Which year did Newton first work with calculus: 1664,1665 or 1666?

[user079622]

Which exactly year Newton first time write about calculus, 1664, 1665 or 1666?

I find three years circles in many sources, 1664, 1665 and 1666 , do yo maybe know some thrusted source where we can find correct information?

Here is 1665 https://cosweb1.fau.edu/~jordanrg/LLS_05/WWW4/lecture_4.pdf

Here is 1666 https://en.wikipedia.org/wiki/Leibniz–Newton_calculus_controversy

etc..

Same thing with "Year of Wonders", somewhere is 1665 or 1666.
Do we have any papers that can validate this dates or people just roughly guess the dates?

 

[fresh_42]

You can date when Newton became a professor (1669), published the Principia (1687), or when Leibniz stayed in Paris (1672).

All other dates can only be letters, in my opinion. At least I couldn't find any sources. I heard just yesterday (on tv) that Newton had been forced into "home-office" due to a general "lockdown" because of the plague in London. And that was 1664-1665. So he probably was very productive in these two years. But it wasn't as it is today, now that we measure science by publications. Also, "first time write about calculus" isn't particularly precise. Is it when he first set a dot above the $x$? However, $\dot{x}$ was to Newton simply a velocity. Is that already calculus?

 

[user079622]

You can date when Newton became a professor (1669), published the Principia (1687), or when Leibniz stayed in Paris (1672).

All other dates can only be letters, in my opinion. At least I couldn't find any sources. I heard just yesterday (on tv) that Newton had been forced into "home-office" due to a general "lockdown" because of the plague in London. And that was 1664-1665. So he probably was very productive in these two years. But it wasn't as it is today, now that we measure science by publications. Also, "first time write about calculus" isn't particularly precise. Is it when he first set a dot above the $x$? However, $\dot{x}$ was to Newton simply a velocity. Is that already calculus?

Which calendar do you use it when talk about this years, new or old english?( He was born in 1643(new) and 1642 old calendar.

He write calculus in his pocket notebook, that was way before principia.


https://cudl.lib.cam.ac.uk/collections/newton/1

 

[user079622]

quote from https://cudl.lib.cam.ac.uk/view/MS-ADD-04004/1 :
" By autumn 1665, Newton had worked out a method for replacing the use of infinitesimal increments of space in his calculations with instantaneous changes in the velocity of a moving point by which curved lines were described. Stimulated entirely by his reading, Newton had invented the method of fluxions, or calculus, through the working in his ‘Waste Book’"

 

[fresh_42]

Which calendar do you use it when talk about this years, new or old english?( He was born in 1643(new) and 1642 old calendar.

He write calculus in his pocket notebook, that was way before principia.


https://cudl.lib.cam.ac.uk/collections/newton/1

I use 1642 as in Jean Dieudonné, Geschichte der Mathematik 1700-1900, Vieweg Verlag 1985.

But I haven't found any direct references besides a very short biography. Newton's name is mentioned a few dozen times. I think that Dieudonné's references were other books about Newton, i.e. I have only the first level of research and one has to dig deeper in the library. As said, I doubt that there is anything reliable other than letters. And Newton wasn't exactly famous for exchanges by letters.

 

[user079622]

Do you agree that most important year in history of physics is 1665, calculus, law of motions and gravity?

 

[fresh_42]

Do you agree that most important year in history of physics is 1665, calculus, law of motions and gravity?

No, I do not. This isn't how science works in my opinion. There is a reason that Leibniz, Newton, and very likely some French mathematicians developed calculus at nearly the same time. The time had come! The famous quotation - sometimes erroneously attributed to Newton ...

Dicebat Bernardus Carnotensis nos esse quasi nanos gigantum umeris insidentes, ut possimus plura eis et remotiora videre, non utique proprii visus acumine, aut eminentia corporis, sed quia in altum subvehimur et extollimur magnitudine gigantea

"Bernhard of Chartres said [ed.: around 1120] that we are, as it were, dwarves sitting on the shoulders of giants in order to be able to see more and more distant things than them - of course not thanks to our own sharp eyesight or physical size, but because the size of the giants lifts us up."

