220 // Anti-Atheism

whole number, then the sum of its divisors, including n itself, is written as sðnÞ. (Here s is the lower-case Greek letter `sigma'.) So

sð24Þ ¼ 1 þ 2 þ 3 þ 4 þ 6 þ 8 þ 12 þ 24 ¼ 60

sð12Þ ¼ 1 þ 2 þ 3 þ 4 þ 6 þ 12 ¼ 28

and so on. In 2002 Jeffrey Lagarias proved that the Riemann Hypothesis is equivalent to the inequality

sðnÞ4eHn log Hn

for every n. Here Hn is the nth harmonic number, equal to

1 1 1 1

1 þ þ þ þ ...

...........................................

2 3 4 n

Anti-Atheism Godfrey Harold Hardy, a Cambridge mathematician who worked mainly in analysis, claimed to believe in God ­ but unlike most believers, he considered the Deity to be his personal enemy. Hardy had it in for God, and he was convinced that God had it in for Hardy, which was only fair. Hardy was especially worried whenever he travelled by sea, in case God sank the boat. So before travelling, he would send his colleagues a telegram: `HAVE PROVED RIEMANN HYPOTHESIS. HARDY.' He would then retract this claim on arrival.

As just discussed, the Riemann Hypothesis is the most famous unsolved problem in mathematics, and one of the most important. And so it was in Hardy's day, too. When his colleagues asked him why he sent such telegrams, he explained that God would never let him die if that would give him credit ­

........................................... however controversial ­ for proving the Riemann Hypothesis.

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