Annus mythologicus

Almost inevitably Newton’s so-called Annus mirabilis has become a social media meme during the current pandemic and the resulting quarantine. Not surprisingly Neil deGrasse Tyson has once again led the charge with the following on Twitter:

When Isaac Newton stayed at home to avoid the 1665 plague, he discovered the laws of gravity, optics, and he invented calculus.

Unfortunately for NdGT and all the others, who have followed his lead in posting variants, both positive and negative, the Annus mirabilis is actually a myth. So let us briefly examine what actually took place and what Isaac actually achieved in the 1660s.


Portrait of Newton at 46 by Godfrey Kneller, 1689 Source: Wikimedia Commons

We will start with the calculus, which he didn’t actually invent at all, neither in the 1660s nor at any other time. Calculus has a more than two thousand year history stretching back to fourth century BCE. The development of calculus accelerated in the seventeenth century beginning with Kepler and Cavalieri and, previous to Newton, reaching a high point in the work of John Wallis. What Newton, like Leibniz, did was to collate, order and expand the work that others had already produced. Let us take a closer look at what Newton actually achieved in the 1660s.

But before we start, one point that various people have made on the Internet is that during this time Newton was a completely free agent with no commitments, obligations or burdens, a bachelor without children. In college his chambers were cleaned by servants and his meals were prepared by others. At home in Woolsthorpe all of his needs were also met by servants. He could and did devote himself to studying without any interruptions.

Newton, who entered Trinity College Cambridge in June 1661, was an indifferent student apparently bored by the traditional curriculum he was supposed to learn. In April 1664 he was due to take a scholarship exam, which would make him financially independent. The general opinion was not positive, however he did pass as he also passed his BA in the following year, when the prognosis was equally negative. Westfall suggests that he had a patron, who recommended that Cambridge retain him.

Freed by the scholarship, Newton now discovered his love and aptitude for the modern mathematics and set off on a two-year intensive study of the subject, almost to the exclusion of everything else, using the books of the leading mathematicians of the period, Descartes (but in the expanded, improved Latin edition of van Schooten), Viète and Wallis. In October 1666 Newton’s total immersion in mathematics stopped as suddenly as it had begun when he wrote a manuscript summarising all that he had internalised. He had thoroughly learnt all of the work available on the modern analytical mathematics, extended it and systematised it. This was an extraordinary achievement by any standards and, although nobody knew about it at the time, established Newton as one of the leading mathematicians in Europe. Although quite amazing, the manuscript from 1666 is still a long way from being the calculus that we know today or even the calculus that was known, say in 1700.

It should be noted that this intense burst of mathematical activity by the young Newton had absolutely nothing to do with the plague or his being quarantined/isolated because of it. It is an amusing fact that Newton was stimulated to investigate and learn mathematics, according to his own account, because he bought a book on astrology at Sturbridge Fair and couldn’t understand it. Unlike many of his contemporaries, Newton does not appear to have believed in astrology but he learnt his astronomy from the books of Vincent Wing (1619–1668) and Thomas Street (1621–1689) both of whom were practicing astrologers.

I said above that Newton devoted himself to mathematics almost to the exclusion of everything else in this period. However, at the beginning he started a notebook in which he listed topics in natural philosophy that he would be interested in investigating further in the future. Having abandoned mathematics he now turned to one of those topics, motion and space. Once again he was guided in his studies by the leaders in the field, once again Descartes, then Christiaan Huygens and also Galileo in the English translation by Thomas Salusbury, which appeared in 1665. Newton’s early work in this field was largely based on the principle of inertia that he took from Descartes and Descartes’ theories of impact. Once again Newton made very good progress, correcting Descartes errors and demonstrating that Galileo’s value for ‘g’ the force of acceleration due to gravity was seriously wrong. He also made his first attempt to show that the force that causes an object to fall to the ground, possibly the legendary apple, and the force that prevents the Moon from shooting off at a tangent, as the principle of inertia says it should, were one and the same. This attempt sort of failed because the data available to Newton at the time was not accurate enough. Newton abandoned this line of thinking and only returned to it almost twenty years later.