... describes in my opinion that even big discoveries haven't occurred out of thin air but were ultimately logical consequences of the discoveries and developments before. Faraday (1831-1854) came before Maxwell (1865), Michelson-Morley (1881) came before Einstein (1905), Sophus Lie (1872-1886) came before Emmy Noether (1918). Maxwell, Einstein, Noether are all synonyms for ground-breaking results. But every one of them had predecessors that paved their ways. I do not think that it was any different for Newton.

P.S.: Otto Lilienthal was earlier than the Wright brothers and Philipp Reis was earlier than Graham Bell, Joseph Swan earlier than Edison, and Armat and Fuhrmann were earlier than the Lumière brothers, and, of course, earlier than Edison.

 

[phinds]

Which exactly year Newton first time write about calculus, 1664, 1665 or 1666?

Well, if you pick the wrong one, you could be off by a maximum of a whopping one half of a percent. Do you really care?

 

[user079622]

No, I do not. This isn't how science works in my opinion. There is a reason that Leibniz, Newton, and very likely some French mathematicians developed calculus at nearly the same time. The time had come! The famous quotation - sometimes erroneously attributed to Newton ...

"Bernhard of Chartres said [ed.: around 1120] that we are, as it were, dwarves sitting on the shoulders of giants in order to be able to see more and more distant things than them - of course not thanks to our own sharp eyesight or physical size, but because the size of the giants lifts us up."

... describes in my opinion that even big discoveries haven't occurred out of thin air but were ultimately logical consequences of the discoveries and developments before. Faraday (1831-1854) came before Maxwell (1865), Michelson-Morley (1881) came before Einstein (1905), Sophus Lie (1872-1886) came before Emmy Noether (1918). Maxwell, Einstein, Noether are all synonyms for ground-breaking results. But every one of them had predecessors that paved their ways. I do not think that it was any different for Newton.

P.S.: Otto Lilienthal was earlier than the Wright brothers and Philipp Reis was earlier than Graham Bell, Joseph Swan earlier than Edison, and Armat and Fuhrmann were earlier than the Lumière brothers, and, of course, earlier than Edison.

Even this is not topic, what is statistical probability that Newton and Leibniz discover calculus in same time?
I think someone must see other work.

(George Cayley was before Otto..)

Well, if you pick the wrong one, you could be off by a maximum of a whopping one half of a percent. Do you really care?

Yes.

 

[fresh_42]

(George Cayley was before Otto..)

I close my case.

 

[fresh_42]

What counts is availability for others, letters and books. Newton's notes are irrelevant since nobody else had access to them. The Principia are all that matter, and that was 1687 (the year on the cover of the book).

 

[user079622]

Well, if you pick the wrong one, you could be off by a maximum of a whopping one half of a percent. Do you really care?

Artist will draw a picture( for a birthday) of Newton and write "Annus Maribilis" so it would be good not to miss a year..
1665 or 1666

 

[berkeman]

Artist will draw a picture( for a birthday) of Newton and write "Annus Maribilis" so it would be good not to miss a year..
1665 or 1666

If your artist uses stylized cursive lettering, a 5 and a 6 look very similar. Just sayin'.

 

[fresh_42]

Artist will draw a picture( for a birthday) of Newton and write "Annus Maribilis" so it would be good not to miss a year..
1665 or 1666

I love it when real life produces jokes like this!

Nobody will ever associate Newton with either 1665 or 1666. What the educated person will associate is the great plague epidemic in London! What a picture: plague = annus maribilis!

 

[Astronuc]

Like most scientific discoveries, the discovery of calculus did not arise out of a vacuum. In fact, many mathematicians and philosophers going back to ancient times made discoveries relating to calculus.

https://amsi.org.au/ESA_Senior_Years/SeniorTopic3/3b/3b_4history_1.html

James Gregory (1638-1675) was the first Regius Professor of Mathematics at St Andrews. This remarkable man was the first to prove a version of the Fundamental Theorem of Calculus and wrote a textbook explaining the historical source behind the subject’s teaching here: 100 years before Cambridge

https://www.thesaint.scot/post/the-secret-scientific-history-of-st-andrews

But wait Calculus created in India 250 years before Newton: study
https://www.cbc.ca/news/science/calculus-created-in-india-250-years-before-newton-study-1.632433

Along the lines of 'discoveries do not arise out of a vacuum'.

