Srinivasa Ramanujan made profound and significant contributions to the mathematics, including:

• Number Theory
  1. Partition Function: Created approximate formulas for partition functions and unearthed Ramanujan’s tau function.
  2. Ramanujan Prime: Defined Ramanujan primes and provided characteristics regarding prime numbers.
  3. Studied and explored highly composite numbers.
• Infinite Series
  1. Ramanujan Summation: Devised techniques for assigning finite values to infinite series that do not converge.
  2. Have made important advancements in the field of q-series and continued fractions.
• Modular Forms
  1. Mock Theta Functions were found, leading to the advancement of the theory of modular forms.
  2. Explored modular equations and transformations.
• Elliptic Functions: Played a key role in the development of elliptic functions and their associated areas.
• Mathematical Analysis
  • Discovered and demonstrated the Rogers-Ramanujan identities.
  • The Master Theorem by Ramanujan: Offered a useful technique for calculating definite integrals and infinite series.
• Advanced in the field of continued fractions, offering fresh findings and perspectives.

Ramanujan’s deep understanding of mathematics, along with his many innovative findings and speculations, some of which were not even proven by modern scientists for some years has had a long-lasting effect, impacting different fields (like String Theory by Stephen Hawkings used the infinite number series of Ramanujan) and motivating further studies.