166 A History ofMathematics
Modern scholars (see particularly Hall 1980) are agreed that Newton’s communication was both
too late and too obscure to exercise any serious influence on what was effectively anindependent
discovery by Leibniz, with his own ideas and notation. He too delayed publication, and was only
forced into a brief announcement of his results in 1684 by fears that he in turn was losing priority.
It took about 20 years, and the rapid success of the Leibnizian calculus in the 1690s, for any
question of priority/plagiarism to arise; and it entered its acute phase about 1710. Both players
had by then acquired schools of students, defenders and partisans. Newton’s attitude to those who
disagreed with him, whether scientifically or politically, is often described as hostile to the point
of paranoia; and while Leibniz, committed to a rational belief that this is the best of all possible
worlds, was in many ways a contrast, he did not like suggestions that his own ideas were in any way
unoriginal.^4 Following accusations and counter-accusations, the Royal Society in March 1712
appointed a committee composed almost entirely of Newton’s supporters to investigate whether
Leibniz had been unjustly accused by the quarrelsome Newtonian John Keill. Newton supplied the
committee with documents proving his priority (his unpublished manuscripts, and letters from
various of the parties involved), and apparently also drafted the final report (pompously titled
Commercium epistolicum, the exchange of letters), which concluded:
That the Differential Method [Leibniz] is One and the same with the Method of Fluxions [Newton] Excepting the name
and Mode of Notation...and therefore wee take the Proper Question to be not who Invented this or that Method but
who was the first Inventor of the Method...
For which Reasons we Reckon Mr Newton the first Inventor; and are of Opinion that Mr Keill in Asserting the same
has been noways Injurious to Mr Leibniz. (Newton 1959–77, 5 , p. xxvi)Those who are looking for examples of Anglo-Saxon hypocrisy can find plenty in theCommer-
cium epistolicum, and still more in the ‘Report’ on it which Newton wrote for the Royal Society’s
Transactions—an anonymous review of a document which he had largely written. (It is from this
review that the quotation at the head of the chapter is taken.) All the same, the document did make
clear, as Newton had never previously done, the nature and extent of his early work, and thus,
however partisan, it cleared up the question of priority. The charge of plagiarism against Leibniz,
who died soon afterwards, was never serious enough to stick; indeed one could ask what is the
nature of intellectual property in mathematics, and how far plagiarism is to be condemned. Pierre
de Montmort, one of several who heroically tried to reconcile the parties, made the key point: one
should look at who used it, how, and with what results.
On the invention of the calculus he [Montmort] would not comment, he said, but Leibniz and the Bernoullis had been
its true and almost sole promoters.
It is they and they alone who taught us the rules of differentiation and integration, the way to use the calculus to find
tangents to curves, their points of inflection and reversal,...& who finally, by many and beautiful applications of the
calculus to the most difficult problems of mechanics, such as the catenary, the sail, the spring, the quickest descent,
and the paracentric, have set us and our descendants on the path of the most profound discoveries. (Westfall 1980,
pp. 784–5, citing Montmort’s letter to Brook Taylor of 18 December 1718,Corr.7, 21–2)
It was Leibniz’s calculus which was most successfully used, and which still dominates our notation;
and when in the twentieth century the record was finally set straight with the publication of his
manuscripts from the 1670s, no one was left to care.
- His most devoted student Jakob Bernoulli found this to his cost early on when he misguidedly suggested that Leibniz’s methods
were similar to the earlier ones used by Isaac Barrow. He had to make a humble apology for what was clearly a mistake, but
understandable when the calculus was still not fully understood, and Leibniz himself was not helping to make it clearer.