A history of the calculus​

https://mathshistory.st-andrews.ac.uk/HistTopics/The_rise_of_calculus/

Newton wrote a tract on fluxions in October 1666. This was a work which was not published at the time but seen by many mathematicians and had a major influence on the direction the calculus was to take. Newton thought of a particle tracing out a curve with two moving lines which were the coordinates. The horizontal velocity x′x′ and the vertical velocity y′y′ were the fluxions of xx and yy associated with the flux of time. The fluents or flowing quantities were xx and yy themselves. With this fluxion notation y′/x′y′/x′ was the tangent to f(x,y)=0f(x,y)=0.

In his 1666 tract Newton discusses the converse problem, given the relationship between xx and y′/x′y′/x′ find yy. Hence the slope of the tangent was given for each xx and when y′/x′=f(x)y′/x′=f(x) then Newton solves the problem by antidifferentiation. He also calculated areas by antidifferentiation and this work contains the first clear statement of the Fundamental Theorem of the Calculus.

Leibniz learnt much on a European tour which led him to meet Huygens in Paris in 1672. He also met Hooke and Boyle in London in 1673 where he bought several mathematics books, including Barrow's works. Leibniz was to have a lengthy correspondence with Barrow. On returning to Paris Leibniz did some very fine work on the calculus, thinking of the foundations very differently from Newton.

Newton considered variables changing with time. Leibniz thought of variables x,y as ranging over sequences of infinitely close values. He introduced dx and dy as differences between successive values of these sequences. Leibniz knew that dy/dx gives the tangent but he did not use it as a defining property.

 

[user079622]

I love it when real life produces jokes like this!

Nobody will ever associate Newton with either 1665 or 1666. What the educated person will associate is the great plague epidemic in London! What a picture: plague = annus maribilis!

I dont agree. How cares about 1687(Principia) if he discovered all this things 20s years before.
I dont care when papers are published, I care when ideas were born.

https://en.wikipedia.org/wiki/Annus_mirabilis
"In 1666, Isaac Newton, aged 23, made revolutionary inventions and discoveries in calculus, motion, optics and gravitation. It was in this year that Newton was alleged to have observed an apple falling from a tree, and in which he, in any case, hit upon the law of universal gravitation (Newton's apple). "

 

[fresh_42]

I care when ideas were born.

This is scientific dishonesty because you cannot know. You prefer guesswork over facts! How do you even know that what you call ideas weren't already present in notebooks in Paris or Leipzig? You call it a wonder based on partial information. That's religion, not science; or art in this case.

Science is not a sequence of milestones. It is a long and winding path with milestones along the road.

 

[user079622]

https://amsi.org.au/ESA_Senior_Years/SeniorTopic3/3b/3b_4history_1.html


https://www.thesaint.scot/post/the-secret-scientific-history-of-st-andrews

But wait Calculus created in India 250 years before Newton: study
https://www.cbc.ca/news/science/calculus-created-in-india-250-years-before-newton-study-1.632433

Along the lines of 'discoveries do not arise out of a vacuum'.

A history of the calculus​

https://mathshistory.st-andrews.ac.uk/HistTopics/The_rise_of_calculus/

Is any discovery in math/physics comes out of vacuum, something completly new?

 

[fresh_42]

Is any discovery in math/physics comes out of vacuum, something completly new?

I'd say yes. Show me a counterexample! Even 'Pythagoras' had been known many centuries earlier! I would have compared your fixation on 'wonders' with discoveries that can be dated. Unfortunately, I had immediately thought of Columbus who was lost in the Caribbeans due to his miserable navigation skills, and Eric the Red who at least had arrived on the continent and not on some islands somewhere.

 

[user079622]

This is scientific dishonesty because you cannot know. You prefer guesswork over facts! How do you even know that what you call ideas weren't already present in notebooks in Paris or Leipzig? You call it a wonder based on partial information. That's religion, not science; or art in this case.

Science is not a sequence of milestones. It is a long and winding path with milestones along the road.

