In a new film now out on Netflix and iTunes, The Man Who Knew Infinity, Dev Patel plays math genius Srinivasa Ramunujan. From a town in India and with limited formal training in mathematics, Ramunujan made contributions to Number Theory and infinite series that are still used by mathematicians today. After Ramanujan drafted letters to leading mathematicians at Cambridge University, he spent nearly five years in Cambridge studying with famous English mathematician G. H. Hardy before he tragically contracted tuberculosis and died at the age of 32.
The film The Man Who Knew Infinity is touching and brings Ramanujan’s personal story to life, but if you’ve watched the film you may be wondering exactly what Ramanujan discovered and why his work is considered so extraordinary today.
To shed light on Ramunujan’s life as a mathematician, we talked to LSU mathematician Karl Mahlburg, assistant professor in the Department of Mathematics. Mahlburg’s research is also focused on Number Theory.
“Ramanujan has also certainly had a large influence on me personally; almost all of my mathematical activities owe a debt to Ramanujan.” - Karl Mahlburg
LSU College of Science: What does the title of the film refer to? Did Ramanujan work on mathematical equations that deal with infinity?
Karl Mahlburg: Mathematics is a basic language of science. This means that we cannot describe, measure, or understand natural or scientific phenomena without using mathematical language. When a mathematician discusses "infinity," this is not just an abstract idea, but rather refers to a way of modeling large-scale or long-term behavior.
So yes, one of the reasons that Ramanujan is often referred to as "the man who knew infinity" is that he demonstrated incredible skill in understanding these limiting behaviors. For example, he developed a theory for efficiently constructing very large networks on which it is easy to communicate; today these are known as "Ramanujan graphs" (see below). Modern mathematicians continue to be amazed that Ramanujan was able to develop his incredible insights while working in isolation, without access to even a major library, let alone modern computers!
LSU College of Science: In the film, Ramanujan was quoted as saying, "Imagine if we could look so closely we could see each grain, each particle. You see there are patterns in everything." How does this analogy relate to math? Are there really patterns in nature that can be solved with math?
Karl Mahlburg: In one sense, this quote is simply meant to illustrate the character of a brilliant mathematician like Ramanujan - that he is constantly driven to seek meaningful patterns and order in the world. However, this quote also has a deeper purpose, which is to highlight that the development of mathematics has always been intertwined with applications in other sciences, industry and military.
For example, some of the early developments in calculus arose from attempts to mathematically model the trajectories of cannonballs and other ballistics on the battlefield, where it is vital to understand the effects of a small change in angle or the amount of gunpowder. As another example, although an unexpected storm can still ruin plans, weather forecasting has actually improved significantly in recent decades. And this is mainly due to significant advances in mathematical modeling of turbulent systems, rather than improvements in radar.
LSU College of Science: In the film, Ramanujan is frustrated by having to spend time on proofs to publish his work as opposed to thinking of and working on new equations. How does this relate to how mathematics is done today? Is there opportunity still for mathematicians to "dream" new equations to solve unsolved problems?
Karl Mahlburg: A famous quotation of Thomas Alva Edison states that "[g]enius is one percent inspiration, ninety-nine percent perspiration." This is absolutely true of mathematics, where the "inspiration" might involve a feeling that a striking claim is true (say, that there are infinitely many prime numbers) and the "perspiration" involves writing down a proof, which is a careful logical argument that will convince any other scientist of its truth beyond a shadow of a doubt.
The "inspiration" is what Ramanujan was referring to, as it can be tedious and painstaking to record mathematical results in a formal proof. Mathematics is a living, active science - for example, no one would have thought to ask questions about efficient ways to transmit data over a network of a billion computers before the development of the internet, and this has led to rich developments in the mathematical field of Graph Theory. "Inspiration" is certainly still a vital part of mathematics!
LSU College of Science: What is your favorite aspect of Ramanujan's life story or mathematical work?
Karl Mahlburg: I think Ramanujan's basic life story contains an inspiring message for anyone, scientist or not. He was a man of humble origins and limited opportunity, but he had an unbreakable passion for mathematics. Moreover, he had the courage to leave his home and sacrifice everything for his dream, which resulted in him becoming one of the greatest mathematicians history has ever known.
LSU College of Science: How are Ramanujan's equations being used today? Do you use any of his equations in your mathematical work?
Karl Mahlburg: Ramanujan's contributions to mathematics absolutely remain relevant today. His highly original ideas inspired entire mathematical research areas throughout the twentieth century, including Additive Number Theory, Modular Forms, Integer Partitions, and Graph Theory. For example, mathematicians have recently used "Ramanujan Graphs" (which are based on his ideas) as a model for network communication, which has led to more efficient data transfer on the internet.
