July 28, 1991|By Rachel Nowak

THE MAN WHO KNEW INFINITY:

A LIFE OF THE GENIUS

RAMANUJAN.

Robert Kanigel.

Scribners.

438 pages. $27.95. "The one truly romantic incident of my life," said Cambridge don G. H. Hardy of his collaboration with Ramanujan, the self-taught mathematical genius from India. It was a collaboration that began in 1913 when Ramanujan, then an unknown office clerk at the port of Madras, sent Hardy an envelope stuffed full of intriguing mathematical formulae. It ended a short seven years later, with Ramanujan a Fellow of the Royal Society and of Trinity College, Cambridge -- and dead, at 32 years old.

In "The Man Who Knew Infinity," biographer Robert Kanigel -- who teaches in the Writing Seminars at Johns Hopkins University -- describes in poignant detail how fat, innocent, lovable Ramanujan doggedly strove to have his mathematical gifts recognized. When he gained recognition, it far exceeded his wildest expectations, leading him to Cambridge, England, for several intense creative years of math research; to emotional and physical burnout; and then back to India, sick and cantankerous, to die.

Ramanujan, as an orthodox Hindu, was forbidden to cross the sea in the first place. He did travel to Cambridge after initially refusing to do so, and that transgression led many relatives to boycott his funeral.

Religious conviction was just one of numerous barriers that threatened to stop Ramanujan's genius ever being tapped. As a poor clerk, his contact with other mathematicians and access to contemporary mathematical texts were severely limited. (Indeed, on several occasions he discovered afresh mathematical truths already ensconced in standard texts -- some for over a century.) Consequently, Ramanujan was totally unschooled, and his mathematical methods -- even in terms of the symbols he used -- were bizarre. In Ramanujan's unorthodox approach lay both his major hurdle to recognition and also his brilliance.

When Hardy first clapped eyes on Ramanujan's theorems his reaction was total bewilderment. "I have never seen anything in the least like them before," he wrote. Similar reactions had led two Cambridge mathematicians to dub Ramanujan a crank, unworthy of patronage. Fortuitously, Hardy, after doing battle with his own ingrained skepticism, realized that the formulae could have been written only by "a mathematician of the highest quality, a man of altogether exceptional originality and power."

Pure mathematicians, like Ramanujan, invent theorems, represented by formulae, that say something interesting about numbers -- for example, they might predict the pattern of occurrence of prime numbers as you count from 1 to infinity. Then by means of a proof, usually a long, intricate manipulation of symbols, they attempt to demonstrate that the formulae is true, that it is invariable.

Once proven, the theorem can be used as a tool to tackle other mathematical problems. The proof can require inordinate technical proficiency, fancy footwork as it were. But it is the invention of the theorem that requires the creative insight, the flashes of inspiration.

Creative insight was Ramanujan's forte; proofs were not. Hardy, on the other hand, was a stickler for watertight proofs, for what mathematicians call "rigor." Theirs was a remarkable combination of talents, leading to numerous stunning discoveries and an enduring mathematical legacy.

But Ramanujan suffered from the unique collaboration. Mr. Kanigel portrays Hardy as a hard taskmaster, insensitive to Ramanujan's needs in any other sphere but math. Ramanujan, brought to Cambridge at Hardy's urging, and largely dependent on him, suffered both emotionally and physically.

He attempted suicide. He became malnourished -- food for a vegetarian Hindu diet was scarce in wartime England, and in any case, consumed by math and his desire to please Hardy, he scarcely had time to eat. Ramanujan contracted tuberculosis and died. To this day, mathematicians ponder what further mathematical heights Ramanujan would have soared had he been discovered a few years earlier, or lived a few years longer.

In the final chapter, Mr. Kanigel bemoans the fate of all non-mathematicians, who, unschooled in the language, are destined to appreciate Ramanujan's work only indirectly, to "sit on the sidelines and, on the authority of the cognoscenti, cheer."

But Mr. Kanigel does not do himself justice. Without breaking story-telling step, he neatly demystifies symbols such as the surprised-looking X!; explains how theorems are conceived, proved and used; and describes how number theory -- a major part of Ramanujan's work -- seeks out the patterns and properties of everyday numbers.

Because he refuses to sever Ramanujan's life from his vocation, Mr. Kanigel provides a ripping good biographical yarn, as well as glimpses of the "richness, beauty, and mystery -- [the] sheer mathematical loveliness" of Ramanujan's work.

Ms. Nowak is a writer living in Washington.