When Your Number’s Up : THE MAN WHO KNEW INFINITY: A Life of the Indian Genius Ramanujan, <i> By Robert Kanigel (Charles Scribner’s Sons: $27.95; 427 pp.)</i>

Had Srinivsa Ramanujan Iyengar excelled at music, literature or art, perhaps he would have been a household name today, seven decades after his death at 32. But because he blazed new trails in a field that is far beyond the imagination of the masses--numbers theory--the name Ramanujan (Rah-MAH-na-jun) is familiar only to hard-core theoretical mathematicians, and even then, mainly because of the Indian’s affiliation with his equally eccentric mentor, early 20th-Century British mathematical giant G. H. Hardy.

At the core of Robert Kanigel’s “The Man Who Knew Infinity” is the bizarre relationship between the young Hindu clerk and the Cambridge fellow who recognized and nurtured his incredible talent. It’s a story at least as compelling as Brian Epstein’s discovery of the Beatles, but in order to argue that the results were as far-reaching, one would have to look not to pop culture but to such esoteric topics as particle physics, computer science and space travel--all, curiously, endeavors that were nonexistent in Ramanujan’s lifetime.

Besides, as Kanigel makes clear, Ramanujan (and Hardy) were purists--any practical application for their complex equations was extraneous to the pursuit of mathematical truths for their sheer beauty alone. For Ramanujan, it was an exploration so monomaniacal that it cost him his health and, ultimately, his life.

Ramanujan’s tale is the stuff of fable--child prodigy who leaves his home (India) and family to seek a guru (Hardy) who provides sustenance for his astonishing intellect, even as a foreign land and culture (World War I Britain) destroys his soul, spirit and body, striking him down at the very height of his powers.

What enriches their drama is their wildly dissimilar backgrounds and personalities, merging only at the nexus of their shared fascination for numbers. Though Hardy arranged for Ramanujan to work daily under his tutelage at Cambridge, theirs was truly a meeting of the minds--and little else. Therein lies both the biography’s chief weakness and strength. We yearn to learn more of this odd couple’s interrelationship; yet, it becomes clear, we end up learning far more about Ramanujan’s thoughts, beliefs and dreams than even Hardy himself ever did.

Kanigel paints an exquisite portrait of Ramanujan’s privileged boyhood as a member of the learned Brahmin caste. A gifted student, he quickly surpassed his classmates and even his teachers. It wasn’t until he was 16, however, that Ramanujan became infatuated with mathematics, having stumbled upon a textbook with thousands of rote equations that he set out not to memorize (as was intended) but to prove and expand upon. This led to one of the many curious ironies and dualities that envelop his life story: As he delved exclusively into math, Ramanujan abandoned his other studies, endangering his scholastic career. Flunking out of school, however, provided him the precious time that enabled him to develop his math prowess.

It was only because Ramanujan, mired in a clerical job, reached out to Hardy in a carefully crafted 10-page letter--and that Hardy responded to his plea for recognition--that his work is even available to us today.

Hardy not only lured Ramanujan to England, he brought him to the world’s attention. “It is not just that he discerned genius in Ramanujan that redounds to his credit today: It is that he battered down his own wall of skepticism to do so,” writes Kanigel. “That Hardy’s impressions of Ramanujan would be so relentlessly quoted, and would go so far toward fixing Ramanujan’s place in history, owes not only to his close relationship with Ramanujan but to the sheer grace with which he wrote about them.”

In the ensuing years, the intellectually stimulated Ramanujan kept the notebooks containing “thousands of theorems, examples, corollaries” upon which his fame rests. These notebooks, writes Kanigel, “would frustrate whole generations of mathematicians, who were forever underestimating the sheer density of riches they contained.”

Hardy coerced his pupil to amplify his amazing, spiritually rooted intuitive abilities with the discipline of hard, rigorous proof--the stuff of modern science. By Kanigel’s reckoning, this may have been the professor’s greatest achievement: “Hardy brought Ramanujan mathematically up to speed without muzzling his creativity or damping the fires of his enthusiasm.”

Sadly, Ramanujan did not prosper in chilly England. Forced to Westernize his hair style, his wardrobe, his mannerisms, he finally succumbed to culture shock. As he became more obsessed with math, he eschewed meals, sleep, human contact. As he valiantly tried, for religious reasons, to adhere to vegetarianism, he deprived himself of fresh air and sunshine. Before long, he was committed to a sanatorium, afflicted with tuberculosis, increasingly prone to misery and emotional instability.

Bitter and quarrelsome in his final years, Ramanujan even attempted to throw himself in front of a train. His was a self-destruction rooted not in excess but in asceticism. But even as his physical health deteriorated, he was pioneering the discovery of third-order mock theta functions. Sullen, angry, more temperamental than ever, Ramanujan worked rabidly until the bitter end. He died a hero in his country--the Einstein of India--at age 32.

Even today, the world’s most erudite numbers theorists still puzzle over Ramanujan’s fabled notebooks, marveling not only over the unfulfilled promise of what could have been--Hardy compared him with Euler and Jacobi, the most towering mathematicians of their ages--but over what is right there on the page. As recently as 1974, a Belgian mathematician proved Ramanujan’s tau conjecture--a milestone of 20th-Century mathematics. Kanigel compares the 1976 discovery of a “lost notebook” to the hypothetical discovery of Beethoven’s Tenth Symphony. And in the past decade alone.

Kanigel’s richly detailed road map to strange, wondrous, foreign cultures--not just British and Indian but also the culture of higher mathematics--makes for the rarest of literary experiences: a compendium of challenging philosophical ideas that is actually a compelling read. He expertly intertwines the details of Ramanujan’s odd, doomed life with his soaring professional accomplishments, a task that would naturally come easier to the biographer of, say, a Pablo Picasso or a Jim Morrison, or anyone whose output we could filter through our primary senses. Indeed, the metaphor of mathematician as artist is pervasive. As a student, writes Kanigel, Ramanujan built “an intimacy with numbers (just as) the painter lingers over the mixing of his paints, or the musician endlessly practices his scales.”

There’s not enough math here to appease or enlighten even an MIT undergrad--the first quarter of the book is equation-free--but there is just enough to intimidate the uninitiated. A patient tour guide, Kanigel walks us through concepts as complex as infinite series while retaining a proper sense of wonder at the mysteries that still remain beyond our reach.

“What Ramanujan did will live forever,” concludes Kanigel. “It will not, to be sure, live in the hearts of the masses of men, like the work of Gandhi, Shakespeare or Bach. Still, his ideas and discoveries, percolating through those few minds tuned to them, will mingle with the intellectual energy of the cosmos, and thence into the deep, broad pool of human knowledge.”