The Man Who Knew infinity
Mon Sep 7, 2015
The Man Who Knew Infinity
Washington Square Press (June 1992)
The many gifts of Robert Kanigel are on display in his wonderful book about the life, death, and legacy of the great Indian Mathematician Ramanujan. More than a straightforward biography, Kanigel has used his talents to weave a remarkable tale that conveys the lifestyle and culture of early 19th century Britain and South India and that delve into the early, formative years of the main protagonist and his mathematical patron-partner G.H. Hardy while also conveying something beautiful about the mathematics that made this rags-to-intellectual-riches story possible. In Kanigel’s words, writing the book required overcoming the “barriers of two foreign cultures, a challenging discipline, and a distant time,” making the florid outcome all the more impressive. It seems that being a foreigner to England, to India, and to Math aided him in being able to describe these worlds to the reader. The reader is left with a visceral feeling of the material and social pressures that shaped the two men; can percieve the deep cultural divide facing an Indian transplant to England in the early 1900’s and is led to comprehend the strong draw of mathematics in the lives of two individuals whose lives were given sustenance by ideas most can never comprehend.
Ramanujan and Hardy
As I have just given the book a resoundingly positive review I suppose I should convey a bit about why I enjoyed it so thoroughly. Part if it is the romantic story of Ramanujan - a buoyant boy whose genial-genius is recognized but completely unsupported but who manages against steep odds, to nonetheless secure recognition and celebrity of the highest order. So the story itself is compelling. But Kanigel’s treatment of his characters draws out interesting questions about these two men and their relationship to mathematics, to one another, and often highlights a theme that plays a recurring role in his writing: what is the nature and source of creativity in science and math? His book about creativity and scientific lineages in the biomedical sciences ( Apprentice to Genius) highlighted how the top scientists has a knack for picking the right answer on a hunch. They would “take a flyer” on this project. Similarly, Kanigel relates how mathematical intuition plays an important role to mathematicians in a way that seems entirely irrational and in a manner that often end up invoking divinity. In a respectable mathematical tradition including Newton and Pascal, Ramanujan would credit his mathematical insight as a gift from the gods, going so far as to give credit to his family’s primary deity, Namagiri, for writing the equations on his tongue. But, in a juxtaposition made for TV (a movie based on this book is pending), Hardy was the polar opposite; a rationalist enemy-of-religion and superstition that bluntly rejected religion where Ramanjuan’s spiritual self in which religious inspiration coexisted peacefully with his mathematical insight without. Hardy laments that some of his happiest moments (of cricket) are to be found “in hearing distance of a Roman Catholic Church,” while Ramanujan weeps when his hair is cut in western style in anticipation of his trip to England.The contrast of men and beliefs is interesting and forms a major theme, especially as the excellent recreations of Hardy’s and Ramanujan’s childhoods evoke such vastly different worlds. Though Hardy takes Ramanujan at his word that he is non-religious and rational, Kanigel’s book seems to suggest otherwise - that the early devotional aspects of Ramanujan’s life put him more in the tradition of Newton or Pascal than the Cambridge circle of devoted atheists Hardy was part of.
This chasm of disbelief in the form of rational men aghast by a contemporary whose religious life seems to peacefully coexist with otherwise fully rational mind brought to mind two recent pairs of men in similar circumstances. The first pair is Oliver Sachs and his cousin, Nobel Laureate John Aumann. As recounted in one of Sach’s last public piece before his death chronicled his reconnection Aumann who was both a scientist and devout Jew. The second pair is from the obituary of the Magician James Randi who was great friends with science writer and skeptic Martin Gardner (blessed be his name) and who was stunned that on his death bed this “rationalist supreme” would allow the existence of an afterlife and find the idea of a personal god comforting and plausible. In these two cases, and in the Hardy-Ramanujan pairing we are confronted with two people who have devoted their lives to the pursuit of truth and may have shared a significant portion of their lives working for common cause in which rationality and science play an important role, but who, at the end of the day, for whatever reason of disposition or history stand apart in some fundament way. I was stunned myself upon learning that Martin Gardner, that guiding light of philosophy and lodestone for clear, straightforward empiricism was not an atheist. I can imagine a similar chasm of understanding between these two towering intellects who were so devoted to the mathematics they shared in common.
Of course Kanigel doesn’t bring out the religious beliefs of H&R simply for show, but rather as part of an exploration on that ineffable aspect of the human mind from which creativity arises. And he is clever about how he does it. Are the burst of creative insight due to religious intervention? Do not many mathematicians and creative scientists describe leaps of intuition that leave them befuddled as to their origin - writing answers their mind’s don’t know of until it is on paper? He recounts many. Do not many great mathematicians (and scientists) attribute their success and genius to divinity, even “divining” answers to solutions? He recounts many. BUT, pace Hardy, why must we jump to divinity when facing the unknown? Cannot something be simply unknown without hazarding that it will be forever unknowable? Kanigel has a light touch and I enjoyed this section a fair bit: “the rational mind can be the most irrational of minds”
The Queen of Sciences.
Although not a mathematician, I can appreciate quantitate analysis and use statistical thinking in my day-to-day work. I suppose all of us in the natural sciences subscribe to the notion laid out by Eugene Wigener that mathematics is indeed unreasonably effective. But effectiveness is not the measure of success of top caliber mathematicians: Hardy had nothing but aristocratic disdain for mathematics that was “useful.” What is it these mathematicians actually DO? Why does it matter? Who cares? Why, a century after his death, does Ramanujuan’s name and work still resonate? Kanigel’s approach to answering these questions is to enter the world of mathematics and to try to introduce the ideas and problems of numbers, to introduce us to mathematics as the mathematician sees it, to glimpse the “true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, [that is to be ] found in mathematics as surely as in poetry,” as Bertrand Russel put it. This is not an easy task though I give Kanigel credit for trying.
Kanigel spends his greatest effort in walking through Ramanujan’s work on “partitions” - or the manner in which numbers can be factored. This section is enjoyable and allows you follow a bit but still necessarily leaves one out in the cold on the power and originality of Ramanujan’s intellect, requiring us to take it on good authority. On Hardy’s scale of raw mathematical talent he rates himself a 25, Littlewood a remarkable 30, and Ramanujan an otherworldly 100. Even if one does not understand the particulars a reader can still feel the infectious power that the love of math had in Ramanujan’s life, and in Hardy’s. The excitement of proving something if palpable as is the grasping, frustrating battle with the problem that precedes victory. The trial and error of trying to prove a formula seemed similar to the old saying that science is the act of going down alley’s to see if they are blind. In describing Ramanjan’s approach to Math we also get a sense of his mental agility and of the humbling effect he had on other mathematicians who followed him. I doubt that this book will be a popular-science gateway drug to mathematics that Ian Stewart’s books’s might be, but the effort expended in explaining math solidifies the story, giving a much deeper insight into the mania of H&R in their work together and strengthening the supposition that only the “cold and austere” field of Mathematics could a largely self-made genius be recognized as such, if only barely and at great cost. We can glimpse, even if we cannot understand, that subject that allowed a man to fulfill his destiny against odds, and to appreciate that the mathematical world was to Hardy, and likely to Ramanujan as well, the “the one great permanent happiness of my life.”
A Few Notes
The book has a number of really nice asides. My favorite is the origin of the term “POSH” which means rich/flashy and comes from a section of the British-to-India voyage through the Red Sea where unforgiving sun blasted the ship and in-the-know passengers secured the shade-side rooms which were “Port-Out; Starboard-Home”.