Far beyond ‘how many?’

I have been reading a novel, The Death of Vishnu, by Manil Suri. It is a novel set in India and revolves around a man named Vishnu who does odd jobs for tenants in a building and sleeps in the landing of the stairs. Reading it makes me enter the world of Vishnu and his dreams. I have had it for some time but I only noticed that it won the Discover Award and a finalist for the PEN and Faulkner Award. But the real revelation was that the author is a professor of mathematics at the University of Maryland.

I told a mathematician I know about Manil Suri and his novel. He was not at all surprised that a mathematician like Suri would write a novel. He said that knowing something deeply in any field, such as math, brings you to recognize the powers behind the knowledge but also, its limitations. Trysts with one’s own literary imagination forms part of a novelist’s romance and easily lends itself to recognition – like a blush. But that kind of romance does not inhabit mathematics. If not, then, what does mathematics give us and what does it tell us about who we are and our possibilities as human beings? I wanted to find out so I had coffee with a mathematician.

Dr. Joey Balmaceda, a professor of mathematics at the University of the Philippines, says mathematics is innate in all. He says all kids find it irresistible to count and stare and figure out various shapes even at a very early age. I guess this is why when Dr. Balmaceda and I had a chance to work together to train teachers (I did their training in science and he did theirs in math), I saw his teachers come out of their rooms with folded papers in different shapes, clipped on their heads.

So what happens between that stage when we seem to be such natural mathematicians and now, when most of us are repelled by the idea of doing any kind of math? Dr. Balmaceda says it usually starts at Grades 4 and 5 when the kids begin to encounter sets of rules to do mathematics. This is when the ones inclined to do math begin to be winnowed from the rest. He cited that some cultures, particularly the French, think that mathematics is not for all and so only concentrate on the few who could, and train them intensively. And yes, the French are known to be excellent in mathematics.

So maybe some are really wired to be mathematicians and some are not. Dr. Balmaceda thinks that even if we cannot all be mathematicians, an appreciation of mathematics should be open to all. After all, he said, mathematics evolved in the social, cultural, political, religious context. We needed not only to count but know what the numbers mean in the context of specific purposes – such as in times of war, dividing the harvest or elections. He said that the evolution of math in the history of the human mind is also seen in the philosophers who were then philosophers, scientists and mathematicians rolled into one. Now, mathematicians and scientists collaborate to understand nature better. In crystallography, where X-ray is used to take a look at molecular structures, math comes in to understand the molecular arrangement by using group theory. Beyond the double helical structure, when scientists look at the knotted nucleotide bases of ATCG, mathematics unravels a better understanding with its knot theory. And now that we are now moving on from the genome (genetic map) to the proteome (the map of the proteins which genes code for), mathematics enters to help with its understanding of "small world networks." They are coming together again – mathematics and science, each with a better understanding based on the rigor of each of their fields.

Dr. Balmaceda dispels the popular misconception that math is only about quantities (how many). He says that what most fail to see is the creative aspect of mathematics, how they unravel an aspect of truth, by using the logic of numbers, However, this "truth" he speaks of has nothing to do with ancient beliefs about how to live our lives. It has to do with abstract concepts that flow with the deep logic of mathematics. To mathematicians, "truth" is what you arrive at, given a set of assumptions. This "truth" changes when you change the assumptions. In science, it is similar in the sense that there are no absolute truths. Truth is something tentative – we hold on to something right now because overwhelming evidence has said it is the correct view at this time. It could change. It could not. It all depends on the evidence and testing.

Both science and math, however, require the rigor that most do not really want to get into. In October 2006, a study by the Brookings Institution’s Brown Center on Education Policy found that the nations whose school kids scored the best in math, have students who claimed that they are not happy doing it. This turned the good old beliefs in education that when kids are having fun learning, they will do better. It turns out that when it came to learning good math and demonstrating it, you need not be happy doing it.

I think that happiness and learning math in school is not a conscious link that those rare minds who choose mathematics as their life’s work, like Dr. Balmaceda’s, forge. I think these minds are really especially wired to take math to the reaches that they do, beyond mere popular puzzles and card tricks. Take, for instance, Grisha Perelman, a brilliant Russian mathematician who has been most vehemently resistant to the trappings of fame. He is the man who solved the Poincare Conjecture, one of the Millennium Questions (another mathematician, Richard Hamilton started to solve the problem and Perelman completed it.) The Millennium Questions are seven mathematical problems that have eluded solution for at least a hundred years and for which the Clay Mathematics Institute are prepared to give $7 million for those who can solve them ($1 million for each problem). The rest of the six questions are: Birch and Swinnerton-Dyer Conjecture, Hodge Conjecture, Navier-Stokes Equations, P vs NP, Riemann Hypothesis, and Yang-Mills Theory. Some will have implications in physics if proven.

If and when these problems get solved, we would still have to get up in the morning and work and eat. In other words, the world will go on, and in an overwhelming majority of lives, about the same as before the millennium problems were solved. But for these mathematical minds, they would have pushed the rock further uphill in our journey of intellectual possibilities. They would have also demonstrated that apart from the tantalizing roles of numbers in elections, marketing and stock exchanges and personal bank accounts, there is something also uniquely romantic about tracing the elegant flow of nature’s logic with the combing sway of a mathematical mind, even without million dollar prizes. It elevates what is so ordinary about the counting human. There, I think, is where lies, the real power of numbers.

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