Once again, the progress that the young Newton made in this area were quite impressive but his efforts were very distant from his proof of the law of gravity and its consequences that he would deliver in the Principia, twenty year later. For the record Newton didn’t discover the law of gravity he proved it, there is an important difference between the two. Of note in this early work on mechanics is that Newton’s concepts of mass and motions were both defective. Also of note is that to carry out his gravity comparison Newton used Kepler’s third law of planetary motion to determine the force holding the Moon in its orbit and not the law of gravity. The key result presented in Principia is Newton’s brilliant proof that Kepler’s third law and the law of gravity are in fact mathematically equivalent.

The third area to which Newton invested significant time and effort in the 1660s was optics. I must confess that I have absolutely no idea what Neil deGrasse Tyson means when he writes that Newton discovered the laws of optics. By the time Newton entered the field, the science of optics was already two thousand years old and various researchers including Euclid, Ptolemaeus, Ibn al-Haytham, Kepler, Snel, and Descartes had all contributed substantially to its laws. In the 1660s Newton entered a highly developed field of scientific investigation. He stated quite correctly that he investigated the phenomenon of colour. Once again his starting point was the work of others, who were the leaders in the field, most notably Descartes and Hooke. It should be clear by now that in his early development Newton’s debt to the works of Descartes was immense, something he tried to deny in later life. What we have here is the programme of experiments into light that Newton carried out and which formed the basis of his very first scientific paper published in 1672. This paper famously established that white light is made up of coloured light. Also of significance Newton was the first to discover chromatic aberration, the fact that spherical lenses don’t sharply focus light to a single point but break it up into a spectrum, which means the images have coloured fringes. This discovery led Newton to develop his reflecting telescope, which avoids the problem of chromatic aberration.


Newton’s sketch of his crucial experiment. Source: Royal Society

Here trying to establish a time line of when and where he carried out these experiments is very difficult, not alone because Newton’s own statements on the subject are contradictory and some of them are provably false. For example he talks about acquiring a second prism from Sturbridge Fair in a year when one didn’t take place. Also Newton’s source of light was sunlight let into a darkened room through small hole in the shutters. This was only possible at certain times of year and certain times of day when the sun is in the right position respective the window. Newton claims experiments made at times where these conditions weren’t met. That not all the experiments were made in Woolsthorpe Manor is clear, as many of them required two operators, which means that they were made when Newton was back in his chambers in Trinity College. The best guestimate is that this programme of experiments took place over the period 1660 to 1670, so once again not in Newton’s year of quarantine.

Another thing that keeps getting mentioned in connection with this story is that during his experiments on light Newton, shock-horror, stuck a pin in his eye! He didn’t. What he did was to insert a bodkin, a flat, blunt, threading needle, into his eye-socket between his skull and his eyeball in order to apply pressure to the back of his eyeball. Nasty enough, but somewhat different to sticking a pin in his eye.

All in all the developments that the young Newton achieved in mathematics and physics in the 1660s were actually spread out over a period of six years. They were also not as extensive or revolutionary as implied in Neil deGrasse Tyson brief tweeted claim. In fact a period of six intensive years of study would be quite normal for a talented student to acquire the basics of mathematics and physics. And I think we can all agree that Newton was very talented. His achievements were remarkable but not sensational.

It is justified to ask where then does the myth of the Annus Mirabilis actually come from? The answer is Newton himself. In later life he claimed that he had done all these things in that one-year, the fictional ones rather than the real achievements. So why did he claim this? One reason, a charitable interpretation, is that of an old man just telescoping the memories of his youth. However, there is a less charitable but probably more truthful explanation. Newton became in his life embroiled in several priority disputes with other natural philosophers over his discoveries, with Leibniz over the calculus, with Hooke over gravity and with Hook and Huygens over optics. By pushing back into the distant past some of his major discoveries he can, at least to his own satisfaction, firmly establish his priority.

