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Principia was completed in 1686 and published in 1687, but he discovered calculus, gravity and laws of motion long before (1665-1666 "Year of Wonders").Is this correct?

He wrote book Method of Fluxions in 1671 and book was published posthumously in 1736.

Why Isaac Newton published his discoveries so much later than he discovered them?

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    $\begingroup$ There was no pressure to publish at all then. $\endgroup$
    – Jon Custer
    Commented May 26 at 17:24

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The question virtually quotes some blanket statements about Newton's willingness (or not) to publish, and about when he made certain discoveries, etc. It is true that such statements certainly have appeared in recent print.

The questioner very properly asks about them "Is this correct?". The situation was more complicated than the common blanket statements imply. An answer 'partly yes and partly no' is to be gathered from reputable and reliable reference sources: among the most useful of these are --

  1. the biography of Newton by R S Westfall entitled "Never at Rest". This has probably the best reputation among Newton biographies. It is a good source for outline description of what work Newton did, and when.

  2. the collection of 17th-century letters published in the 19th century under the editorship of the Rigauds, father and son, followed some time later by a guide and index to their contents. Letters in the collection give information about many of the matters relevant to the question (and often amount to primary historical evidence free from dubious or mistaken modern interpretations).

For details of these sources, see below.

In a nutshell, the sources show how Newton was ready to publish some parts of his work even in the 1670s, and less ready in respect of others. His attitudes were affected by the circumstances of each subject matter, e.g. there are indications he thought on occasion that the work was superseded or needed updating, or was still incomplete.

Also, book-publication in mathematics and science in England in the 1670s and 1680s was not easy, partly because of the devastation caused to the London printers and booksellers by the city fire in 1666. This event had completely destroyed the 'St Pauls Churchyard' district where the book businesses kept most of their premises and stocks, and it destroyed much else besides, including the old St Pauls cathedral itself.

The surviving London book businesses in Newton's time did not look with favour on mathematical and scientific books that would lose them money. The Rigaud volumes include numerous letters from John Collins to Newton and others explaining the contemporary position. John Collins is now often described as a 'mathematical intelligencer'. He was in touch with many people who would be consumers/readers or producers/authors of mathematical and scientific works. Part of his activity was to be almost a kind of mail-order bookseller, and then he also acted as a kind of agent for authors or editors in their dealings with the printers and booksellers who might bring their work into book form.

A further point is that the word 'publication' now seems often to be taken to cover only printed publication, e.g. of books. Several of Newton's works reached an audience in his own time through the circulation of manuscript copies. This applies to some of Newton's work that was eventually printed but only much later. A mistaken impression is sometimes created that there was secrecy about them, when in fact they had had circulation to an interested public. It is not quite right in terms of 17th-century realities to call these things 'unpublished'.

The practice of manuscript circulation, especially in Newton's time, has also been considered in works by Niccolo Guicciardini, which are well worth the reading.

References:

R S Westfall (1981) "Never at Rest" (https://books.google.com/books/about/Never_at_Rest.html?id=3ngEugMMa9YC)

S P and S J Rigaud (eds.), "Correspondence of Scientific Men of the Seventeenth Century" (vol.1) (1841) (https://books.google.com/books?id=oBnP1vRoAOcC)

--"-- vol.2 (1841) (https://archive.org/details/bub_gb_0h45L_66bcYC)

A de Morgan (1862), Contents (and index) of the two Rigaud volumes (google metadata is misleading about this contents/index volume), (https://books.google.com/books?id=iA9UAAAAcAAJ)

Niccolo Guicciardini (2018), "Isaac Newton and Natural Philosophy", (https://press.uchicago.edu/ucp/books/book/distributed/I/bo28433514.html) -- and other books and papers by N Guicciardini.

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