Isaac Newton

His Amazing List
of Contributions

They Changed Social and
Scientific History
(They dispelled many
superstitions and false dogmas,
saving and improving many lives.)

(2014 Sep blog post)

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This page on Isaac Newtons' amazing contributions
to rational human knowledge

! Note !
A few more 'contributions' ... and web links
may be added --- if/when I re-visit this page.


In retirement, I have had a chance to read many books on science and mathematics that I did not have a chance to read in my working years after getting an advanced degree in mathematics.

When I read (circa 2012) books like 'Journey through Genius' by William Dunham (a mathematician), I started getting an idea of some specific mathematical contributions of Isaac Newton.

But I did not get a good idea of Newton's applications of his mathematical techniques.

About a year after reading that book, I was reading a biography of Isaac Newton by James Gleich.

When I got to pages 134 to 139 of that book (title 'Isaac Newton'), I was struck by the list of scientific contributions that Isaac Newton made.

To realize what sweeping contributions Newton made, one needs to be aware that, at that time (around 1660 to 1720), the state of human knowledge in many areas was more superstition and false dogmas than fact-based knowledge.

For example:

  • There were confusing, non-quantitive ideas about weight and falling bodies and moving bodies --- not helped by some long-taught ( 2,000 years !! ) ideas of Aristotle that were quite 'off-base' and never tested by experiment (until Galileo made a great start).

  • There was very little good data on the rise and fall of tides, resulting in essentially no progress in determining why they occurred and what were their characteristics (regularities, irregularities, etc.).

  • There were many superstitious and false ideas about the nature of comets.

  • There was not enough verifying evidence that the sun and planets did not rotate in circles (or epicycles of Hipparchus and Ptolemy --- circles-on-circles) around the earth.

    And the Vatican insisted that anyone, who did not believe in the earth-centered view of the heavens, change their views to that of the Vatican (or suffer death).

    Giordano Bruno paid with his life (burned at the stake) and Galileo almost paid with his.

    Descartes is said to have been quite aware that he had to be quite careful what he said and wrote, after he saw the fates of Bruno and Galileo.

Early in his scientific career at Cambridge, Newton had written a work on Optics that stirred up a lot of resistance to some of his views on the nature of light.

He did not enjoy having to defend his views.

After that experience, he tended to keep most of his scientific investigations to himself.

Eventually, Edmond Halley (after whom Halley's comet is named), encouraged Newton --- through much flattery and coaxing --- to publish many of his discoveries in a initial short work --- which was later expanded into an extensive work known by its shortened title 'Principia Mathematica'.

Halley even paid for the initial printings when Newton did not feel so inclined.

Some of Newton's Contributions/Discoveries

Here are some of Isaac Newton's contributions --- many of which I have gleaned from pages 134-139 of James Gleich's book on Isaac Newton.

As Newton himself said, he stood on the shoulders of giants.

For example, he used data from predecessors such as Copernicus, Kepler, and Galileo to develop and verify his observations and techniques.

And he used mathematical techniques based on the work of others, such as Euclid, Archimedes, Wallis, Barrow (his mentor at Cambridge), and others.

Often you read of Newton being famous for Newton's 3 laws of motion --- but I think it is much more impressive and meaningful to be aware of the following feats he accomplished.

  • From the period of moon's orbit around earth, Newton calculated the acceleration due to gravity of a body near the surface of Earth:

    15 feet, 1 inch, and 1 and 7/9 lines (twelfths of an inch).

  • In Book 3 of 'Principia Mathematica', titled 'System of the World', Newton calculated the orbital periods and greatest distance between:

    • 5 planets around the sun
      (Mercury, Venus, Mars, Jupiter, Saturn)

    • Earth and its moon

    • 4 moons of Jupiter and Jupiter

  • Demonstrated Jupiter's influence on Saturn's motion, via gravitational calculations.

  • Calculated weights of a given mass on various planets.

  • Calculated densities of planets.
    (Found Earth to be 4 times denser than Jupiter or the sun.)

  • Calculated the shape of the Earth.

    (Predicted a bulge at the equator because of rotation of the Earth. At the time, there were some who said the Earth bulged at the Poles rather than at the equator. Later measurements confirmed that Newton was right.)

  • Calculated that a given mass weighs differently at different altitudes.

    (This was later confirmed by measurements, for example, on mountain tops versus at sea level. Galileo thought that gravitational acceleration was the same at all heights above Earth.)

  • Explained the slow 'precession' of Earth's rotation.

    (The orientation of Earth's axis of rotation, against the background of the stars, changes about 1 degree every 72 years --- due to gravitational pull of the sun and moon on earth's equatorial bulge.)

  • The individual masses of a decomposition of a sphere exert a gravitational force as if the masses were concentrated at the center.

