, showing that certain properties repeat in regular patterns. His conjectures inspired decades of research and were later confirmed by subsequent mathematicians.
The exchange of letters between Ramanujan and British mathematician G.H. Hardy led to Ramanujan's international recognition and produced major mathematical results. This remarkable collaboration demonstrated Ramanujan's self-taught mathematical genius.
Ramanujan discovered astonishing properties of continued fractions and established complex functional equations linking various special functions. This work enriched the theory of elliptic and hyperbolic functions.
Anecdotes
In 1913, Ramanujan wrote a letter to the English mathematician G.H. Hardy listing 120 mathematical formulas he had discovered on his own. Hardy, deeply impressed, immediately recognized him as a genius and invited him to come to Cambridge. This letter became one of the most famous pieces of correspondence in the history of mathematics.
Ramanujan had an extraordinary memory for the properties of numbers and could instantly recall detailed information about complex figures. During a hospital visit, Hardy mentioned he had arrived in taxi number 1729, calling it 'a rather dull number.' Ramanujan replied at once: 'No, it is the smallest number expressible as the sum of two cubes in two different ways.' That number became known as the Hardy–Ramanujan number.
Ramanujan developed his mathematical formulas without access to a university library and without any formal advanced training, working in the Indian town of Kumbakonam. He relied on his remarkable mathematical intuition, filling entire notebooks with results that often anticipated the later discoveries of Western mathematicians.
At Cambridge, Ramanujan struggled constantly with homesickness and found it difficult to adapt to English food and daily life. Although he produced groundbreaking mathematical work in just a few years, his health deteriorated and he returned to India in 1919. He died in 1920 at only 32 years old, leaving behind hundreds of formulas that mathematicians continue to study to this day.
Ramanujan's notebooks, filled with mathematical discoveries but lacking complete proofs, kept mathematicians busy for decades after his death. Researchers spent years verifying his seemingly magical formulas, finding that nearly everything he had written was correct — a testament to a mathematical intuition that remains difficult to explain.
Primary Sources
During the years 1914-1919 Ramanujan was in England, and his notebooks were largely filled with results in the theory of partitions, the theory of modular forms, and allied subjects.
I was extremely interested by your letter and by the theorems which you state. You will see that I am returning the letter you sent me; and I should be very much obliged if you would send me proofs of some of your outstanding theorems.
The formulas discovered by Ramanujan in his notebooks reveal an extraordinary mathematical intuition, notably identities concerning theta functions and infinite series.
Your letter put me at once in a state of great suspense, for very slowly I prime began to see that the letter was far more in the nature of a remarkable document.
Key Places
City in Tamil Nadu where Srinivasa Ramanujan was born on December 22, 1887. It is the starting point of his life and his remarkable journey in mathematics.
City in Tamil Nadu where Ramanujan grew up and attended school. It was here that he developed his passion for mathematics from a very young age.
Institution where Ramanujan briefly studied and where he was recognized for his exceptional mathematical talents before receiving financial support to continue his research.
Prestigious university where Ramanujan worked alongside mathematician G.H. Hardy from 1914 to 1919. It was the heart of his international recognition and his major contributions to number theory.
The British capital where Ramanujan stayed during his years in England, attending conferences and engaging with the British mathematical community.
City in Kerala where Ramanujan returned in 1919 after his time in England, weakened by illness. He died there on April 26, 1920, at the age of 32.
Liens externes & ressources
Références
Œuvres
Articles dans le Journal of the Indian Mathematical Society
1911-1914
Highly Composite Numbers (Nombres hautement composés)
1915
Formule de Ramanujan-Hardy (méthode du cercle)
1918
Congruences de Ramanujan
1919
Fonctions mock thêta (Lost Notebook)
1919-1920
Les Carnets de Ramanujan (Notebooks)
1903-1914
