Mathematics and faith, God and infinity

A couple of early passages from David Leavitt’s The Indian Clerk, about the relationship between the great British mathematician G H Hardy and the untrained genius Srinivasa Ramanujan, whom Hardy invited to study under him at Cambridge in 1913. The first passage is from Hardy’s childhood, with a young vicar attempting to teach him the importance of religious faith.

“As I have been trying to explain to your son,” the vicar said, “belief must be cultivated as tenaciously as any science. We must not allow ourselves to be reasoned out of it.”

“Harold is very good at mathematics,” his mother said. “At three he could already write figures into the millions.”

“To calculate the magnitude of God’s glory, or the intensities of hell’s agonies, one must write out figures far larger than that.”

“How large?” Harold asked.

“Larger than you could work out in a million lifetimes.”

“That’s not very large, mathematically speaking,” Harold said. “Nothing’s very large, when you consider infinity.”

The vicar helped himself to some cake. “Your child is gifted,” he said, once he had swallowed. “He is also impudent.” Then he turned to Harold and said, “God is infinity.”

“God is infinity”: the linking of a mathematical concept with something that is built on faith rather than reason. This is interesting, given that most people see math as a cold, staunchly rational science based on numbers that confer a sense of order. Not much scope here for the “what if”, it would seem. But as this next passage suggests, the very conflict between rationalism and faith can be expressed in mathematical terms.

Often the simplest theorems to state were the most difficult to prove. Take Fermat’s last theorem, which held that for the equation x^n + y^n = z^n, there could be no whole number solutions greater than 2. You could feed numbers into the equation for the rest of your life, and show that for the first million n’s not one n contradicted the rule. Perhaps, if you had a million lifetimes, you could show that for the first billion n’s, not one contradicted the rule – and still, you would have shown nothing. For who was to say that far, far down the number line, far past the magnitude of God’s glory and the intensity of hell’s agonies, there wasn’t that one n that did contradict the rule? Who was to say there weren’t an infinite number of n’s that contradicted the rule?

In a way I think this is a good encapsulation of the agnostic dilemma – the minuscule doubt that continues to exist in the face of all reason; the impossibility of reaching a definite conclusion (or the unwillingness to reach a definite conclusion).

(Will write about the book at length once I’ve finished it - it’s been very absorbing so far, though Ramanujan hasn’t made an appearance yet and most of the early chapters deal with the Cambridge Apostles, a society that Hardy was a member of and that included, at the time, such intellectuals as Bertrand Russell, Lytton Strachey, John Maynard Keynes and Ludwig Wittgenstein. Apparently they spent much of their off-time in lengthy discussions of subjects such as “Should a Picture be Intelligible?” and “Does Absence Make the Heart Grow Fonder?”, and in the contemplation of sodomy.)