Ramanujan has also certainly had a large influence on me personally; almost all of my mathematical activities owe a debt to Ramanujan. I have also had the great privilege of visiting Kumbakonum, India as an invited speaker at a conference in Ramanujan's honor. While there we visited Ramanujan's home, which is now a museum, as well as the Hindu temple where he devoutly spent many hours, frequently doing mathematics on his small slate. It was very humbling to have a first-hand view of the circumstances of Ramanujan's life, and also inspiring to realize that I could nevertheless share in his mathematics.
LSU College of Science: What does your own mathematical research involve?
Karl Mahlburg: My research is primarily focused on an area of mathematics called Number Theory. At its most basic level, this subject has grown from the study of counting numbers (1,2,3, ...) and arithmetic. A fundamental property of the counting numbers is that they factor into fundamental building blocks called prime numbers, which are numbers like 2, 3, 5, 7, 11, and 13, numbers that cannot be factored [“broken down”] any further. For example, the prime factorization of 442 is 2*13*17.
It is a famously difficult problem to find the prime factorization of a very large number such as 234,177,800. Even with today's fastest computers, it is almost impossible to factor a 100-digit number in a reasonable amount of time.
Number Theory continues to be an area of active research because these simple ideas from arithmetic have proven to be fundamentally important for modern computer security and cryptography, which is the study of secure communication and secret codes. In short, the data that you store on your computer or enter into a website on the internet (such as a credit card number) is typically represented by a large number. In order to safely transmit this data, it is "encoded" by performing a mathematical operation similar to multiplying by very large prime numbers. As mentioned above, it is very difficult for a hacker to factor this product and recover your data, but (with some additional mathematical theory) it is actually possible for your bank, for example, to have a secret factorization "decoder" so that your financial data is communicated.
LSU College of Science: What is your favorite mathematical equation and why?
Karl Mahlburg: Most mathematicians or scientists would find this to be a difficult question to answer! If I were constantly fixated on a single idea, I would neither enjoy nor be successful in my career; instead I am constantly getting excited about learning new things, and then sharing them with others. In fact, when I teach freshmen or sophomore level courses I like to incorporate "Math Fun Facts" at the beginning of most lectures in order to share my own enthusiasm.
To share an example of a Math Fun Fact, it turns out that cicadas (yes, everyone's favorite buzzing pest) have “learned" to do Elementary Number Theory! Each species has a life cycle in which they only hatch after fixed number of years, such as 13-year or 17-year cicadas. These cycle lengths are prime numbers, which are positive integers like 2, 3, 5, 7, 11, etc., that are not divisible by any other number. These prime number cycles are vital for minimizing competition amongst different species. Why? Suppose that there were non-prime cicadas, such as 12-year and 18-year cycles. Every 36 years they would both be active at the same time, which would cut the available food supply in half. In contrast, the 13-year and 17-year cicadas only overlap every 221 years! And it is a provable fact from Number Theory that prime-number cycles are the best choice.
LSU College of Science: Your PhD advisor was the chief mathematical consultant for the movie The Man Who Knew Infinity, which is very exciting. Is there much opportunity in mathematics to help media and film organizations "get the science right"?
Karl Mahlburg: For anyone in a specialized professional field, it is always a challenge to accurately represent the nature of the work to the general public - ask any lawyer for a list of the inaccuracies in TV courtroom dramas! In the case of the film, Professor Ken Ono of Emory University was the mathematical consultant (and he was indeed my Ph.D. advisor when I attended graduate school at the University of Wisconsin-Madison). I am happy to report that by his account the producers and actors were very receptive to his input, and the result is a portrayal that is very accurate mathematically (even including some of Ramanujan's rare and infamous mistakes!) Furthermore, the actors Jeremy Irons and Dev Patel spent some time in their character studies learning to appreciate mathematical proofs.
I would like to close by turning this question around. As much as it benefits math and all sciences to have positive, accurate portrayals of our research activities in popular and news media representations, it is also the responsibility of the scientific community to effectively communicate the value of what we do, including direct economic impacts of new technologies, practical training in critical and quantitative reasoning, and the long-term value provided by an educated workforce. I hope that by participating in this Q&A I have helped in some small way by highlighting the inspiring story of Ramanujan's life, and the lasting impact of his mathematics.
Check out The Man Who Knew Infinity on Netflix and let us know what you think! Does the film and this Q&A make you think about math differently?
Enjoy getting a science-based "behind-the-scenes" look at your favorite movies? Join us for a tweet-a-science-movie night at the LSU CxC Science studio on Nov 1, 2016! More details here.