Who first invented calculus - Newton or Leibniz?
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From: Immortalist on 4 Jan 2010 22:27 Development of the quarrel The quarrel was a retrospective affair. In 1696, already some years later than the events that became the subject of the quarrel, the position still looked potentially peaceful: Newton and Leibniz had each made limited acknowledgements of the other's work, and L'Hospital's 1696 book about the calculus from a Leibnizian point of view had also acknowledged Newton's published work of the 1680s as 'nearly all about this calculus' ('presque tout de ce calcul'), while expressing preference for the convenience of Leibniz's notation. At first, there was no reason to suspect Leibniz's good faith. In 1699 Nicolas Fatio de Duillier had accused Leibniz of plagiarizing Newton, but Fatio was not a person of consequence. It was not until the 1704 publication of an anonymous review of Newton's tract on quadrature, a review implying that Newton had borrowed the idea of the fluxional calculus from Leibniz, that any responsible mathematician doubted that Leibniz had invented the calculus independently of Newton. With respect to the review of Newton's quadrature work, all admit that there was no justification or authority for the statements made therein, which were rightly attributed to Leibniz. But the subsequent discussion led to a critical examination of the whole question, and doubts emerged. Had Leibniz derived the fundamental idea of the calculus from Newton? The case against Leibniz, as it appeared to Newton's friends, was summed up in the Commercium Epistolicum of 1712, which referenced all allegations. That document was thoroughly machined by Newton. No such summary (with facts, dates, and references) of the case for Leibniz was issued by his friends; but Johann Bernoulli attempted to indirectly weaken the evidence by attacking the personal character of Newton in a letter dated 7 June 1713. When pressed for an explanation, Bernoulli most solemnly denied having written the letter. In accepting the denial, Newton added in a private letter to Bernoulli the following remarks, Newton's claimed reasons for why he took part in the controversy. "I have never," he said, "grasped at fame among foreign nations, but I am very desirous to preserve my character for honesty, which the author of that epistle, as if by the authority of a great judge, had endeavoured to wrest from me. Now that I am old, I have little pleasure in mathematical studies, and I have never tried to propagate my opinions over the world, but I have rather taken care not to involve myself in disputes on account of them." Leibniz explained his silence as follows, in a letter to Conti dated 9 April 1716: Pour répondre de point en point à l'ouvrage publié contre moi, il falloit entrer dans un grand détail de quantité de minutiés passées il y a trente à quarante ans, dont je ne me souvenois guère: il me falloit chercher mes vieilles lettres, dont plusiers se sont perdus, outre que le plus souvent je n'ai point gardé les minutes des miennes: et les autres sont ensevelies dans un grand tas de papiers, que je ne pouvois débrouiller qu'avec du temps et de la patience; mais je n'en avois guère le loisir, étant chargé présentement d'occupations d'une toute autre nature." ["In order to respond point by point to all the work published against me, I would have to go into much minutiae that occurred thirty, forty years ago, of which I remember little: I would have to search my old letters, of which many are lost. Moreover, in most cases I did not keep a copy, and when I did, the copy is buried in a great heap of papers, which I could sort through only with time and patience. I have enjoyed little leisure, being so weighted down of late with occupations of a totally different nature."] While Leibniz's death put a temporary stop to the controversy, the debate persisted for many years. To Newton's staunch supporters this was a case of Leibniz's word against a number of contrary, suspicious details. His unacknowledged possession of a copy of part of one of Newton's manuscripts may be explicable; but it appears that on more than one occasion, Leibniz deliberately altered or added to important documents (e.g., the letter of June 7 1713, in the Charta Volans, and that of April 8 1716, in the Acta Eruditorum), before publishing them, and falsified a date on a manuscript (1675 being altered to 1673). All