    (This makes it sensible to treat a planet like the Earth as if its entire mass were located at the center of the Earth. Principia 590. This paved the way for his showing that planet orbits can be deduced to be elliptical in shape.)

  • Deduced Kepler's 3 laws of planetary motion from the inverse-square law of gravitational attraction.

    • planetary orbits are elliptical

    • planets sweep out 'equal areas in equal time'

    • "The square of the periodic times are to each other as the cubes of the mean distances."

  • Demonstrated that paths of comets (ellipses, parabolas, hyperbolas) can be calculated based on gravitational forces, for example, the gravitational force of our sun.

  • Newton made it known that he realized that most of his calculations were approximations that did not take into account the gravitational forces of all the planets.

    In other words, he realized the 3-body problem is not resolvable to a simple algebraic formula/curve like that of an ellipse --- and that the N-body problem, N > 3, is even more challenging.

    He wrote "Each time a planet revolves, it traces a fresh orbit, as happens also with the motion of the moon, and each orbit is dependent upon the combined motions of all the planets, not to mention their actions upon each other. Unless I am much mistaken, it would exceed the force of human wit to consider so many causes of motion at the same time, and to define the motions by exact laws which would allow of an easy calculation."

    One can only wonder what he would have done if electronic-digital-computers had been available in his day.

    He may have gone on to develop much of today's numerical methods for solving differential equations --- thus attacking the N-body problem, rather than stopping with the above statement.

  • Newton blew apart Descarte's notion of 'vortices' to (qualitatively) explain various astronomical phenomena.

    And, going much further than that, Newton had the courage to promote 'action at a distance' (gravity) when most 'natural philosophers' of the time (including Galileo and Huygens) considered such a notion as 'occult'.

  • Newton did not claim to be able to provide a cause for gravity.

    He did not even offer a conjecture.

    He wrote
    "It is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea."

And Newton even presented results on fluids.

    (On his family farm, he was known to be interested in observing the flow of water around rocks in a brook.

    He made sketches of fluid flow in his notebooks.

    Apparently, these were early signs that he would be motivated to deduce how gravity and the properties of fluids could be used to explain some fluidic motions.)

  • He determined what shape let an object pass through a fluid with the least resistance.

  • He explained tides (2 high tides per 25 hours) by pull of the sun and moon on the fluidic sea.

    (It took a lot of effort on Newton's part to accumulate data on tides, in order to verify the results of his calculations.

    The data on tides were rare and/or poor --- i.e. 'full of holes' --- when Newton wrote 'Principia Mathematica'.)

The 'Books' of 'the Principia' :

In the book 'Six Great Scientists' by J. G. Crowther, on pages 120 to 121, I found a nice overview of the 3 books of the 'Principia'.

"The whole work contains about a quarter of a million words, and is divided into three books."

  1. "In the first book, Newton completes Galileo's work on the laws of motion, and expresses it in the modern form which has enabled it to be used to solve most of the practical tasks of the machine age."

  2. "In the second book, he analyzed the complex problems of the motions of bodies in resistant media.

    He had been led to this in order to dispose of Descartes' theory of the universe, as a system of vortices in some kind of medium."

    "He worked out how a solid body could move in a gas or a liquid, and from his results concluded that the planets must be free from any kind of resisting medium."

    "Incidentally, he founded the mathematical theory of gases and liquids.

    He showed that Boyle's law, which states that when the pressure of a mass of gas is doubled its volume is halved, could be deduced from the conception of a gas as a collection of elastic [colliding] atoms."

    "His mathematical analysis of the effect of pressure on gases led him to calculate the speed of sound-waves.

    He incidentally gave the first mathematical treatment of wave motion".

    "His analysis of the motion of bodies in fluids led to the foundation of the science of hydrodynamics.

    He even gave the shape of the body of least resistance for going through a liquid, and conceived that it might 'be of use in the building of ships'.

    He gave no immediate hint of how he had discovered it, but in order to solve it he must have known the principles of the calculus of variations, which was not re-discovered until a hundred years later, by Lagrange."

    "He tranformed the knowledge of gases and liquids from empiricism to a mathematical science.

    He provided the forthcoming age of steam and machinery with its basic theory."

  3. The third book, 'The System of the World', "was more spectacular and contained his astounding account of the mechanics of the heavens.

    He revealed the whole operations of the known cosmos as a system of attracting and revolving bodies, almost like an all-comprehending cosmical watch, in which every little movement and rotation could be calculated down to [very fine] detail."

    Although, scientifically speaking, the first 2 books were as important as the 3rd, it was the 3rd book that had great social impact --- essentially stopping the killings and torturings of the Catholic Inquisitions, and opened the way for 'natural philosophers' in European countries to research nature with much less fear of being burned at the stake or being tortured.

