not, because he cannot make out what the voice is saying. He sighs and buries himself in his studies.
He reads about prime numbers in Nature. He learns that the distribution of energy level spacings of excited uranium nuclei seem to match the distribution of spacings between prime numbers. Feverishly he turns the pages of the article, studies the graphs, tries to understand. How strange that Allah has left a hint in the depths of atomic nuclei! He is barely familiar with modern physics—he raids the library to learn about the structure of atoms.
His imagination ranges far. Meditating on his readings, he grows suspicious now that perhaps matter is infinitely divisible. He is beset by the notion that maybe there is no such thing as an elementary particle. Take a quark and it’s full of preons. Perhaps preons themselves are full of smaller and smaller things. There is no limit to this increasingly fine graininess of matter.
How much more palatable this is than the thought that the process stops somewhere, that at some point there is a pre-preon, for example, that is composed of nothing else but itself. How fractally sound, how beautiful if matter is a matter of infinitely nested boxes.
There is a symmetry in it that pleases him. After all, there is infinity in the very large too. Our universe, ever expanding, apparently without limit.
He turns to the work of Georg Cantor, who had the audacity to formalize the mathematical study of infinity. Abdul Karim painstakingly goes over the mathematics, drawing his finger under every line, every equation in the yellowing textbook, scribbling frantically with his pencil. Cantor is the one who discovered that certain infinite sets are more infinite than others—that there are tiers and strata of infinity. Look at the integers, 1, 2, 3, 4…Infinite, but of a lower order of infinity than the real numbers like 1.67, 2.93, etc. Let us say the set of integers is of order Aleph-null, the set of real numbers of order Aleph-One, like the hierarchical ranks of a king’s courtiers. The question that plagued Cantor and eventually cost him his life and sanity was the Continuum Hypothesis, which states that there is no infinite set of numbers with order between Aleph-Null and Aleph-One. In other words, Aleph-One succeeds Aleph-Null; there is no intermediate rank. But Cantor could not prove this.
He developed the mathematics of infinite sets. Infinity plus infinity equals infinity. Infinity minus infinity equals infinity. But the Continuum Hypothesis remained beyond his reach.
Abdul Karim thinks of Cantor as a cartographer in a bizarre new world. Here the cliffs of infinity reach endlessly toward the sky, and Cantor is a tiny figure lost in the grandeur, a fly on a precipice. And yet, what boldness! What spirit! To have the gall to actually classify infinity…
His explorations take him to an article on the mathematicians of ancient India. They had specific words for large numbers. One purvi, a unit of time, is seven hundred and fifty-six thousand billion years. One sirsaprahelika is eight point four million Purvis raised to the twenty-eighth power. What did they see that caused them to play with such large numbers? What vistas were revealed before them? What wonderful arrogance possessed them that they, puny things, could dream so large?
He mentions this once to his friend, a Hindu called Gangadhar, who lives not far away. Gangadhar’s hands pause over the chessboard (their weekly game is in progress) and he intones a verse from the Vedas:
From the Infinite, take the Infinite, and lo! Infinity remains…
Abdul Karim is astounded. That his ancestors could anticipate Georg Cantor by four millennia!
That fondness for science…that affability and condescension which God shows to the learned, that promptitude with which he protects and supports them in the elucidation of obscurities and in the removal of difficulties, has encouraged me to compose a short work on calculating by al-jabr and al-muqabala, confining it to what is easiest and most useful in arithmetic.
—Al Khwarizmi, eighth century Arab mathematician
Mathematics came to the boy almost as naturally as breathing. He made a clean sweep of the exams in the little municipal school. The neighborhood was provincial, dominated by small tradesmen, minor government officials and the like, and their children seemed to have inherited or acquired their plodding practicality. Nobody understood that strangely clever Muslim boy, except for a Hindu classmate, Gangadhar, who was a well-liked, outgoing fellow. Although Gangadhar played gulli-danda on the streets and could run faster than anybody, he had a passion for literature, especially poetry—a