Even though the U.S.-based Clay Mathematics Institute is
offering $1 million to the first person to prove Riemann's
Hypothesis, it's not the money that motivates mathematicians, it's
the beauty of the proof.
'Beauty is a concept used by mathematicians (and other scientists) when they find something that combines truth and simplicity,' writes Karl Sabbagh in Prospect, the British magazine on culture and current affairs. 'Like the use of the word in everyday life, you know it when you see it. It is possible to distinguish superficial from less superficial beauties in maths, just as you can between trite and subtle harmonies in music. But in Wittgensteinian terms: one cannot explain, one can only show.'
Undertaking a proof is no small endeavor. Sabbagh points out that describing a solution can span a hundred pages, maybe more for the 143-year-old Riemann's Hypothesis that states that non-trivial zeros of the Riemann zeta function all have real part equal to H. Sabbagh spends a couple paragraphs explaining the theory, but the main question concerns prime numbers, those integers that cannot be divided by other whole numbers.
To understand Riemann's theory and other similarly complex ideas, there is a kind of passion that drives mathematicians. Talking about her own motivation, Andre Weil says she, like many others, has achieved a 'state of lucid exaltation' that can last for hours.
'For many mathematicians,' Sabbagh writes, 'the pleasure of practising mathematics outweighs almost any other mental or physical pleasure.'
--Sara V. Buckwitz