I do not know what I may appear to the world; but to myself I seem to have been only like a boy, playing on the sea shore, and diverting myself, in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay undiscovered before me.
- Isaac Newton

Newton's scientific works are manifold, but the two great planks of his fame are the two books he published, Principia Mathematica and Opticks. Principia catapulted him to widespread fame in his youth. The publication of Opticks (which, despite the title, ranged widely across a number of disciplines) in his later life cemented him as a lifelong scientist in the public mind, although in truth the work it contained mostly predated the Principia.

Undergraduate

Right from his first year at university, Newton knew what his interests were. He set out in his notebook a section labelled Quaestiones quaedam Philosophicae - 'Some Questions in Philosophy' - with 72 sub-headings, covering the breadth of human knowledge, from 'Air', 'Meteors' and 'Motion' to 'Vacuum' and 'Reflection'. It appears that he started this mid-lecture in 1663, judging from its position in his notebook. Like many a teenager before or since, Newton was setting out to discover all human knowledge. He was doing it in a rather more organised manner than typical and, of course, he would come to greater success than most. This notebook contains not only a discussion of existing philosophical concepts (such as the existence of atoms, an idea Newton clearly agreed with), but also ideas for experiments that might be performed to evaluate them. At the time, this was an entirely novel idea.

In line with contemporary orthodoxy, Newton does not seem to have distinguished his philosophical pursuits - there was no clear contradiction for him between what we would now call 'theology', 'philosophy' and 'science'. This was also quite in line with the curriculum - but as in his school years, Newton showed little interest in the curriculum. His notes suggest that he started all his textbooks, but finished none. His exam results tell a similar story. Having noted that Euclid was so obvious he wondered why anyone bothered to read him, Newton promptly failed his mathematics exam. Why this did not result in him being 'sent down'¹ is not clear - again, it seems likely that Newton's influential sponsors were involved, either in the form of Francis Babington (the family friend who seems to have been influential in getting him his place at Cambridge) or senior tutor (and first Lucasian Professor) Isaac Barrow.

In those early days, Newton was clearly under the influence of the Cambridge Platonists. This was a loose description of some like-minded thinkers centred around Henry More. An influential idea was Pierre Gassandi's 'Christianised atomism', an attempt to show that ancient Greek ideas were consistent with Christian theology. This may sound strange to modern ears, used to thinking of the ancient Greeks as pre-Christians, but the academic orthodoxy at the time was that there had been a 'Classical Age' in the past when the greats like Pythagoras knew everything worth knowing, and that this knowledge had since been lost or hidden. 'Research', therefore, meant looking at ancient texts in order to rediscover lost knowledge.

It was against this background that Newton had possibly the most radical idea of his life. At the Sturbridge Fair in 1663, he bought a prism, and began carrying out optical experiments in his rooms - actually trying things out to see what would happen. This was not a totally new idea - Galileo had done something similar a lifetime earlier - but Newton would go on to bring a mathematical rigour to his studies that Galileo could not match. It was using this prism that Newton deduced that white light was a combination of all the colours, and that each colour travelled at a different speed - the refraction so familiar to fans of Pink Floyd.

Among Newton's early experiments with light was looking at the Sun for several hours. This so damaged his sight that he had to rest in a darkened room for three days. He also decided to test the theory that light was a form of 'pressure' that travelled through the ether. He did this by applying pressure to the rear of his eyeball in the most direct way he could - he pushed a bodkin² into his own eye-socket between the bone and the eyeball³.

He was also starting to take a serious interest in mathematics. He may have sneaked in to the lectures given by Isaac Barrow, the Lucasian Professor (as a sizar⁴, Newton was not permitted to attend - but since attendance was optional, Barrow may have been pleased simply to have someone in his audience), or it may have come from his readings on astrology and Euclid.

As at school, Newton's problem was that his interests did not coincide with the examination syllabus. It seems that the same problem followed him to Cambridge. Having already scraped through his entrance exam at the second attempt, Newton just barely graduated. He 'lost his groats' - meaning that his results were so low that the porters retained the deposit of small change he had left when going into the exam. He effectively had a viva⁵ to demonstrate his knowledge of Euclid. Nevertheless, he obtained his Bachelor of Arts in 1664 or 1665.

