Three friends take a bet in a coffee house

Casual wagers among male friends tend to home in on the trivialities of human existence. They are usually taken in order to resolve questions that are of no importance to anyone but the gamblers themselves. For example, a bet might arise from a sudden and compelling need to determine which of the assembled company can drink a pint of beer the quickest. Or there’s the perennial jousting over whose football/rugby/netball/cricket/hockey/synchronised swimming team will prevail in the coming season, followed by a demand to put one’s money where one’s mouth is.

Doubtless much the same thing went on in the taverns, inns and coffee houses of London in late 17th-century England. However, it was at one particular coffee house – a famous hang-out for academics and scientists called The Grecian – that three friends cut from a different cloth were about to agree on a wager that would change the face of science forever. The three, all of whom were members of the Royal Society, were Edmond Halley (he of the comet), architect Christopher Wren (of St Paul’s fame) and the natural philosopher (i.e. scientist) Robert Hooke.

When a trio with such brilliant minds finds itself in close proximity, the conversation is likely to be highbrow, and indeed the three men were famous for their coffee-house discussions on the scientific and philosophical issues of the day. However, on one occasion in 1684 they managed to outdo even their own lofty standards of erudition, for they ended up laying money on which of them could show the workings for why the path of planets around the Sun was elliptical. In more precise terms, the winner of the wager would be the first of them to produce a mathematical description of the path of an orbiting planet around the Sun if the force of attraction on the planet exerted by the Sun were reciprocal to the square of the distance between them.

It’s a problem we’ve probably all wrestled with ourselves at some point. The difference in this case is that Halley, Wren and Hooke not only had the motivation of the bet to drive them towards an answer, but they also all shared a mistaken belief that no one had managed to come up with one before. It was, they felt, long overdue that someone should, for it had been 75 years since the astronomer Johannes Kepler had shown by observation that the course of Mars around the Sun was elliptical. Beyond that, virtually nothing was known about the path of planets. On account of some work done by Christiaan Huygens on centrifugal force, the three coffee drinkers at The Grecian had a hunch that the answer lay in the relationship between gravity and the square of the distance between the planet and its Sun, and were mustard-keen to set out the maths behind it.

Hooke showed his hand first, claiming that he had come up with the solution, but his workings rather fell apart on closer examination by his two associates. Halley was so energised by the problem that he took himself off to Cambridge – still something of an undertaking in the 1680s – to seek out a certain man at the university who had garnered a name for himself as a mathematician. That man was Isaac Newton.

Newton was 41 years old, a farmer’s son from a hamlet in Lincolnshire. He was born prematurely, barely survived his first few months, and was then dumped on his grandmother at the age of three when his mother remarried (his father having died before he was born). It was not an auspicious start in life and he was dogged thereafter by a sense of insecurity. Things turned around when he went to stay with an apothecary while attending the King’s School in Grantham. This was his introduction to chemistry, a subject to which the 12-year-old Isaac took immediately and in which he was evidently naturally gifted. Six years later, his uncle, Rev William Ayscough, talked Isaac’s mother into letting him study at Cambridge University as he himself had done. Newton was duly granted a place as a subsizar, a student who worked his passage by acting as a waiter and valet for other students.

He continued his studies at the university until 1665, when the Great Plague forced a retreat to Lincolnshire. Newton was not one to let the grass grow under his feet, however. It was there that he formulated his method of infinitesimal calculus and had an apple fall on or near his head – if the legend be true – triggering his ‘Eureka!’ moment with regard to gravity. He returned to Cambridge in 1667 and two years later became a professor, lecturing on light and its colours, his favourite topic of the moment. His work Opticks: Or, A Treatise of the Reflections, Refractions, Inflections and Colours of Light was virulently attacked by one Robert Hooke, sparking a bitter rivalry that would last for years.