Crowther's account of Isaac Newton's life points out that, in the mid-1500's, King Henry the 8th of England "removed England from the domination of the Catholic Curch" and thus King Henry "created the conditions in which her scientists could work, free from the persecution of the Vatican."

Unlike Copernicus, Kepler, Galileo, and Descartes, Newton did not have to fear publishing researches, while he was alive, that might lead the Vatican to torture or kill him.

Newton grew up as Cromwell and the Puritans overthrew the English kings --- and he lived through the restoration of the monarchy and James the 2nd trying to re-establish Catholicism in place of the Anglican and other protestant religions.

Fortunately, James II was not able to reinstate Catholicism as the only religion --- neither at Cambridge University nor throughout England.

    (Interestingly, Newton had a hand in turning back both those attempts --- first at Cambridge University, and later nation-wide, as a member of Parliament, representing Cambridge.)

Crowther's account points out:

The effects of Newton's Principia was "staggering. Hitherto the universe had been regarded as a vague, palpitating, mysterious object.

Now it was revealed as operating according to known laws, so that every little feature of it could [theoretically] be precisely calculated."

"The whole universe was brought under the subordination of the human intellect [well ... except for the weather, earthquakes, volcanos, tsunamis, lightning, viruses, bacteria, parasites, and various insects such as mosquitoes and ants], so that the mind of man seemed suddenly to be enormously extended, and raised in dignity.

It strengthened the confidence in human powers, and contributed to the optimism which characterized the Age of Reason, and helped to inspire the French Revolution and the rise of modern scientific civilization."

"No wonder Newton appeared to his contemporaries as almost superhuman."

And no wonder that, when Newton died, England gave him burial honors that were usually reserved for royalty and national military heroes.

Note that in the process of providing 'laws' from which details of all these natural phenomena could be deduced, Newton drastically reduced the amount of superstition and hocus-pocus in the world --- in particular, reducing the number of human abuses/deaths due to Inquisitions.

The Vatican Censorship Continues

You would think that more than 300 years after Newton's amazing set of deductions, and after Newton proved that Giordano Bruno and Galileo were certainly much more 'on the mark' about the nature of 'the heavens' than the Pope and his bishops, the Vatican would have learned a lesson about interfering where physicists tread.

    The Sun out-weighs the Earth by about a million times, and the Sun 'slings' the Earth around far more than the Earth does any slinging of the Sun.

But NO. 'The Church' still seems to think it needs to provide its 'infallible' guidance to physicists.

In 2014, I was reading Stephen Hawking's book 'The Illustrated Brief History of Time', and I read the following astounding paragraph (page 145).

I quote Hawking directly to make sure I convey exactly what he said.

Note, in particular, the sentence in bold, below.

    Hawking wrote
    "... in 1981, my interest in questions about the origin and fate of the universe was reawakened when I attended a conference on cosmology organized by the Jesuits in the Vatican.

    The Catholic Church had made a bad mistake with Galileo when it tried to lay down the law on a question of science, declaring the sun went round the earth.

    Now, centuries later, it [the Vatican] had decided to invite a number of experts to advise it on cosmology.

    At the end of the conference, the participants were granted an audience with the Pope.

    He told us that it was all right to study the evolution of the universe after the big bang, but we should not inquire into the big bang itself because that was the moment of Creation and therefore the work of God."

    Hawking continued :

    "I was glad then that he did not know the subject of the talk I had just given at the conference --- the possibility that space-time was finite but had no boundary, which means that it had no beginning, no moment of Creation.

    I had no desire to share the fate of Galileo ..."

I am not really shocked at this Pope/'Church' behavior.

The new pope 'Francis' in 2013 was almost immediately announcing that we are all sinners in need of the Church's redemption.

    (I do not feel that I am a major sinner, and I certainly do not feel that I need to confess my paltry sins regularly to one of the Pope's priests.)

And another reason I am not really shocked is that when my wife wanted our daughter to be baptised in the Catholic church, I was informed by the local priest that our less-than-one-year-old daughter was already a sinner who needed to be baptised to absolve her of her sins.

Nice racket they have going.

Declare even new-borns to be sinners and in need of 'the Church'.

And another reason I am not really shocked is because the Church continues its shocking behavior in its Church-directed 'musical chairs' with pedophile priests (moving them around from one diocese to another).

This odious activity by 'the Church' hierarchy continues scarcely abated in 2014.

The Newton versus Leibniz Debate
on the inventor of 'Calculus'

Newton essentially invented the basic techniques of 'the calculus' in order to prove his many results on gravitational effects.

