The question “why do you do maths?” sparks a flurry of emotions. The mind struggles to formulate an explanation that feels even remotely adequate; and the final answer leaves a lingering buzz of frustration as the eyes of the questioner remain unlit by the same fire that burns within you.
There are, of course, earthly, comprehensible, easy-to-describe reasons that drive us. There is no Nobel Prize in Mathematics, but Cédric Villani’s Birth of a Theorem speaks of the author’s obsession with winning its mathematical equivalent: the Fields Medal.
Then, occasionally, monetary prizes are offered for the solution of mathematical problems.
Chalkdust recently tweeted about the offer of an ounce of fine gold for the proof or disproof of a conjecture regarding the sum of squared logarithms, although certainly more famous is the $1m offered by the Clay Mathematics Institute of Cambridge (Massachusetts) for the solution to any one of the seven Millennium Problems. These problems range from proving or disproving that the Navier-Stokes equations – the foundations of our understanding of fluid flow – will always give a ‘realistic’ solution; to proving the Riemann Hypothesis, vitally important in the field of Number Theory, with mathematicians in this field usually having to assume it to be true in order to make any progress (interestingly, the prize will not be given for providing an example of it being false). The solution to one of the seven Millennium Problems will have huge and far-reaching consequences not just to the sphere of science and technology, but to us all.
Indeed, one of the main reasons for offering prizes is to focus the minds of the best researchers on finding a solution to problems facing a nation or humankind as a whole. Just over 300 years ago, on the 8th July 1714, the British parliament passed the Longitude Act, saying that the discovery of an accurate method to determine the longitude of a ship at sea was “of such consequence to Great Britain for the safety of the Navy and Merchant Ships as well as for the improvement of trade”. The steady rotation of the Earth means that there is a direct relationship between time and longitude: by comparing the time where the ship is (the local time) – easily obtainable by observing the sun – with the time at some fixed reference point (such as Greenwich) one can calculate the longitude. However, there was no way of telling the time at a given reference point, since the rolling, pitching and yawing of ship as it was buffeted by the wind and waves would knock the pendulum-based clocks of the era out of sync. People sailed either by estimating longitude using the vessel’s direction and speed (which could not be measured accurately either and resulted in shipwrecks, such as one off the Isles of Scilly in 1707); or sailing in a North-South direction until they hit the same line of latitude as their destination and then moving along it (determining latitude only required a sight of the sun, but sailing in such a way increased distance).
The British government’s concern was, indeed, not new. The discovery of the Americas and expanding trade routes had made the search for an accurate method ever more pressing and most of the major sea-faring nations had already offered prizes: Spain in 1567 and again in 1598; the Netherlands in 1636; and France had made it one of the main tasks of their newly-founded Académie Royale des Sciences in 1666. The offer of a substantial prize and funding for research certainly galvanised the British scientific establishment, and the proposals came flooding into the Board of Longitude; with the mathematician George Airy claiming in 1858 that the Board’s papers would “probably form one of the most curious collections of the results of scientific enterprise, both normal and abnormal, which exist.”
Although nobody ever won the full prize of £20,000, John Harrison received a total of £23,065 over his lifetime for his work on “a new invented machine, in the nature of Clock Work, whereby he proposes to keep time at sea with more exaction than by any other instrument or method hitherto contrived”. John Harrison revolutionised clock making: he got rid of the need for oil, which eventually became sticky, as a lubricant by using rolling as opposed to sliding contacts; he developed a bimetallic strip to overcome the problem of metals expanding in the higher temperatures closer to the Equator; he used counterbalanced springs to control the moving parts, making the clock independent of the direction of gravity, thereby partly overcoming the havoc caused by a ship’s movement; and he proposed high frequency oscillators for greater accuracy. His final design (the H4) was little bigger than a pocket watch, ticked five times a second and was a spectacular success: on a trip lasting 63 days from England to Jamaica in 1761-62 it lost only 5.1 seconds. The threshold for the best prize under the Longitude Act was 2.8 seconds a day.
A new Longitude Prize, funded by the charity Nesta, was launched in 2014 on the 300th anniversary of the original Longitude Act. Following a public vote, £10m was offered for creating a “cost-effective, accurate, rapid and easy-to-use test for bacterial infections that will allow health professionals worldwide to administer the right antibiotics at the right time”. It’s hoped that spurred on by this reward, scientists will begin to fight the ever growing threat of antibiotic-resistant bacteria.
But for mathematicians, money and recognition rarely figure. In 2003, Grigori Perelman proved the Poincaré Conjecture, one of the Millennium Problems, and yet turned down both the $1m offered by the Clay Institute and the Fields Medal the International Mathematical Union wanted to award him, saying “I’m not interested in money or fame. I don’t want to be on display like an animal in a zoo”.
So why do we do maths? Some might talk about the way it helps us understand physical or social phenomena; others will speak of the process of exploration and sharing of ideas; more will attempt to share the moment when the final piece is fitted into a ten-thousand piece jigsaw. Most, though, will aim, however unsuccessfully, to capture its beauty or the wonder of, in the words of Eduardo Sáenz de Cabezón, discovering “eternal truths”: truths that just are, regardless of our world’s existence. For in the words, once more, of Perelman: “Everyone understands that if the proof is correct then no other recognition is needed”.
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