India has produced many world-renowned mathematicians, making it difficult to designate a single "No. 1" mathematician. However, a few names stand out due to their immense contributions to mathematics:
1. **Srinivasa Ramanujan (1887–1920):**
Ramanujan is often considered one of the greatest mathematicians in history, known for his groundbreaking work in number theory, continued fractions, and infinite series. His results and insights, despite having little formal training, have inspired much of modern mathematics. He developed the famous *Ramanujan primes* and worked on the *Ramanujan theta function* and *mock theta functions*.
2. **C. R. Rao (1920–Present):**
A highly respected statistician, Rao is celebrated for his contributions to multivariate statistical theory. His work is foundational to areas like the theory of estimation and design, and he's made numerous contributions to statistics and mathematics.
3. **Manjul Bhargava (1974–Present):**
A Fields Medalist (2014), Bhargava is known for his contributions to algebraic number theory. His work on Gauss' composition law and his development of new techniques in number theory have significantly advanced the field. His achievements in mathematics have brought him international acclaim.
4. **Harish-Chandra (1923–1983):**
Known for his work in representation theory and harmonic analysis, Harish-Chandra made fundamental contributions to both mathematics and physics, and his research has had long-lasting impacts in many branches of mathematics.
5. **K. R. Parthasarathy (1934–Present):**
A distinguished mathematician, Parthasarathy is recognized for his contributions to stochastic processes, particularly stochastic analysis, and his work on Markov processes.
While Ramanujan is arguably the most celebrated mathematician associated with India, the titles or rankings among mathematicians vary and depend on the specific areas of mathematics being discussed.