For more than 300 years the debate has raged on (or simmered) --- over whether Newton or Leibniz invented 'the calculus' --- because Leibniz published first.

I contend that Leibniz probably deserves a lot of credit for presenting calculus in a way that was eventually more popular than the 'fluxions' and 'fluents' of Newton.

BUT Newton certainly seems to have provided a WEALTH OF APPLICATIONS of 'the calculus' --- APPLICATIONS that blew away a multitude of superstitions and falsehoods of the day.

The list of Newton's applications of the methods of 'calculus' to astronomy and gravitational attraction on Earth --- and even applications to fluids --- appears to dwarf any applications of 'the calculus' that Leibniz may have written down.

Leibniz not totally independent of Newton

In addition, it is known that Leibniz had visited England and had communicated (both in person and by letters) with many in England who knew of some of Newton's published and unpublished works --- for example, Henry Oldenberg and John Collins.

Leibniz even had some communications with Newton --- although Newton was not very generous with details in his written communications with Leibniz, especially in their later letters.

Leibniz probably got some hints and inspiration from some of those communications.

So I don't think anyone can validly argue that Leibniz invented 'the calculus' totally independently of Newton.

The human side of Newton
(and his contemporaries)

It is sad to read that Newton spent a lot of time in his last years of life in putting down Leibniz as an inventor of 'the calculus'.

After Leibniz died, Newton even gloated over 'breaking the heart' of Leibniz.

There were plenty of applications and developments of calculus to be worked on.

Newton did not publish a 'be all and end all' work on 'the calculus'.

It certainly seems that Newton could have been more magnanimous.

It appears that he was only human after all --- insecure and even petty in some ways.

It seems that Newton was not alone in the 'poor behavior' department, among English 'natural philosophers' of the time.

Newton had many run-ins with Robert Hooke and John Flamsteed, who also demonstrated pettiness, jealousy, and other not-very-admirable human traits.

The English mathematician John Wallis is said to have encouraged Newton to assert a claim as inventor of 'the calculus'.

Although this seems to be mean-spirited by Wallis, it is rather surprising that Wallis was such a supporter of Newton, for if Newton's works had not been published, Wallis would probably have stood out as England's leading mathematician of the period.

Some of Newton's mathematical results were built directly on work of Wallis.

It seems that Wallis was a champion of English mathematicians over German, French, and other mathematicians --- so much so that those nationalistic feelings over-rode any feelings of jealousy that he may have been tempted to have toward Newton.


In 2014, I saw a YouTube video inteview of Neil deGrasse Tyson in which he was asked who he thought was the greatest physicist (so far).

He said Newton --- because of his many deductions from his codification of the laws of gravity and motion --- and the influence of those deductions on the course of human history.

When you see a list of Newton's many deductions (like the list above), it is hard to disagree with Tyson's choice --- even though there have been some amazing additions to the body of physical (astronomical and atomic) knowledge in the 20th century and beyond --- such as Einstein's contributions, on both the cosmic and atomic levels.

Some proposed additions to this page

If I can find a nice summary list of the 'propositions' of Newton's 'Principia Mathematica' (or any of his other works), I plan to make the list(s) available via this page.

In addition:

It is said by some that Newton must have actually derived many of his results using more algebraic methods than the heavily geometric methods that he used in the Principia.

Some say that he decided to use more geometric methods for his published proofs, because that is what scholars would be more likely to accept.

So Newton followed the rigorous geometric exposition example that Euclid set in the 'Elements'.

Newton presented his results in the Principia as a sequence of propositions or theorems for which he supplied proofs with copious geometric diagrams.

However, there is no evidence he ever devised a more algebraic development of results in the Principia.

I was motivated to find a re-write of most of the important results of the Principia in a more modern form (like dy/dx and delta-x notation, and Cartesian x-y-z coordinates).

I wanted to find his geometric proofs rendered in a more modern and, hopefully, a more understandable form.

I found many books of that kind by various mathematicians and physicists, and I have made a list of those books available on a Newton Math References page of this site.

A common story that you see in biographies of Newton is that one Cambridge student, upon seeing Newton, said, "There goes the man that writt a book that neither he nor anybody else understands."

Fortunately, there were many, like Halley, who were eager to read the book and understand it.

A few more references:

There is a 1729 translation of the Principia (from Latin to English), done by Andrew Motte (1696-1734).

There is a summary of Motte's translation of the many sections of the 3 books available at

A re-write of Motte's translation was started by Florian Cajori around 1929.

In 1999, a new translation of the Principia was published, with commentary, by Professor I. B. Cohen of Harvard.


For further info on the many types of contributions Newton made to the body of human knowledge, here are some links to WEB SEARCHES on keywords related to Newton's various contributions.

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Isaac Newton - Amazing Contributions
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