We dont know nothing, we just know what historians write, of course that can be true or false.

 

[fresh_42]

We dont know nothing, we just know what historians write, of course that can be true or false.

So you do indeed celebrate the plague because this was the ultimate reason for Newton's private time to research. Cambridge had been closed! Interesting point of view. I think I prefer to stay with publications.

 

[Vanadium 50]

1666. What the educated person will associate is the great plague epidemic in London!

Or the Great Fire.

 

[Vanadium 50]

IBTL. Asking us to figure out when something first popped into Newton's head, and not when it was written down, seems unrealistic. After 350 years, it seems silly to the point of unseriousness.

 

[fresh_42]

Or the Great Fire.

Damnit. Now I have this Great Balls of Fire earworm. And the philosophical mantra that everything is related to everything.

@user079622 Seriously. Newton's great achievement was the book because others had something to reference. Gauß's great achievement was the book. Noether's great achievement was the printed journal, not the speech months before. Late Euler was blind and he dictated his thoughts. Wherever you look, it is a written version at the center of ideas. There is a reason why we consider Gutenberg's invention a revolution. And, yes, I do know that the Chinese had moveable signs centuries before! Another example of my point of view. The Chinese had the idea, but nobody in Europe knew. Gutenberg, however, paved the way to liberate knowledge - from monasteries into libraries!

 

[Vanadium 50]

Damnit. Now I have this Great Balls of Fire earworm.

Please. No profanity. An alternative would be "Goodness Gracious!"

 

[fresh_42]

The essential points of this discussion here are as far as I can see it:

1. Should science be reduced or can it be seen as a sequence of its milestones?
   
   I do not agree with such a point of view for the reasons I have mentioned above. I know, that this is how science is usually recognized by the public but I think we should fight such a one-dimensional perspective and not support it. Newton's Principia were such a milestone without any question. Reducing the entire calculus to one idea, namely setting a point on location and calling it a velocity is a bit too narrowing and doing injustice to all other scientists who contributed after, but also before Newton.
   
   
2. What is a milestone in science?
   
   This is the original question. Is it what historians can dig up in left properties and notes - Fermat and Galois would be other prominent examples - or is it when others recognized it? I very much favor the second version because we cannot know what sensations other scientists left in their notes before, and even worse, those might have been lost. Furthermore, there were always others who set those milestones into position. It was always a publication plus the recognition of someone else that put a certain text into the position of a milestone. "On the Electrodynamics of Moving Bodies" or "Invariant Variation Problems" sound like boring papers, not like the sensations they were attributed afterward. Without the Principa nobody would have ever searched in Newton's left properties. That makes 1687 the milestone, and not the closure of Cambridge due to the plague.

 

[phinds]

We dont know nothing

Well, to be fair, some of us DO know grammar.

 

[Mark44]

Well, to be fair, some of us DO know grammar.

Double negatives are perfectly fine in Spanish -- Nosotros no sabemos nada -- and Russian -- Мы не знаем ничего. Both translate to "We don't know nothing."

 

[phinds]

Double negatives are perfectly fine in Spanish -- Nosotros no sabemos nada -- and Russian -- Мы не знаем ничего. Both translate to "We don't know nothing."

Literally, I will take your word for it, and that would explain the grammar used, but I'm sure you would agree that a correct translation would be "we don't know anything". A literal translation is often not a correct translation.

EDIT: I do appreciate the info about the literal translation.

 

[Mark44]

I'm sure you would agree that a correct translation would be "we don't know anything".

Yes. In English we don't cotton to no double negatives, nohow.

 

[BillTre]

Yes. In English we don't cotton to no double negatives, nohow.

We need a not dislike response!

 

[Astronuc]

1665 or 1666

Which year may depend on which calendar one uses as a reference.

Prior to 1752, the Julian calendar was in use in England. In this calendar, the new year began on 25 March each year, so 31 Dec would be followed by 1 Jan of the same year, and 24 Mar would be followed by 25 Mar the following year. This applied up to 31 Dec 1751, after which the Gregorian calendar was adopted. 31 Dec 1751 was followed by 1 Jan 1752.

https://www.lan-opc.org.uk/dates.html

The move to the Gregorian calendar had taken place in Europe some years earlier, in 1582. As part of this, a greater understanding of the true length of a year had resulted in ten days being 'removed' from the calendar in Europe between 4 Oct 1582 and 15 Oct 1582. After England moved to the Gregorian calendar in 1752, a similar change was made, to bring dates back into line with Europe, and 2 Sep 1752 was followed by 14 Sep 1752.

