Robert Kanigel on Srinivasa Ramanujan

“Ramanujan learned from an older boy how to solve cubic equations. He came to understand trigonometric functions not as the ratios of the sides in a right triangle, as usually taught in school, but as far more sophisticated concepts involving infinite series. He'd rattle off the numerical values of π and e, "transcendental" numbers appearing frequently in higher mathematics, to any number of decimal places. He'd take exams and finish in half the allotted time. Classmates two years ahead would hand him problems they thought difficult, only to watch him solve them at a glance. … By the time he was fourteen and in the fourth form, some of his classmates had begun to write Ramanujan off as someone off in the clouds with whom they could scarcely hope to communicate. "We, including teachers, rarely understood him," remembered one of his contemporaries half a century later. Some of his teachers may already have felt uncomfortable in the face of his powers. But most of the school apparently stood in something like respectful awe of him, whether they knew what he was talking about or not. He became something of a minor celebrity. All through his school years, he walked off with merit certificates and volumes of English poetry as scholastic prizes. Finally, at a ceremony in 1904, when Ramanujan was being awarded the K. Ranganatha Rao prize for mathematics, headmaster Krishnaswami Iyer introduced him to the audience as a student who, were it possible, deserved higher than the maximum possible marks. An A-plus, or 100 percent, wouldn't do to rate him. Ramanujan, he was saying, was off-scale.”

“Ramanujan was an artist. And numbers — and the mathematical language expressing their relationships — were his medium. Ramanujan's notebooks formed a distinctly idiosyncratic record. In them even widely standardized terms sometimes acquired new meaning. Thus, an "example" — normally, as in everyday usage, an illustration of a general principle — was for Ramanujan often a wholly new theorem. A "corollary" — a theorem flowing naturally from another theorem and so requiring no separate proof — was for him sometimes a generalization, which did require its own proof. As for his mathematical notation, it sometimes bore scant resemblance to anyone else's.”

“Ramanujan was a man for whom, as Littlewood put it, "the clear-cut idea of what is meant by proof ... he perhaps did not possess at all"; once he had become satisfied of a theorem's truth, he had scant interest in proving it to others. The word proof, here, applies in its mathematical sense. And yet, construed more loosely, Ramanujan truly had nothing to prove. He was his own man. He made himself. "I did not invent him," Hardy once said of Ramanujan. "Like other great men he invented himself." He was svayambhu.”