India and England · 1887-1920
Srinivasa Ramanujan
Pronunciation: sree-nee-VAH-suh rah-MAH-noo-jun
An Indian mathematician whose extraordinary formulas and insights reshaped number theory, infinite series, continued fractions, and partition theory.
Ramanujan’s notebooks, papers, letters, and collaboration with G. H. Hardy extensively document his mathematics.
6-8, 9-12, College
The person and the work
Biography
Srinivasa Ramanujan developed mathematics largely through independent study in southern India. He filled notebooks with identities, series, and number-theoretic observations, often without the detailed proofs expected in formal journals.
After writing to G. H. Hardy, Ramanujan traveled to Cambridge and produced influential work despite illness and the difficulties of wartime life far from home.
Mathematical contribution
What this hero added or preserved
Partitions and number theory
Ramanujan found deep patterns in the number of ways integers can be written as sums and in many related arithmetic functions.
Infinite series and continued fractions
His formulas revealed unexpected relationships and continue to influence modern mathematics and physics.
Why this matters
The larger lesson
Pattern recognition can open a door, but proof explains why the door is real. Ramanujan’s work shows the creative tension between intuition, computation, and rigorous justification.
Place the work in time
Timeline
- 1913
Ramanujan writes to Hardy
A letter containing striking formulas begins a major mathematical collaboration.
- 1914-1919
Research at Cambridge
Ramanujan publishes influential work in number theory and analysis.
Key idea
Integer partitions
A partition of a positive integer is a way to write it as a sum of positive integers without treating order as different.
The partitions of 4 are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1, so p(4)=5.
Try it yourself
Count partitions
List every partition of 5 and count them.
- Begin with 5 alone.
- Work downward by largest part.
- Ignore rearrangements such as 3+2 and 2+3 as duplicates.
Show the answer
There are 7 partitions: 5; 4+1; 3+2; 3+1+1; 2+2+1; 2+1+1+1; 1+1+1+1+1.
Math at work
Advanced patterns can become practical tools
Results from number theory and series appear in cryptography, statistical mechanics, signal processing, and high-precision computation.
Keep curiosity alive
A little-known fact
A final letter from Ramanujan introduced mock theta functions, ideas that became important in later research.
Ramanujan worked without learning from books or other mathematicians.
He was largely self-directed, but studied mathematical texts and later developed his work through collaboration and formal research.
Keep exploring
Connected learning paths
Related math terms
- Integer partition
- Infinite series
- Continued fraction