TheCalculus 165
3. The priority dispute
We shall not discuss the shamefully bitter controversy as to the priority and independence of the inventions by Newton
and Leibniz. (Boyer 1949, p. 188)
In one word he told me the secret of success in mathematics: Plagiarize! (Tom Lehrer, song, ‘Lobachevsky’)Boyer represents a gentlemanly school of thought (now rather old-fashioned) according to which
mathematicians should behave courteously towards one another. In this view, the controversy
which opposed the supporters of Newton and Leibniz between 1700 and 1720 (with an acute
period in the 1710s) was an unfortunate aberration. The most superficial look at the long history
of mathematics and mathematicians shows that this is not in fact the case. We have already seen
the quarrels of Tartaglia and Cardano in the sixteenth century, and there have been many worse
ones since: one could cite Pascal and Torricelli on the cycloid, (1650s), Legendre and Gauss on the
method of least squares (1790s), and countless others (an internet search for ‘priority dispute’ is
instructive throwing up an instance in topology from 1996 in particular). What gave the argument
about the calculus its peculiar bad taste was the involvement of the Royal Society, and of its
president Newton, in adjudicating on the dispute.
Regrettable or not—and history can rarely afford regrets—the dispute provides a useful way
into the history of the calculus and its diffusion. In fact, it is clear from the way in which the
arguments developed that in 1690 ‘the invention of the calculus’ was not a subject for discussion,
while 20 years later it was generally agreed that something of great importance had been invented,
and the question of who had copied whose prior invention was vital. British chauvinism (which
one might suppose to be a major factor) played its part, but was a secondary issue. Indeed, Newton
in his youth was notably more open to Continental ideas, those of Descartes in particular, than
his seniors; and he continued to show repect for those foreign scientists, such as Huygens, who
were not in direct competition. Equally, he had frequently engaged in more or less acrimonious
disputes with British colleagues such as Hooke and Flamsteed. The scientific milieu of the time
was generally suspicious and paranoid; discoverers withheld publication for fear of being copied,
and then, when their unpublished discoveries were found by another, accused them of plagiarism.
(And, one must suppose, they were sometimes right.) The practice of anonymous publication (in
which authors often referred to themselves in the third person—‘the distinguished Mr Leibniz has
proved’) was unhelpful, both in establishing who had done what, and in subsequent controversies
often conducted via anonymous or pseudonymous attacks.
The question of priority (as distinct from plagiarism) was in fact settled quite early. As we shall
see, Newton’s version of the calculus was very similar to Leibniz’s, both in its qualities and its
defects, and dated from about 10 years earlier (1665 as against 1675). The question of plagiarism
is more unpleasant and complex, since Newton’s version was not published in his lifetime, but was
seen in manuscript by a number of people. Leibniz in the early 1670s knew of some of Newton’s
work, chiefly by accounts in letters from London; and most famously, by two devious and obscure
letters from Newton himself, which contained references to his most important work in the form of
anagrams, which Leibniz was hardly in a position to decipher. This may seem absurd as a way of
communicating scientific results but was again not uncommon at the time, and this may give some
indication of what was supposed to constitute ‘publication’. As Gjertsen says (in his entertaining
article ‘Anagrams’, 1986, p. 16):
The advantages of the ploy were obvious. Priority was established yet nothing was givenaway topotential
rivals...Invariably in Latin, clueless, and of immense length, they were virtually insoluble.