Anni Mirabili

The trigger for Newton's greatest outpouring of genius was, ironically, the closure of Cambridge. As plague threatened both town and University, the authorities required that all students and staff retreat to the countryside. In London, a city of a million people, 70,000 died. In 1665, Newton duly returned to his family farm in Woolsthorpe. It was there that he had his greatest insights, during his so-called anni mirabili - 'miraculous years'. It was in the yard outside the family home that, he would later claim, he watched an apple fall from a tree, and wondered how it could be affected without being touched (a question Newton would never answer, and indeed one which has never been entirely satisfactorily answered). It was there also that Newton began to push his mathematical knowledge beyond that of his contemporaries.

As Newton said himself, 'I keep the subject constantly before me, till the first dawnings open slowly, by little and little, into the full and clear light.'

Initially, his interest was not in gravity or in mathematics, but in optics. Using the crystal he had bought at the fair, he refracted light, showing that white light was in fact made up of all the other colours. He then carried out his 'experimentum crucis', further refracting one of the refracted colours. By this means, he showed that coloured light was 'pure', and could not be further split; and that blue light was refracted through a greater angle than red.

Using this knowledge, Newton began work on a radically new design of telescope, of his own devising. He would complete it in 1669, the year that he became Lucasian Professor, and it would seal his entry into the Royal Society a couple of years after that. His design - based on curved reflecting mirrors rather than refracting lenses, in order to minimise 'chromatic aberration' (the distortion caused by the different refraction of the different colours of light) - allowed a smaller telescope to produce a clearer image at greater magnification, and was a direct result of the combination of his theoretical researches and his practical skills - he built the telescope himself by hand, using mirrors he made himself, using tools he fashioned and designed himself!

Newton remained at Woolsthorpe for two years, broken only by a 'false all-clear' from Cambridge for a few weeks. By the time he returned, he had laid the intellectual foundations for a reputation that would last for his entire career - but had published nothing, and seems to have had no intention of doing so. As well as the penny (or rather, the apple) dropping about gravity, he had developed his 'method of fluxions' for calculating the area under a curve - what would later be called calculus.

And his imagination ran wild beyond that. He conceived of an explanation for gravity, a series of rays rather like light, that could be refracted. He used his 'fluxions' to calculate the elliptical paths of the planets, based on an inverse square law of gravity. At first, he had great success - until he tried to apply it to the Moon's orbit. Here, he struggled in vain, unable to get his calculations to match up with observations. What he did not know was that a key piece of data he was using, the size of the Earth as calculated by Galileo, was wrong. Uncharacteristically, he dropped the idea and moved on.

The Professor

By 1667, Cambridge was clear of the plague (the Great Fire of London in 1666 had accelerated the disease's decline in England) and Newton could return, to obtain his MA and a Fellowship.

A few years later, in 1669, Mercator (of map projection fame) published a book called Logarithmotechnia. In it, he duplicated parts of Newton's work. Newton seems to have been a little shocked by this - he already regarded himself as an almost divine messenger, and to see someone else equally capable would be a threat to him throughout his life. On this first occasion, however, he almost shrugged the matter off. Mercator had no way of knowing of Newton's work, and had clearly not progressed as far. Newton set his own techniques down in a short essay, De Analysi per Aequationes Numeri Terminorum Infinitas, which he dispatched to his contact in London, Isaac Barrow. Barrow was immediately impressed, and pushed Newton to allow him to publish it. Ever secretive, Newton refused.

Instead, Newton continued to push back the bounds of human knowledge, whilst keeping that knowledge from humanity. He took the single greatest objection to the geocentric Copernican system - that a spinning Earth would throw people from its surface into space - and demonstrated that the force of gravity pulling objects down to the surface of the Earth is something like 300 times as strong as the centrifugal force pushing them up. Just as significantly, he based these calculations on his own experimental observations. At a stroke, he had come up with conclusive proof of the Copernican system (in his own eyes, and the eyes of his contemporaries - modern philosophers of science might have a rather different view of what constitutes a logical proof) and invented the scientific method as it is now understood; theory followed by calculation followed by prediction followed by empirical test. He told no-one but his most intimate friends.

When Barrow resigned his Chair, he recommended the 26-year old prodigy Isaac Newton as his successor. Newton had recently been voted into the Royal Society, on the 11th January 1672, on the basis of the reflecting telescope he had presented to the Society the previous year. Perhaps more significantly, the February 1672 edition of the Society journal, the Philosophical Transactions, contained Newton's paper on the Theory of Light and Colours - the first time that experimental evidence had been used to alter a traditional theory.

