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Srinivasa Ramanujan's life is often told as pure genius: a clerk in Madras writes to a Cambridge mathematician and is recognised almost overnight. The verified record is more interesting, and more useful to a student, because it shows years of self-directed practice, letters that went unanswered, and a hard lesson about proof.
Who was Ramanujan?
From the MacTutor biography at the University of St Andrews:
He was born on 22 December 1887 in Erode, Tamil Nadu.
At Town High School he came across G. S. Carr's Synopsis of elementary results in pure mathematics, a book of theorems, formulae and short proofs. It let him teach himself, but its very concise style also shaped how he later wrote mathematics.
He won a scholarship to Government College in Kumbakonam in 1904 but lost it the next year because he "devoted more and more of his time to mathematics and neglected his other subjects."
At Pachaiyappa's College in Madras he took the First Arts examination, passed in mathematics, failed his other subjects, and so could not enter the University of Madras.
In 1912 he began work as a clerk in the accounts section of the Madras Port Trust.
For years, MacTutor notes, he worked on mathematics "without any help and without any real idea of the then current research topics other than that provided by Carr's book."
How did his work with Hardy begin?
In January 1913, Ramanujan wrote to G. H. Hardy at Cambridge, enclosing a long list of unproved theorems. He had already written to E. W. Hobson and H. F. Baker; neither replied. His letter to Hardy began: "I have had no university education but I have undergone the ordinary school course."
Hardy and J. E. Littlewood studied the list. Hardy's reply on 8 February 1913 said he was "exceedingly interested," but that "it is essential that I should see proofs of some of your assertions." He sorted the results into three groups: some already known, some new but interesting more for their curiosity than their importance, and some new and important.
Ramanujan reached Cambridge in 1914. He earned a BA by research in 1916 for work on highly composite numbers, was elected a Fellow of the Royal Society in 1918, and became a Fellow of Trinity College the same year. He returned to India in 1919 and died at Kumbakonam on 26 April 1920, aged 32.
Hardy described the challenge of teaching him: "The limitations of his knowledge were as startling as its profundity." Littlewood, asked to teach him rigorous methods, found that whenever a topic came up, Ramanujan's response was "an avalanche of original ideas."
What is in Ramanujan's notebooks?
MacTutor says Ramanujan left "a number of unpublished notebooks filled with theorems that mathematicians have continued to study." Bruce Berndt, who began editing them in 1977, said in an interview recorded in 2001 that he counted 3,254 entries, while stressing that "it is not really an official count" because it depends on how you count. Berndt wrote five volumes on these notebooks.
A separate manuscript, the "lost notebook," was discovered by George Andrews in spring 1976, as noted in the same interview. Andrews and Berndt have since published a multi-volume edition, Ramanujan's Lost Notebook, with Springer.
MacTutor also records the other side: Ramanujan "had only a vague idea of what constitutes a mathematical proof," and "some of his theorems on prime numbers were completely wrong."
What can a student learn from Ramanujan?
A unique life shouldn't be turned into a study hack. But a few lessons follow from the record.
Keep a working notebook. Ramanujan filled notebooks with results he found. Keep one just for things you worked out yourself: a derivation, a shortcut you noticed, a pattern in previous-year papers. Date each entry.
Work through a compact source, then go beyond it. Carr's book was a list of results he worked through himself. Your formula sheet can play that role if you derive the results instead of memorising them. See making your own formula sheet.
Check what you find. Some of Ramanujan's results were wrong. Test every shortcut on a case where you know the answer, for example with dimensional analysis checks.
Don't neglect the other subjects. He lost a scholarship and failed an exam because he neglected everything except mathematics. In JEE or NEET, your weakest subject counts as much as your favourite.
Keep asking people who can judge your work. Two mathematicians didn't reply; the third changed his life. Show your work to teachers and mentors, and ask for specific feedback.
Where Fermi fits
Checking your own results works best with good feedback. The Fermi Problem Library has a step-by-step solver that explains the reasoning, so you can compare your derivation with a worked one. For curiosity beyond the syllabus, Fermi Courses are university-level courses taught by working scientists.
Start a working notebook this week and write down one thing you derived yourself.