By the time of his meeting with Edmond Halley, Newton had gone through a nervous breakdown, not helped by the subsequent death of his mother, which had seen him withdraw from public life for six years. However, during this time Hooke had written to him with the suggestion that the path of planetary orbits might be worked out with a formula that contained inverse squares, an idea that was to resurface in the coffee-house wager.

The story of the encounter between Halley and Newton is recorded by Abraham De Moivre, who heard it from the lips of Newton himself:

In 1684 Dr Halley came to visit him at Cambridge. After they had been some time together, the Dr asked him what he thought the curve would be that would be described by the planets supposing the force of attraction towards the sun to be reciprocal to the square of their distance from it.

Sir Isaac replied immediately that it would be an ellipse. The Doctor, struck with joy and amazement, asked him how he knew it. Why, saith he, I have calculated it. Whereupon Dr Halley asked him for his calculation without any farther delay. Sir Isaac looked among his papers but could not find it, but he promised him to renew it and then to send it him…

Newton’s scientific investigations were somewhat haphazard and sometimes bordered on the eccentric. His fascination with alchemy, for example, often diverted him from what might have been more fruitful avenues of research. However, Halley’s visit stung him into action. He sat down and began to lay out a comprehensive solution to the mathematical problem he had been posed. As he worked on it, the scope of his response widened as, for the first time, he set down in a methodical way the ideas he had had over the years on universal gravitation and mechanics.

The first Halley knew of this came three months later in November 1684. A messenger knocked on his door in London and handed him a nine-page exposition entitled De Motu Corporum In Gyrum (On the Motion of Bodies in Orbit). The scientist was gripped by what he read, immediately recognising its importance. He raced back up to Cambridge and cajoled, coaxed and finally convinced Newton that he should expand the treatise into a paper that he could deliver to the Royal Society at the earliest possible opportunity.

Newton abandoned his more arcane pursuits and concentrated on the task Halley had persuaded him to take on. Over the following two years he wrote Philosophiæ Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy), a three-volume work of extraordinary genius.

It is at this point, just as this revolutionary masterpiece is delivered to the Royal Society, that the story descends into bathos. The society regretted that it could not publish Mr Newton’s work because it was financially embarrassed: all its funds had just been spent on a book about fish that had sunk like a stone.

Although far from being a rich man, Halley immediately stepped in, organising and paying for the publication, an event that took place in 1687. It did not take long for the scientific community to realise that nothing quite like Principia (as it is better known today) had been attempted before.

It was a breathtaking achievement: its author had methodically explained the physics behind so much of what happened not only on the Earth, but in the universe beyond.

Among the vast catalogue of achievements in Principia are laws which, over 300 years later, are still found to be valid. Its three laws of motion have formed the bedrock for classical mechanics. It also includes an explanation of the behaviour of orbiting celestial bodies; his law of universal gravitation; the reasons for the movements of the tides; and even the evidence for the Earth not being the perfect sphere that scientists of the time believed it to be but a planet that is slightly flattened at both poles. And all of this in Latin.

Principia remains a towering landmark in the scientific landscape, undiminished by the passing years and the advances in the understanding of our universe that have been made since its publication. It formed the groundwork for a revolution in not just one but three realms: physics, mathematics and astronomy. Furthermore, the clarity with which he expressed his ideas set the standard for those who came in his wake. The three volumes – which he updated twice – have been the basis on which scientists have made myriad discoveries of their own, thus shaping our world today. And they simply wouldn’t have been written if it hadn’t been for a bet that Newton himself didn’t even take part in.

It’s also intriguing to note that, given the extraordinary scope of Principia and its roots in Halley’s visit to Newton, nowhere in the pages of the first edition will you find a solution to the problem posed in the Grecian wager. Newton delivers the maths that shows that a planet is subject to the inverse-square force as set out in the bet, but not the maths that describes the ellipsis itself. The author merely states that one follows from the other. Newton later made the claim that he had left out the solution to the problem simply because it was ‘very obvious’. If you’re a genius, that’s the kind of excuse you can get away with.