I was honored to discover that the July 2015 issue of Prabuddha Bharata magazine, illustrated above, had run a two-page review of MWA, under the byline of Swami Vidyanathananda. But I was also puzzled until I figured out that Swami Vidyanathananda is also the mathematician known as Mahan Mj, or Mahan Maharaj, a distinguished specialist in hyperbolic geometry who teaches mathematics at the Ramakrishna Mission Vivekananda University at Belur Math, where he lives as a monk. (It shouldn’t be necessary to mention that “Math” in “Belur Math” has nothing to do with mathematics.) The Times of India published a nice interview entitled “Vidyanathananda, the wizard who became a monk,” when the wizard in question won the Shanti Swarup Bhatnagar Award for mathematics in 2011.
Our paths crossed a month or so later when we both spoke at a conference at the Tata Institute of Fundamental Research in honor of Raghunathan’s 70th birthday. At the time I had just discovered the philosophy of Nagarjuna (I don’t remember how) and was looking for confirmation for my suspicion, which developed into one of the underlying themes of Chapter 7, that the fundamental antinomies of western philosophy of mathematics — realism vs. nominalism, discovery vs. invention — would look very different, and less fraught, if approached from the standpoint of Indian metaphysics. I tried to explore the question with a few of my Indian friends at TIFR but in retrospect it’s clear that I should have asked Swami Vidyanathananda.
The review in Prabuddha Bharata is very flattering — when it calls MWA “at times refreshinly irreverent,” for example — and I’m pleased to see that its author and I have much in common with regard to the nature and goals of mathematics — or, to quote the review, “the What, Why, and How of it.” This passage about Chapter 7, for example, is very much in line with my intentions:
There are a couple of analogies that might help to clarify. One from religious hagiology—thenotion of an avatara; and one from philosophy— the idea of Plato’s cave. Both suggest an ideal or a hidden structure one would like to uncover, while at the same time admitting that what one has in hand are only vague suggestions. But these vague suggestions are not less valuable as they tend to give us direction in uncovering some tantalising mystery that remains at the core of certain phenomena. This mystifying yet deliciously tantalising aspect of mathematics is what leads the human mathematician on and adds to its romance and adventure.
Swami Vidyanathananda does allude to the chapter’s dominant metaphor, borrowed from Grothendieck, of the avatar, but doesn’t mention Nagarjuna. No doubt this is a delicate way of letting me know that my attempt at mobilizing classical Indian metaphysics is as hopelessly naive as one might have expected. I do hope that the theme is pursued by someone more knowledgeable.
Lest the reader suspect me of concealing a religious agenda, I quote the relevant passage in the preface:
One of the most exciting trends in history of mathematics is the comparative study across cultures, especially between European (and Near Eastern) mathematics and the mathematics of East Asia. These studies, which are occasionally (too rarely) accompanied by no less exciting comparative philosophy, is necessarily cautious and painstaking, because its authors are trying to establish a reliable basis for future comparisons. I have no such obligation because I am not trying to establish anything; my knowledge of the relevant literature is second hand and extremely limited in any event; and the allusions in the middle chapters do nothing more than provide an excuse to suggest that an exclusive reliance on the western metaphysical tradition (including its anti-metaphysical versions) invariably leads to a stunted account of what mathematics is about. In the same way, the occasional references to sociology of religion or to religious texts are NOT to be taken as symptomatic of a belief that mathematics is a form of religion, even metaphorically. It rather expresses my sense that the way we talk about value in mathematics borrows heavily from the discourses associated with religion.