On Wednesday, Oct. 20, as part of the Natural Science and Mathematics Colloquium Series, Penn State University Professor George Andrews discussed the history of the mathematics genius Srinivasa Ramanujan in his lecture The Indian Genius, Ramanujan: His Life and the Excitement of His Mathematics.
“This is a beautiful place,” said Andrews, after an introduction and being given a Math Club keychain for presenting from Mathematics professor Dr. Alex Meadows.
Andrews’ presentation was given to a large audience of students, faculty members, and members of the community in Schaefer 106 at 4:40 p.m. that Wednesday.
Andrews began with a history of Ramanujan, who was born in Southern India in 1887 to a poor Brahmin family. He showed mathematical prowess by the age of ten, and received awards in high school by the age of 17 for the development of new theories. “He was a child prodigy of mathematics,” said Andrews.
Ramanujan was awarded a scholarship upon graduation to attend the Government College in Kumbakonam, but failed most of his classes that were not mathematics-based. “He was not well-rounded student,” said Andrews. “[He was] a case of great promise lost to the world.”
After not being able to earn a steady job for years and marrying in 1909, Ramanujan earned a clerk’s position in Madras.
Still interested in mathematics, Ramanujan attempted to contact mathematicians in the United States, finally drawing the attention of Godfrey Harold Hardy in 1913.
Hardy noticed in the theories that came with the letter that Ramanujan had not only “discovered” some of Hardy’s already-proven advanced theories, but also that he had found new theorems of his own.
In 1914, Hardy arranged for Ramanujan to come to Cambridge, where Hardy was currently a professor, and Ramanujan was able to work alongside him to solve complex mathematical theories.
Both Hardy and Ramanujan’s work with the Circle Method opened the doors to the development of analytical theory.
“This was a truly exciting time,” said Andrews, “and an exciting period for analytical theory in the 20th century.”
At a young age, Ramanujan was diagnosed with what doctors at the time recognized as tuberculosis, and in 1919 his health improved enough that he wanted to return to India with the hope of staying more healthy. This turned out to be unsuccessful, and after a stage of worsening health Ramanujan died in the Spring of 1920.
On his deathbed, Ramanujan discussed some of what is regarded by some today as “the most advanced mathematics known” in his notebooks and in his notes, which were eventually collected at Trinity College in Cambridge, United Kingdom but lost during storage. Mock-theta functions, included in Ramanujan’s work, were also crucial to analytical mathematics.
In his efforts to study the mock-theta functions as part of his thesis project, Andrews came across Ramanujan’s notebook at Trinity College. Recognizing Ramanujan’s handwriting from older textbooks in college, Andrews worked to interpret Ramanujan’s notes and theories, coming across third and fifth-ordered mock-theta functions believed to be undiscoverable or unsolvable at that time.
What Ramanujan had referred to in the last letter to Hardy (before his death in 1920) as “several new functions” was detailed in Ramanujan’s notes.
Andrews went on to discuss several of Ramanujan’s theories, including the practical use of Mock-Theta functions in the Heat Equation, the expansion of five Taylor series (sums in mathematics represented by single, expandable expressions based on notation) that led to the discovery of the Mock-Theta functions, and (while slightly unrelated) Hardy and Ramanujan’s work in solving p(n), or the number of ways to solve an integer “n” by adding other integers together.
Andrews concluded his lecture with a discussion of a potential film production of Ramanujan’s life, and the potential impact of the story on the Indian and mathematics communities due to the dramatic, fictional addition of a love interest of Ramanujan’s while he was in the United States.
There’s “no evidence that this occurred,” said Andrews, who served as full consultant for the movie production.
“I need to sleep more,” said sophomore Josh Kaminsky, at the conclusion of the presentation. “Ramanujan accomplished more in mathematics while sleeping than I ever did while awake.”
“Ramanujan is awesome,” said senior Brian Tennyson, who also attended the lecture. “It is incredible that the work he did during his illness is still applicable to mathematics research today, even at the undergraduate level.”
The next NS&M Colloquium lecture will be held on Nov. 3 and will discuss protein regulators during squid embryonic development, followed by a lecture on the H1N1 virus and potential influenza vaccines on Nov. 10.