Is any discovery in math/physics comes out of vacuum, something completely new?

Probably, but perhaps a long time ago, e.g., the realization (or first developments) of algebra and mathematical equations, and some of the earliest insights (developments) in science.

 

[Vanadium 50]

Which year may depend on which calendar one uses as a reference.

The offset is only eleven days, though.

 

[Astronuc]

The offset is only eleven days, though.

Yes, but, note the example on dates before 1752.

In the case of Isaac Newton, his death date is given as 20 March 1726/27.
From Lancashire Parish Clerks Online:

To avoid any ambiguity, we record dates between 1 Jan and 24 Mar of each year prior to 1752 as dual dates. So for example, 31 Dec 1746 is followed by 1 Jan 1746/7, 2 Jan 1746/7 and so on until 24 Mar 1746/7, then 25 Mar 1747.

In a Wikipedia article, a note on Newton's birth date:

Isaac Newton was born (according to the Julian calendar in use in England at the time) on Christmas Day, 25 December 1642 (NS 4 January 1643)

and https://en.wikipedia.org/wiki/Isaac_Newton#cite_note-OSNS-5

During Newton's lifetime, two calendars were in use in Europe: the Julian ("Old Style") calendar in Protestant and Orthodox regions, including Britain; and the Gregorian ("New Style") calendar in Roman Catholic Europe. At Newton's birth, Gregorian dates were ten days ahead of Julian dates; thus, his birth is recorded as taking place on 25 December 1642 Old Style, but it can be converted to a New Style (modern) date of 4 January 1643. By the time of his death, the difference between the calendars had increased to eleven days. Moreover, he died in the period after the start of the New Style year on 1 January but before that of the Old Style new year on 25 March. His death occurred on 20 March 1726, according to the Old Style calendar, but the year is usually adjusted to 1727. A full conversion to New Style gives the date 31 March 1727.

I encounter this mess when trying to determine birth/baptisms, marriages and deaths of ancestors from England, Scotland, Wales and Ireland prior to 1752.


In a summary of Newton's early life, while at the University of Cambridge.

In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton obtained his BA degree at Cambridge in August 1665, the university temporarily closed as a precaution against the Great Plague.

https://en.wikipedia.org/wiki/Isaac_Newton#Early_life

By September 1664, Newton had started to use some of the pages for the optical and mathematical calculations, inspired by Descartes and van Schooten, that were beginning to occupy him (see Add. 3996 and Fitzwilliam Museum, MS. 1-1936). Over the next two years, Newton broadened his reading only slightly. Nevertheless, through the study of Wallis’ works and of the other authors (Johann Hudde, Hendrick van Heuraet, and Jan de Witt) whose writings were presented by van Schooten in his edition of Descartes’ Geometria (1639-41), Newton gradually mastered the analysis of curved lines, surfaces, and solids. He learned how to use the method of infinite series and extended it by discovering how to expand binomials with fractional indices. Most significantly, he developed an approach to the measurement of curved lines that mapped the motion that produced them. This arose out of dissatisfaction with the method of infinitesimals and the advances towards describing curves through their tangents that Newton had made with it. By autumn 1665, Newton had worked out a method for replacing the use of infinitesimal increments of space in his calculations with instantaneous changes in the velocity of a moving point by which curved lines were described. Stimulated entirely by his reading, Newton had invented the method of fluxions, or calculus, through the working in his ‘Waste Book’

https://cudl.lib.cam.ac.uk/view/MS-ADD-04004/1

In another summary, https://fee.org/articles/how-isaac-...from-the-great-plague-into-a-year-of-wonders/

Away from university life, and unbounded by curriculum constraints and professor’s whims, Newton dove into discovery. According to The Washington Post: “Without his professors to guide him, Newton apparently thrived.” At home, he built bookshelves and created a small office for himself, filling a blank notebook with his ideas and calculations. Absent the distractions of typical daily life, Newton’s creativity flourished. During this time away he discovered differential and integral calculus, formulated a theory of universal gravitation, and explored optics, experimenting with prisms and investigating light.

