The Longitude Prize gives us a new hero

The implied question was “1729”. The spontaneous answer would prompt one of the best-loved stories in the history of mathematics.

In 1918, the eminent Cambridge mathematician G H Hardy went to visit, in a Putney nursing home, the sickly and fragile Srinivasa Ramanujan: his friend, protégé, collaborator and, above all, a creative thinker in the realm of numbers far beyond even his mentor’s class. “I had ridden in taxi cab number 1729,” Hardy recalled, “and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. ‘No,’ he replied, ‘it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.’” Or, to be precise: 1729 = 13 + 123 = 93 + 103.

Ramanujan, the obscure and penniless port clerk from Madras, had by the year of Hardy’s anecdote already become one of the youngest-ever fellows of the Royal Society. In later accounts, both biography and fiction, he often plays the archetypal part of the low-status outsider who by the sheer force of genius alters the course of human thought. The taxi-number story has a miraculous, lives-of-the-saints quality. All the same, it hints at an almost superhuman intellectual strength in poignant contrast to the weakness of the body that housed the brain. A strict vegetarian, his frail frame weakened further by the privations of Cambridge in the First World War, Ramanujan would die aged 32 in 1920. He once claimed that new formulae came to him via the voice of a goddess in dreams. When first presented in letters with these outlandish theorems from an unknown Indian youth without any degree, Hardy himself judged that they must be true. If not, “no one would have the imagination to invent them”.

Ramanujan has become a sort of mythical deity himself: an avatar of the eerily gifted amateur who leaves academics and professionals dumbstruck in wonder. A century after Hardy’s astonishment, we still yearn to acclaim the inspired autodidact who leaps out of obscurity to stump the experts. Hence the popular appeal of the revived Longitude Prize, a £10m competition announced this week under the supervision of Nesta, the government’s innovation charity. To mark the tercentenary of the original Longitude Prize of 1714, an all-comers’ contest will invite solutions to an urgent problem of the present day.

On 25 June, after a public consultation, one topic will be chosen from the six shortlisted fields of enquiry: zero-carbon flight; sustainable world food supplies; the prevention of antibiotic resistance; restored movement for paralysed patients; safe and clean water for all; independent living for people with dementia. Many onlookers will be craving the emergence of a 21st-century John Harrison. After bruising struggles with Georgian officialdom, in 1765 this gruff Yorkshire clockmaker – the hero of Dava Sobel’s 1996 bestseller Longitude – won the original award for his sequence of stable marine chronometers. Harrison’s parade of horological beauties, from “H1” though to “H4”, allowed ships to pinpoint their exact position at sea and so accelerated the expansion of trade and empire. Now they sit in state at the Royal Observatory in Greenwich.

The romantic idea of the untutored, or at least uncertificated, genius continues to bewitch. Over the past 150 years or so, professional corporations – above all, universities – have stage by stage claimed monopoly powers over the pursuit and management of knowledge. Paper fences have progressively gone up around discovery. That supreme amateur Charles Darwin had published On the Origin of Species in 1859. At around that time, the retreat of learning into institutions with official stamps got under way in earnest. The age of the gentleman-scientist – so often a clergyman or landowner – began to fade.

During the decades before Darwin, major breakthroughs by amateurs had revolutionised astronomy, geology and natural history – the understanding of the stars above our head and the ground beneath our feet. The planet Uranus, for instance, was located in 1781 by the Hanover-born musician William Herschel. His self-designed telescopes would go on to push back the boundaries of the known universe.

As for the solid rock on which we stand, this Wednesday’s “Google doodle” on the search engine’s home page marked the 215th birthday of Mary Anning: the Dorset fossil-hunter who breached barriers of class and gender to discover dinosaurs and transform perceptions of the deepest past.

