Who was the self-taught Indian mathematical genius in the 20th century?

Concept: A person described as “self-taught” in mathematics is one who mastered advanced material largely on their own — outside completed formal university training — as distinct from academics who earned their expertise through a standard institutional education (school, university, doctorate).

Application: Srinivasa Ramanujan (1887–1920) is the classic 20th-century case: with almost no formal training in higher mathematics, he worked largely alone from books such as Carr’s “Synopsis of Elementary Results,” rediscovering and extending results in number theory and infinite series before G. H. Hardy invited him to Cambridge, where his self-derived work was recognised as extraordinary.

Cross-check: Although Ramanujan was born in 1887 (the 19th century), his entire mathematical career, his correspondence with Hardy, his Cambridge years, and his international recognition all took place within the 20th century, and biographical sources (the Royal Society, the MacTutor History of Mathematics archive, and the Government of India) consistently describe him specifically as “self-taught” — confirming the match on both criteria in the question: era of his work and self-education.

Contrasting the other names:

• Aryabhatta belongs to the 5th century CE, an ancient-era astronomer-mathematician — many centuries before the 20th century.

• Sridharacharya was active around the 9th–10th century, part of the medieval period of Indian mathematics — also well before the 20th century.

• Harish Chandra was indeed a 20th-century mathematician, but he pursued extensive formal university education, including a doctorate under Dirac at Cambridge — the opposite of being self-taught.