Year's Best SF 15 - By David G. Hartwell & Kathryn Cramer Page 0,8

hands become bruised and sore quite quickly, and he sighs and thinks about the Sufi poetess Jahanara, who had written, centuries earlier: “Let the green grass grow above my grave!”

I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naivete, unburdened by conventional wisdom, can sometimes be a positive asset.

—Harish-Chandra, Indian mathematician (1923–1983)

Gangadhar, his friend from school, was briefly a master of Hindi literature at the municipal school and is now an academician at the Amravati Heritage Library, and a poet in his spare time. He is the only person to whom Abdul Karim can confide his secret passion.

In time, he too becomes intrigued with the idea of infinity. While Abdul Karim pores over Cantor and Riemann, and tries to make meaning from the Prime Number theorem, Gangadhar raids the library and brings forth treasures. Every week, when Abdul Karim walks the two miles to Gangadhar’s house, where he is led by the servant to the comfortable drawing room with its gracious, if aging mahogany furniture, the two men share what they’ve learned over cups of cardamom tea and a chess game. Gangadhar cannot understand higher mathematics but he can sympathize with the frustrations of the knowledge-seeker, and he has known what it is like to chip away at the wall of ignorance and burst into the light of understanding. He digs out quotes from Aryabhata and Al-Khwarizmi, and tells his friend such things as:

“Did you know, Abdul, that the Greeks and Romans did not like the idea of infinity? Aristotle argued against it, and proposed a finite universe. Of the yunaanis, only Archimedes dared to attempt to scale that peak. He came up with the notion that different infinite quantities could be compared, that one infinite could be greater or smaller than another infinite…”

And on another occasion:

“The French mathematician, Jacques Hadamard…He was the one who proved the Prime Number theorem that has you in such ecstasies…he says there are four stages to mathematical discovery. Not very different from the experience of the artist or poet, if you think about it. The first is to study and be familiar with what is known. The next is to let these ideas turn in your mind, as the earth regenerates by lying fallow between plantings. Then—with luck—there is the flash of insight, the illuminating moment when you discover something new and feel in your bones that it must be true. The final stage is to verify—to subject that epiphany to the rigors of mathematical proof…”

Abdul Karim feels that if he can simply go through Hadamard’s first two stages, perhaps Allah will reward him with a flash of insight. And perhaps not. If he had hopes of being another Ramanujan, those hopes are gone now. But no true Lover has ever turned from the threshold of the Beloved’s house, even knowing he will not be admitted through the doors.

“What worries me,” he confides to Gangadhar during one of these discussions, “what has always worried me, is Gödel’s Incompleteness Theorem. According to Gödel, there can be statements in mathematics that are not provable. He showed that the Continuum Hypothesis of Cantor was one of these statements. Poor Cantor, he lost his sanity trying to prove something that cannot be proved or disproved! What if all our unproven ideas on prime numbers, on infinity, are statements like that? If they can’t be tested against the constraints of mathematical logic, how will we ever know if they are true?”

This bothers him very much. He pores over the proof of Gödel’s theorem, seeking to understand it, to get around it. Gangadhar encourages him:

“You know, in the old tales, every great treasure is guarded by a proportionally great monster. Perhaps Gödel’s theorem is the djinn that guards the truth you seek. Maybe instead of slaying it, you have to, you know, befriend it…”

Through his own studies, through discussions with Gangadhar, Abdul Karim begins to feel again that his true companions are Archimedes, Al-Khwarizmi. Khayyam, Aryabhata, Bhaskar. Riemann, Cantor, Gauss, Ramanujan, Hardy.

They are the masters, before whom he is as a humble student, an apprentice following their footprints up the mountainside. The going is rough. He is getting old, after all. He gives himself up to dreams of mathematics, rousing himself only to look after