If you’ve ever attended or sat in on one of Santosh’s classes, you know that the manner in which he teaches and explores the topic of probability is not the same manner in which many other math and science classes are taught in. In your introductory calculus course, a general lecture may follow a simple path of the form, “Here is a theorem, here is the proof of the theorem, here is how to use this theorem to solve different kinds of problems”. In a class taught by Santosh, a large portion of each lecture is spent motivating the idea behind the topics that will be discussed during the rest of the lecture. These motivations may include historical expositions, intriguing thought experiments, or personal anecdotes. In many cases, Santosh poses questions that directly relate the topic to events that affect our lives every day in both obvious and subtle ways.
By the time you actually start diving into the work of trying to find an answer to the question, the importance of the question is clear, and you are fully invested in traveling down the path that the problem may lead you. As Santosh guides you to the solution, the answer to the initial question arrives sort of obvious. The rest of the class is spent discussing the implications of our answer, and you leave feeling like you’ve learned more than just math. While the lucid style of Santosh’s teaching may suggest that his path to becoming a well-known probability researcher and professor was very certain. This is not at all the case.
Santosh grew up in Kerala, a state in South India. While neither of his parents received a formal education, they ensured that he was able to attend school. “I was extraordinarily fortunate to be born into a good caste system. My parents weren’t really well off. But I had a great childhood.” Back then, he didn’t spend much of his childhood thinking about math and probability. “I would finish all my homework during school so I could come back and play soccer. I played soccer almost every day.” Regardless of his parents' financial struggles, Santosh remembers being a very happy child. Santosh recalled a particularly sweet memory from his childhood.
“When I was very little, my grandfather would take care of things behind the scenes when my father was struggling. He would take me out for walks. Once, he bought me peanuts that had just been heated up over a coal fire. This was a real treat. I would eat the peanuts one by one to savor them. But this was a real treat you see, because the street vendor would put these hot peanuts in a small little cone made out of newspaper. So once I ate the peanuts, I would unwrap the cone, and read everything on that sheet. I would read it over and over again until I memorized it. It is amazing how little it takes to keep a child happy.”
When it came time for him to attend college, he was admitted to St. Xavier's college. He was asked by a professor at the college to choose one of the following tracks: commerce, arts, or mathematics and science.
“That really flummoxed me. I had no conception of what these things meant. I ruled out business immediately because I am a South Indian Brahmin, and we have no business people in our family. Commerce also sounded vaguely like adding up things under candlelight, and that sounded boring. I had always liked arts, and the tapestries of history. Maybe I could become a writer or a journalist! And math… I had always liked math. But I had never done anything beyond basic algebra. I mean it sounded neat, I just didn’t have much of an idea about what math was. I had heard of Einstein and Ramanujan, and what they did sounded cool. I was in an agony of indecision. I could tell the professor was getting impatient and irritable. So in desperation, I reached into my pocket and found a quarter. I said, ‘heads was math and tails was art’. It came out heads. So I chose math. And that's how I ended up studying mathematics.”
It’s interesting to think that a fair coin flip may have determined one of two very different paths for Santosh’s life. However, this uncertainty doesn’t bother him. Many of his students have asked him what he would have done if the coin had landed on the tails side.
“So, what! Look. Natural selection has designed us to not be single purpose entities. We are not designed by natural selection to be bayonets. A bayonet has one function: to poke a hole in someone and kill them. We are more like swiss army knife. We are designed by natural selection to do many things competently, and enjoy those things that we do competently. So if the coin had come up tails, I would be teaching history. Worse could happen.”
While Santosh enjoyed his first two years of college, the prospect of studying for two more years to get his professional degree hadn’t really crossed him until one of his close friends signed him up for the entrance exam for the Indian Institutes of Technology, one of the most well-known engineering universities in India. “I went to my chemistry teacher, who told me I should do this. I asked him, ‘What is this?’ He told me it was an entrance exam for engineering. I said, ‘No, no, no’. To me, engineering sounded like getting underneath a car to fix it and getting all greasy. I did not like grease. Fortunately, he convinced me to take the test anyways.”
Santosh’s test scores gained him admittance to IIT. After attending and graduating from IIT, Santosh decided to attend Caltech to study physics and math after speaking with his advisor at IIT. “Today, you know, it’s foolish. I was operating largely out of uncertainty. I was just going whichever direction life offered me.” At the end of his Caltech education, he ended up at Penn to conduct research and teach about topics related to probability theory.
At Penn, Santosh has focused on a wide range of problems related to probability theory and its applications. These problems range from attempting to answer why our current society is so politically polarized using tools from the theory of spin glasses to trying to figure out how to encode information about a sequence of several Bernoulli trials using one bit of information. One particularly interesting problem Santosh worked on was related to genomic research.
“One day a gentleman by the name of Alon Orlitsky, popped his head into my office and asked if I had a moment to speak with him about a problem in genomics. I didn’t have much of a clue about genomics, but it turned out I didn’t need to. He was curious about how information is encoded in the genome. Well, I asked him a particularly dumb question. I have a propensity for blurting out dumb questions. I asked, ‘How many folds are there in a strand of RNA?’ He replied, ‘Uh, I don’t know’. That wasn’t a question a biologist might usually ask, but it was a question a mathematician might ask. So, we started scribbling on his kitchen table. And we had so much fun, we discovered a lot of structure and wrote a paper on it. I think it was published in the National Academy of Science.”
Santosh never really felt like he was doing work. From his perspective, he has spent his whole life playing, whether it be playing with a soccer ball or playing with an interesting probability question. This approach to playing has also paid off when teaching his students.
As a teacher, Santosh feels that is very gratifying to share the same sense and enthusiasm and excitement he has about probability with his students.
“I enjoy teaching. On a surface level, I am not an incompetent teacher, which helps. But more importantly, there are times when really try to articulate a beautiful concept to a student. Every once in a while, I can see that they see the same beauty in the subject as I do, This is immensely satisfying. If I can make even one student feel this way, then I feel like I have contributed to something.”
Santosh’s himself admits that much of his life's trajectory was governed on grasping whatever uncertain choices life presented to him. As college students, we spend a lot of time trying to figure out what we really want to do. We worry about the fact that walking through an open door may inherently close another door. In regards to these concerns, Santosh provides the following words of wisdom.
“Today’s stresses are stresses of choice. If you have no choices, you just have to do what is given to you. Life doesn’t owe you a comfortable living. You do what is necessary. This is the way I grew up in. If you have choices, how do you know what to do? The best thing you can do is make the best decision possible given your limited information. Talk to students and researchers in various disciplines, take classes, google search your interests, and talk to your parents.”
Santosh argues that you should maximize the amount of information you have to work with so you can make the best possible decision. However, he also argues that at the end of the day, it doesn’t really matter.
“In situations of choice, the difference between zero and one is infinite. No jobs to one job. The difference is infinite. However, the difference between one and two or more is very large, but bounded. You guys have choices! Remember, we are swiss army knives. Pick something, and do your best at it. Everything will work out. There is no use in pondering about the alternate paths your life could have taken if you made a different decision. And if you find things are at a dead end and you can’t seem to make a decision, go ahead and toss that coin.”