So, during 1665 through 1666, Newton was developing what became 'calculus'.

Interstingly, U of Cambridge has his date of his BA as 1664/5
https://venn.lib.cam.ac.uk/cgi-bin/...ll&tex=NWTN661I&sye=&eye=&col=all&maxcount=50

Apparently, the answer to the OP's question can be found in the following publication by Cambridge University Press.
Whiteside, D.T., ed. (1967). "Part 7: The October 1666 Tract on Fluxions". The Mathematical Papers of Isaac Newton. 1. Cambridge University Press.
https://www.cambridge.org/us/univer...-newton-volume-1?format=PB&isbn=9780521045957

The bringing together, in an annotated and critical edition, of all the known mathematical papers of Isaac Newton marks a step forward in the publication of the works of this great natural philosopher. In all, there are eight volumes in this present edition. Translations of papers in Latin face the original text and notes are printed on the page-openings to which they refer, so far as possible. Each volume contains a short index of names only and an analytical table of contents; a comprehensive index to the complete work is included in Volume VIII. Volume I covers three exceptionally productive years: Newton's final year as an undergraduate at Trinity College, Cambridge, and the two following years, part of which were spent at his home in Lincolnshire on account of the closure of the university during an outbreak of bubonic plague.

There are 8 volumes sold separately.
https://www.cambridge.org/us/univer...e/series/mathematical-papers-sir-isaac-newton
and one can buy the 8 volume set
https://www.cambridge.org/us/univer...ts/mathematical-papers-isaac-newton?format=WX

Perhaps we can acknowledge the contributions of both men, which didn't happen in a vacuum.
https://www.ams.org/notices/200905/rtx090500602p.pdf

In his review of the book, The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time by Jason Socrates Bardi (Basic Books, 2007), professor Brian Blank writes:

There is no doubt that Newton’s discoveries preceded those of Leibniz by nearly a decade. Stimulated by the Lucasian Lectures Isaac Barrow delivered in the fall of 1664, Newton developed his calculus between the winter of 1664 and October 1666. Two preliminary manuscripts were followed by the so-called October 1666 tract, a private summation that was not printed until 1962. Because of Newton’s dilatory path to publication, word of his calculus did not spread beyond Cambridge until 1669. In that year, Newton, reacting to the rediscovery of his infinite series for log(1 + x), composed a short synopsis of his findings, the De analysi per aequationes numero terminorum infinitas. The De analysi was written near the end of an era in which scientific discoveries were often first disseminated by networking rather than by publication. Henry Oldenburg, Secretary of the Royal Society, and John Collins, government clerk and de facto mathematical advisor to Oldenburg, served as the principal hubs of
correspondence in England. Dispatched by Barrow on behalf of a “friend of mine here, that hath a very excellent genius,” the De analysi reached Collins in the summer of 1669. “Mr. Collins was very free in communicating to able Mathematicians what he had receiv’d,” Newton later remarked.

Someone else's commentary on Newton's achievements
https://plato.stanford.edu/entries/newton/#NewYeaCamPriPri

By 1664, Newton had begun reaching beyond the standard curriculum, reading, for example, the 1656 Latin edition of Descartes's Opera philosophica, which included the Meditations, Discourse on Method, the Dioptrics, and the Principles of Philosophy. By early 1664 he had also begun teaching himself mathematics, taking notes on works by Oughtred, Viète, Wallis, and Descartes— the latter via van Schooten's Latin translation, with commentary, of the Géométrie. Newton spent all but three months from the summer of 1665 until the spring of 1667 at home in Woolsthorpe when the university was closed because of the plague. This period was his so-called annus mirabilis.

That seems like ~1.5 years (August 1665 through ~March/April 1667)

It is difficult to know which Calendar folks are using, but I often expect the later Gregorian calendar in writings after 1752.

Let's not forget René Descartes (1596–1650)
https://plato.stanford.edu/entries/descartes/