Renowned mathematician Srinivasa Ramanujan led a life of sheer, mysterious genius and catapulted the mathematical world into a new realm with his works whose far-reaching significance is still being uncovered, said University of Wisconsin professor Ken Ono on Tuesday in his lecture “Unearthing visions of a master: The Story and Legacy of Ramanujan.”

Visiting the Dartmouth math department as part of the Dartmouth’s Reese Prosser Memorial Lecture series, Ono aptly described his talk on the legendary Ramanujan as “some history, some math” as he began with a timeline of Ramanujan’s life.

A Brahmin devoted to Hinduism, Ramanujan was born and raised in Erode, India in a tiny village called Kumbakonam. An avid student until college, Ramanujan’s most influential encounter with math was through A Synopsis of Elementary Results in Pure Mathematics, a book whose pages were filled with 6,165 theorems but devoid of proofs. It was after reading this book, Ono said, that Ramanujan become “infatuated with math” and embarked on his own mathematical quest, studying and proving theorems at a prolific rate.

After dropping out of college twice to pursue his mathematical rapture, Ono continued, Ramanujan decided to send a letter with his findings to G. H. Hardy, a leading English mathematician at the time. From what he could decipher, Hardy deemed Ramanujan a genius and invited him to study at Cambridge.

Writing 30 papers in the five years that he attended Cambridge, Ramanujan was eventually elected a Fellow of the Royal Society. He continued his work at a furious pace until he fell ill in 1919, dying in 1920 at the age of 32 after returning to his Indian homeland.

Even after Ramanujan’s death, mathematicians have continued to explore his findings that initially appeared to have little or no applications. There are in fact many nuances in Ramanujan’s work that have served as the bases for the Ramanujan-Petersson Conjectures, Galoi’s representations, Fermat’s Last Theorem, the theory of q-series, the circle method, probabilistic number theory, and other mathematical endeavors.

The most recent research pertaining to Ramanujan’s work, including Ono’s own, has revolved around Ramanujan’s “last letter,” Ono said. When on his deathbed on January 12, 1920, Ramanujan wrote one last letter to Hardy. In this letter were 17 power series that Ramanujan referred to simply and with no explanation as “mock-θ functions.”

Numerous distinguished mathematicians immediately began to examine these 17 mock-θ functions, finding connections between them and numerous areas in math. They “did not have a right” to have the implications that they did, Ono said.

In 1976 some mathematical light was shed on Ramanujan’s last letter when Ramanujan’s “lost notebook” was found. The notebook, which contained 100 pages detailing Ramanujan’s later findings, was sent to England by Ramanujan’s wife shortly after his death, buried in the Trinity College Library, and narrowly missed incarceration when it was dismissed for junk paperwork, Ono said.

As in first notebook, Ramanujan had “very little rhyme and reason to his methods” in his notebook recordings. Nevertheless, though much examination, mock-θ functions have been proven important to such diverse areas as probability theory, black holes, and even cancer research.

In 2002, reaching the forefront of research in mock-θ theories, Dutch mathematician Sander Zwegers made a connection between Ramanujan’s mock-θ functions and real analytic modular forms, the prerequisite to Ono’s own work in Ramanujan’s congruences in partition functions.

At first glance, Ramanujan was a man who “flunked out [of college] twice, was made a Fellow of the Royal Society, and wrote some great papers.” However, “I hope that you see that Ramanujan is incredible. … Many have won awards for figuring out stuff that he figured out scribbl[ing] on a slate,” Ono said in conclusion to his talk.

Further suggested readings on Ramanujan include The Indian Clerk and The Man Who Knew Infinity. Also, a movie titled Ramanujan is anticipated.