The truth is that his most creative years as a scientist were by this stage behind him. His intellectual interests were turning to alchemy and religion. Natural philosophy was, to him, a solved problem, something he could set aside and forget. And if the world knew nothing of optics, calculus, gravity or momentum, what was that to Newton?

'I have calculated it.'

In 1680, a comet appeared in the night sky, slowly growing in magnitude and then fading back to nothing. A few months later, an apparently separate, second comet appeared in another part of the night sky. John Flamsteed, the Astronomer Royal, and Newton each realised that these were in fact the same comet, seen at different points as it orbited the sun (at the time, the idea that the Earth orbited the sun was relatively novel; it was not known that comets did likewise). Flamsteed attempted to explain this with a complex array of vortexes and reversals of forces and was not taken seriously. Newton, on the other hand, borrowed the idea of an 'active principle' - force at a distance - from his alchemical studies, and dispensed with the idea of an ether altogether. But still he published nothing.

In 1684, Edmund Halley approached Newton out of the blue with an unusual question - arguably one of the most pivotal questions in the history of the western world. Halley, Christopher Wren and Robert Hooke had been having a discussion about one of the cutting-edge questions of astronomy of the day. Like other learned minds, they knew that the planets (including the Earth) orbited the Sun in ellipses. This had led to speculation that the force attracting the planets to the Sun - the force that Copernicus and Kepler had labelled 'gravity' - might decrease in proportion to the inverse of the square of the distance separating the two bodies in question. The unresolved question was whether an inverse square law would lead to elliptical orbits.

After a café discussion, Hooke boldly claimed that he had proved this (almost certainly bluster), leading to a wager between himself and Halley, with Wren offering a book worth 40 shillings to whichever of his companions could prove it. When neither man could produce a proof after the agreed two months, Halley decided to approach Newton, a member of the Royal Society with an outstanding reputation for practical mathematical calculations.

Knowing Newton's reclusive and somewhat vain character, Halley made no attempt to make an appointment; he simply turned up at Newton's rooms in Cambridge and asked him, as England's most eminent mathematician, for his opinion.

Newton's response flabbergasted Halley (although in truth it was not dissimilar to Hooke's). Newton immediately confirmed, without a moment's thought, that an inverse square law would give elliptical orbits. Halley, startled, asked how Newton could be so sure. 'I have calculated it,' he assured his interrogator, thinking back to his work on the 'double' comet of 1680.

When Halley asked for a copy of the proof, however, Newton (again, like Hooke) stalled. It is possible that Newton really could not locate the relevant piece of paper in the clutter of his room; but it has also been suggested that he was feeling burned fingers from previous public exposures of errors in his work, and wanted to double-check his workings to prevent another public humiliation. If the latter was indeed the case, he was wise to do so; his early workings did indeed contain some mistakes that needed correction, and he continued to stall Halley (once again like Hooke; we can only assume that Halley's understanding of character allowed him to correctly judge the difference in credibility between the two men).

In private, Newton began to write up his proof. Having already made the original measurements and calculations, he was now effectively peer-reviewing his own work, redoing every calculation with a critical eye and looking for possible mistakes or invalid assumptions. What he produced was a surprisingly brief document, which he titled De Motu Corporum in Gyrum - 'On The Motion of Bodies In Orbit', better known to posterity as De Motu. Although he allowed Halley to see it to settle the wager, it would be another two years before he plucked up the courage to once again expose his inner thoughts to the wider world.

At around the same time, he made an equally radical (and equally private) suggestion in De Aere et Aethere, predicting that a pendulum in a vacuum would swing forever since there was no interaction between its mass and the 'ether'. Although Newton never completed or published this, and did not go quite as far as to suggest that the ether did not exist at all, it was an important step towards that conclusion. At the same time, however, he suggested in alchemical terms that ether was 'broken down air', just as he believed that air was the 'broken down bodies of Earth'.

But before he completed De Aere, Newton came to realise that Kepler's laws of planetary motion - based on the idea of a vacuum in space, rather than a void filled with ether - matched exactly with his observations. His conclusion was inescapable - the slowing effect of the ether on the planets was precisely zero - it simply wasn't there! He now began work on De Gravitatione et Aequipondio Fluidorum - 'On Gravity and the Equilibrium of Fluids', where he concluded that the 'ether' must be largely vacuum.

It was this that led onto De Motu in 1684, and the first draft of the Principia in 1685, transcribed by Newton's new room-mate Humphrey Newton (no relation).