The whole thing is best summarised by Westfall in his Newton biography Never at Rest at the end of his chapter on the topic, interestingly entitled Anni mirabiles, amazing years, not Annus mirabilis the amazing year, on which the brief summary above is largely based. It is worth quoting Westfall’s summary in full:

On close examination, the anni mirabiles turn out to be less miraculous than the annus mirabilis of Newtonian myth. When 1660 closed, Newton was not in command of the results that have made his reputation deathless, not in mathematics, not in mechanics, not in optics. What he had done in all three was to lay foundations, some more extensive than others, on which he could build with assurance, but nothing was complete at the end of 1666, and most were not even close to complete. Far from diminishing Newton’s stature, such a judgement enhances it by treating his achievements as a human drama of toil and struggle rather than a tale of divine revelation. “I keep the subject constantly before me, “ he said, “and wait ‘till the first dawnings open slowly, by little and little, into full and clear light.” In 1666 by dint of keeping subjects constantly before him, he saw the first dawnings open slowly. Years of thinking on them continuously had yet to pass before he gazed on a full and clear light.[1]

Neil deGrasse Tyson has form when it comes to making grand false statements about #histSTM, this is by no means the first time that he has spread the myth of Newton’s Annus mirabilis. What is perhaps even worse is that when historians point out, with evidence, that he is spouting crap he doesn’t accept that he is wrong but invents new crap to justify his original crap. Once he tweeted the classic piece of fake history that people in the Middle Ages believed the world was flat. As a whole series of historians pointed out to him that European culture had known since antiquity that that the world was a sphere, he invented a completely new piece of fake history and said, yes the people in antiquity had known it but it had been forgotten in the Middle Ages. He is simply never prepared to admit that he is wrong. I could bring other examples such as my exchange with him on the superstition of wishing on a star that you can read here but this post is long enough already.

Bizarrely Neil deGrasse Tyson has the correct answer to his behaviour when it comes to #histSTM, of which he is so ignorant. He offers an online course on the scientific method, always ready and willing to turn his notoriety into a chance to make a quick buck, and has an advertising video on Youtube for it that begins thus:

One of the great challenges in this world is knowing enough about a subject to think you’re right but not enough about the subject to know you’re wrong.

This perfectly encapsulates Neil deGrasse Tyson position on #histSTM!

If you want a shorter, better written, more succinct version of the same story then Tom Levenson has one for you in The New Yorker 

[1] Ricard S. Westfall, Never at Rest: A Biography of Isaac Newton, CUP; Cambridge, ppb. 1983, p. 174.



Filed under History of Astronomy, History of Mathematics, History of Optics, Myths of Science, Newton

20 responses to “Annus mythologicus

  1. A nice post, but one paragraph brought me up short:

    Calculus has a more than two thousand year history stretching back to fourth century BCE. The development of calculus accelerated in the seventeenth century beginning with Kepler and Cavalieri and, previous to Newton, reaching a high point in the work of John Wallis. What Newton, like Leibniz, did was to collate, order and expand the work that others had already produced.

    I know what you mean: Archimedes’ “On the Sphere and Cylinder”, Cavalieri’s method of indivisibles, Kepler’s wine casks, Barrow’s contribution. On the other hand, I think “collate, order, and expand” is likely to give a seriously misleading impression to anyone not already familiar with the history, but who has taken the usual college calculus course.

    “Collate, order and expand” suggests very little originality. And while “calculus” doesn’t have a exact definition, it surely suggests a symbolic and semi-mechanical calculation technique, precisely what Archimedes didn’t have. (And yes, I’ve read his “On the method”. It’s not a general technique.)

    Your later sentence,

    Although quite amazing, the manuscript from 1666 is still a long way from being the calculus that we know today or even the calculus that was known, say in 1700.

    is right on point.

    I think I wouldn’t have found the first paragraph so disconcerting had you written “prehistory” instead of “history”.

    • Santarakshita

      I hope this is not rude but are you Weiss of Madsen-Weiss? I only ask because your avatar is a frame of Thurston’s eversion.

