What are some of the lesser known facts about Ramanujan?

 Srinivasa Ramanujan was an Indian mathematician who made significant contributions to number theory, mathematical analysis, and continued fractions. While many people are familiar with his extraordinary mathematical talents and collaboration with British mathematician G.H. Hardy, there are lesser-known facts about Ramanujan:

1. **Self-Taught Genius:** Ramanujan was mostly self-taught in mathematics. With minimal formal training, he developed his own theorems and results independently.

2. **Unorthodox Notations:** Ramanujan's notebooks contained many results written in unusual and unorthodox notations that were unfamiliar to Western mathematicians. Deciphering and proving these results challenged mathematicians for years.

3. **Mock Theta Functions:** Ramanujan introduced mock theta functions, a type of infinite series that behaves like modular forms but doesn't satisfy all the usual properties. These functions have applications in mathematical physics, especially in the study of black holes.

4. **Lost Notebook:** After Ramanujan's death, a "lost notebook" was discovered containing a wealth of unpublished results. This notebook, which came to be known as the "lost notebook" or "second notebook," provided mathematicians with new insights into Ramanujan's work.

5. **Health Struggles:** Ramanujan faced health challenges throughout his life, and his poor health was a significant factor in his untimely death at the age of 32. He suffered from various ailments, including tuberculosis.

6. **Ramanujan-Hardy Number (1729):** The number 1729 is famously known as the "Ramanujan-Hardy number." According to the story, when Hardy visited Ramanujan in the hospital and mentioned that he arrived in a taxi with the dull number 1729, Ramanujan immediately replied that 1729 is an interesting number—it is the smallest positive integer that can be expressed as the sum of two cubes in two different ways: \(1729 = 1^3 + 12^3 = 9^3 + 10^3\).

7. **Ramanujan Primes:** Ramanujan also made contributions to prime number theory. The so-called "Ramanujan primes" are a class of prime numbers related to modular forms and mock theta functions.

8. **Euler's Identity Connection:** Ramanujan discovered a unique and elegant identity for \(e^{\pi \sqrt{163}}\), which connects three fundamental mathematical constants: \(e\), \(\pi\), and \(\sqrt{163}\). This result is often considered a masterpiece in mathematical beauty.

Ramanujan's life and work continue to inspire mathematicians, and his legacy remains influential in various branches of mathematics.