The Principia

No closer to the Gods can any mortal rise
- Edmund Halley, introduction to the Principia

De Motu was to form the core that would become Newton's masterwork, the Philosophiae Naturalis Principia Mathematica ('The Mathematical Principles of Natural Philosophy', generally known as the Principia). Published in 1687, this centred on the workings of De Motu, but greatly expanded it. Published in three volumes, this contained not only the mathematical formulation of gravity, but also Newton's three laws of motion:

1. A body will move at a constant speed (or remain at rest) unless a force acts upon it.
2. Force equals mass times acceleration.
3. For every action, there is an equal and opposite reaction.

And Newton did not stop at calculus, gravity and mechanics. For the first time, he distinguished weight from mass. But perhaps most influentially, the final volume contained the simple statement that heavenly bodies (i.e. the planets) obey the same laws of motion as Earthly bodies. This, although not the best remembered of Newton's achievements, was perhaps his most controversial claim. For the first time, someone had unified the whole of creation. 'As above, so below,' as mythical alchemist Hermes Trismegistus is supposed to have written. If the goal of modern science is a Unified Theory of Everything, it was Newton who first positioned the goalposts and inflated the football.

The final thing that needs to be noted about the Principia is its complex language - unnecessarily complex, in fact. Even today, when Newton's theories are the basis of the A-level⁶ syllabus in maths and physics, his writings are a challenge even to graduates. It is possible that Newton was influenced by the deliberately obscure style of alchemical writings; it is equally possible that he wanted to discourage laymen from reading his work, or finding fault with it. More likely, both elements played some role. Either way, even in English translation, the Principia is far from a page turner. 'There goes the man,' commented a student at Cambridge many years later, on seeing Newton pass, 'that writt a booke neither he nor anyone else understands.' Leibniz (a future enemy of Newton's; see Isaac Newton: The Feuds) was rather more generous, telling the Queen of Prussia many years later that 'taking mathematicks from the beginning of the world to the time of Sir Isaac, what he had done was much the better half.'

It seems strange therefore to say that the Principia nearly never saw the light of day. Even after Newton had been persuaded to publish, and had spent years working day and night (literally, till 3am most mornings) on it, politics nearly got in the way. With Newton's ally, the president of the Royal Society (and scientific near-illiterate) diarist Samuel Pepys away attending to the new King, and both the vice-presidents on holiday, the remaining members of the cash-strapped Society were conscious of the expensive flop of their previous literary venture, De Historia Priscium - 'The History of Fishes', by Francis Willoughby. Then there was the increasingly bitter personal rivalry with Hooke, who demanded credit for the idea of gravity (Newton first removed all references to Hooke, then threatened to withhold the third and final volume).

Even so, the significance of Newton's writing was immediately recognised by the cognoscenti of the day. Although the first print-run of the Principia was not particularly large, even by the standards of the day (300-400 copies, priced at nine shillings), it sold out immediately, guaranteeing a larger second run.

The complicated genesis of the Principia, and the parallels with other thinkers, should not detract from the genius of Newton's work. He unified the Earthly physics of Galileo with the celestial mechanics of Kepler. At a stroke, he had explained seemingly unrelated concepts such as comets, tides and orbital 'wobble'. And he had given the world a new method by which he had made these advances, and by which others might make their own way - science.

From the moment it was published, Newton's reputation as a genius was forever sealed in the public eye. The deliberately obscure style perhaps helped here.

After the Principia

In 1697, Bernoulli set a pair of problems in mathematics that stumped the intellectual elite of Europe. Using his 'method of fluxions' - his still-unpublished version of calculus - Newton was able to solve both within 12 hours of hearing of them. By this point, his reputation had reached its zenith, and he was the undisputed intellectual master of the world.

Newton's final major scientific work was Opticks. Published in 1704, shortly after Newton became President of the Royal Society, it was intended to cement Newton's place as an active scientist. In truth, he had done virtually no research for nearly two decades. Instead, he collected together all the various scraps from earlier in his career. This meant not just the work he had done as a young undergraduate with the prism from Sturbridge fair (it is in the Opticks that he famously insisted on there being seven colours in the spectrum, despite most people being able to see only five; the number seven tied in with his alchemical views). He also discoursed on the scientific method itself.

Newton's later life was not without its great achievements - his tenure at the Mint alone would have marked him out as a great man of the age. But it is his early work that will be his legacy to posterity.