      • I wish! I just liked the sphere eversion ever since I saw the video. You can see my way more modest mathematical endeavors (purely expositions, no original research) at

  2. Once again Newton made very good progress, correcting Descartes errors and demonstrating that Galileo’s value for ‘g’ the force of gravity was seriously wrong.

    Typo: Descartes -> Descartes’

    Strictly speaking, “force” should be “acceleration”, but since this is referring to a time before conceptual clarity had been achieved, perhaps the distinction was not yet so sharp in Newton’s mind!

  3. In my opinion the game changing invention was analytic geometry, also known as graph paper with an x and y axis. Given this tool it seems inevitable that Eudoxus like methods would be used determine the slope of a tangent to a curve at a point. Which Fermat did. Or to find the area under a curve. Which Cavalieri did.

    When I was in high school our algebra teacher told us René Descartes’ invented graph paper with an x and y axis. Which is why number pairs are called Cartesian coordinates. I only recently learned that Fermat was a co-inventor.

    In my opinion Fermat should be credited as the father of calculus. Neither Newton nor Leibniz deserve the title (again, in my opinion).

    • I think I know what Thony would say: he’d accuse you of committing the father of sin. And I’d have to agree with him.

      Of course Fermat was one of the fathers, and not only because of his work on analytic geometry. There’s also his method of tangents, and his Principle of Least Time.

      OTOH, Fermat’s (and Descartes’s) analytic geometry isn’t ours, either! For one thing, neither allowed negative coordinates. As Francis Borceux has remarked, this was a significant obstacle to the effective use of the new technique. (It seems Wallis gets the credit for allowing negative coordinates.)

    • I would certainly make rude noises about any use of father of, I once wrote a blog post about it. Certainly the creation of analytical geometry was an important milestone on the road in the development of analysis and Fermat deserves as much credit as Descartes for its development. Fermat also played a significant role in development of the systematic methodology for calculating tangents and thus derivatives, as Michael correctly points out.

      Interesting is the story behind what are now known as Cartesian coordinates. You won’t find such a rectangular coordinate system by either Descartes or Fermat. They both used any convenient pair of straight lines that crossed including parts of the geometrical figure under discussion. The ‘Cartesian coordinates’ first appear in Van Schooten’s expanded Latin translation of Descartes, which was Newton’s source for analytical geometry.

  4. araybold

    One small point: chromatic aberration is a consequence of dispersion, the result of a medium having different refractive indices at different wavelengths. While simple spherical lenses suffer from it, so do lenses of other shapes, and it is also the mechanism by which prisms produce spectra. There is a solution to be found in compound lenses, assembled from elements having differing dispersion, or including a diffractive element (the latter possibility is new to me.)

  5. V interesting. I notice that this article, and the NY article refereed to, draw from one Newton biography. It would be useful to know if the views presented represent a consensus amongst Newton biographers…

    • Westfall’s analysis is based on a careful examination of Newton’s own manuscripts from the years in question, which are all still extant. If somebody disagreed with Westfall, and as far as I know, and I’ve read a lot of Newton biographies, nobody does they would have to bring some extraordiary evidence, which until now was unknown.

  6. I wonder why the rumour persists, given that Westfall biography was published in the 1980s and is highly respected. I guess it’s the old story that it’s very hard to dislodge a zombie truth once it’s established

  7. Can you suggest me any book history of science book on the role of socio-political and economic factors that led to scientific revolution as opposed to what is generally considered as those discoveries were made in isolation ?

    • There are as you suggest strong socio-political and economic factors involved in the emergence of modern science but I’m afraid I can’t recommend any books that deal specifically with the topic, as I have never read any. I don’t even know if such literature exists, if not, it should.

      • I’m supposed to write an assignment on such a topic but unable to write any resource online . I’ve gone through your posts which helped me a lot . Can you suggest me anything else ?

      • I have to write an assignment on such a topic but unable to find any resource online . I did go through your posts which helped me a lot. Can you suggest me something ?

  8. Pingback: Some Things I’ve Been Reading – nebusresearch

  9. Zeeshan Amin

    The year of plague was the most significant year in Newton’s scientific career; those leisurely studies laid the foundation for his future accomplishments.

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