Ramanujan and mathematical intuition: a maths EPQ idea
A title to start from
How did Ramanujan reach results without proofs, and what does his work say about intuition in mathematics?
Why it works as an EPQ
Some of his results can be checked or proved at a level you can reach, so the essay rests on real mathematics.
Scope and difficulty
Solid. Solid. Choose two or three results you can verify and discuss.
The maths
Builds on these A Level topics: Sequences and series · Proof.
You would learn:
- Partitions
- Series and their convergence
- Numerical verification
One possible plan
- Choose results such as partition congruences or his series and verify them by computation.
- Prove one where a proof is within reach.
- Study his working methods from reliable biographies.
- Judge the role of intuition and proof.
Pitfalls
- A biography with no mathematics.
- Claiming verification is proof.
Where to start reading
- The Man Who Knew Infinity (Robert Kanigel)
- Search for: Ramanujan partition congruences mod 5
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