Take a look at your ready cash and you will find, courtesy of the Bank of England, a little history of the professionalisation of enlightenment. Apart from bushy-bearded Darwin on the £10 note, Adam Smith gazes stolidly out from the £20. The philosopher-economist did hold down a chair at Glasgow University – unthinkable in 18th-century Oxford or Cambridge. Later, though, he reverted to the earlier model of the freelance sage under aristocratic patronage, as tutor to a nobleman. And, if you’re lucky enough to find a £50 in your purse or wallet, it tells a story all its own. Sealed at the Soho Manufactory in Birmingham, the partnership of instrument-maker James Watt and entrepreneur Matthew Boulton steam-powered the Industrial Revolution in the era when dissenting, egalitarian Brum out-thought, out-imagined and out-manufactured the rest of the world.

Sobel’s Longitude, published at the start of the internet age, showed that a character such as Harrison makes the perfect hero for our time. Millions can access a global store of learning from their keyboards, while big science – either state or corporate-controlled – has lost much of its mystique. We all adore a DIY super-brain, preferably rough hewn and provincial. If a smug elite scorns them until the isolated eccentric triumphs over all the odds, so much the better. The Harrison myth inspires and satisfies. Yet it needs a caveat or two.

First, mavericks and heretics are not always right. Look at the sorry story of the MMR vaccine and the challenges over its safety. Sometimes the loner with a heterodox theory will be a crackpot – or even a fraud – rather than a brave rebel with a cause. Many things in science and scholarship remain true even though the horrid establishment says they are. In the case of MMR and its discredited “link” with childhood autism, the cult of the outsider has claimed lives.

Second, the revived Longitude Prize arises from the age of online data. So it will offer a process distinct from the unearthing of a solitary unschooled genius. “Crowdsourcing” comes into play, with the potential to pool and share research. As in some brainier version of the lottery, there could be many individual winners. Even surly, stroppy Harrison got his cash at intervals in dribs and drabs, while the Board of Longitude paid more than £100,000 in all to several other contenders. I can see that £10m now on the table being split many ways. Perhaps the copyright lawyers have already won. They usually do.

In his threadbare Madras digs, Ramanujan needed no more than paper, pen – and mind. Pure maths, like lyric poetry, traditionally opens up a fast track to glory. Yet the penurious young Tamil had received encouragement from local mathematicians. The Madras Port Trust knew of his talents. By 1913, when he wrote out of the blue to Hardy, this type of the solitary seeker already belonged to an intellectual community. As for Boulton and Watt, they flourished within Birmingham’s trailblazing Lunar Society, whose members from Erasmus Darwin to Joseph Priestley met in a climate where science, technology, radical politics and business innovation blended. Even Silesian friar Gregor Mendel, whose experiments with pea plants in the monastery garden laid the foundation of genetics, enjoyed support from his abbot. If great discoveries ever did bloom in splendid isolation, it seems logically likely that we never heard of them.

Last year, when plans for the reset Longitude Prize first emerged, the Prime Minister welcomed the chance to escape reality-show trivia and “get the nation engaged on what the biggest problems are in science”. But a democratic infrastructure of research needs more than a fat cheque or two. It calls for communities of understanding and exchange. So don’t close public libraries, but rather expand them. Make sure that all have access to giant digital resources such as the JSTOR database, with staff who know how to guide users. Protect the peerless Open University and other powerhouses of part-time education. Don’t dumb down the BBC, but wise it up. Give the Young Scientist of the Year award at least a MasterChef- if not a Voice-sized prime-time platform. Could you name this year’s winners? They were Reading twins Ameeta and Aneeta Kumar, aged 18, for their work on early cancer diagnosis.

In the meantime, I have a seventh challenge to add. For would-be prize winners, it may underpin research on all the others, as well as unlocking the power of the kit that informs and connects us. How can we massively extend the active life of lithium ion batteries so that the devices they fuel will no longer grind to a halt? No Royal Navy captain, becalmed in the middle of the Pacific, ever had to scrabble around to find a charger for Mr Harrison’s life-saving chronometer.