this casts doubt on his testimony. Several points should be noted. Considering Leibniz's intellectual prowess, as demonstrated by his other accomplishments, he had more than the requisite ability to invent the calculus (which was more than ready to be invented in any case). What he is alleged to have received was a number of suggestions rather than an account of the calculus; it is possible that since he did not publish his results of 1677 until 1684 and since the differential notation was his invention, Leibniz may have minimized, 30 years later, any benefit he may have enjoyed from reading Newton's work in manuscript. Moreover, he may have seen the question of who originated the calculus as immaterial when set against the expressive power of his notation. In any event, a bias favoring Newton tainted the whole affair from the outset. The Royal Society set up a committee to pronounce on the priority dispute, in response to a letter it had received from Leibniz. That committee never asked Leibniz to give his version of the events. The report of the committee, finding in favor of Newton, was written by Newton himself and published as "Commercium Epistolicum" (mentioned above) early in 1713. But Leibniz did not see it until the autumn of 1714. The prevailing opinion in the eighteenth century was against Leibniz (in Britain, not in the German-speaking world). Today the consensus is that Leibniz and Newton independently invented and described the calculus in Europe in the 17th century. "It was certainly Isaac Newton who first devised a new infinitesimal calculus and elaborated it into a widely extensible algorithm, whose potentialities he fully understood; of equal certainty, the differential and integral calculus, the fount of great developments flowing continuously from 1684 to the present day, was created independently by Gottfried Leibniz." (Hall 1980: 1) One author has identified the dispute as being about 'profoundly different' methods: "Despite... points of resemblance, the methods [of Newton and Leibniz] are profoundly different, so making the priority row a nonsense." (Grattan-Guinness 1997: 247) On the other hand, other authors have emphasized the equivalences and mutual translatability of the methods: here N Guicciardini (2003) appears to confirm L'Hospital (1696) (already cited): "... the Newtonian and Leibnizian schools shared a common mathematical method. They adopted two algorithms, the analytical method of fluxions, and the differential and integral calculus, which were translatable one into the other." (Guicciardini 2003, at page 250) [5] http://en.wikipedia.org/wiki/Leibniz_and_Newton_calculus_controversy
From: John Stafford on 4 Jan 2010 22:36 It matters not. The Calculus was not philosophically rationalized until quite recently. Regardless, it was perfectly useful until then, and remains useful today. For the obsessive of the 'Inductive Reasoning' thread - eat your hearts out. Back to the subnect, it was found that Leibniz's approach was more useful, fewer hacks, more direct. Leibniz wins.
From: Peter Webb on 5 Jan 2010 09:26 Liebniz basically invented the dy/dx notation, right? What was Newton's - the f '(x) notation, or something else?
From: Androcles on 5 Jan 2010 10:16 "Peter Webb" <webbfamily(a)DIESPAMDIEoptusnet.com.au> wrote in message news:4b434c27$0$31487$afc38c87(a)news.optusnet.com.au... > Liebniz basically invented the dy/dx notation, right? > > What was Newton's - the f '(x) notation, or something else? > > "Atque ita summae motuum conspirantium 15 +1 vel 16 +0, et differentiae contrariorum 17-1 et 18-2 semper erunt paartium sexdecim..." -- Principia. "And so the sums of the conspiring motions 15+1, or 16+0, and the differences of the contrary motions 17-1 and 18-2, will always be equal to 16 parts..." Notice that 16 is written as sexdecim. You wanna work in Latin?
From: M Purcell on 5 Jan 2010 10:55
On Jan 4, 7:36 pm, John Stafford <n...(a)droffats.ten> wrote: > It matters not. The Calculus was not philosophically rationalized until > quite recently. Regardless, it was perfectly useful until then, and > remains useful today. How was calculus recently philosophically rationalized? > For the obsessive of the 'Inductive Reasoning' thread - eat your hearts > out. I hope you realize mathematical induction is deductive. > Back to the subnect, it was found that Leibniz's approach was more > useful, fewer hacks, more direct. Leibniz wins. Leibniz also published first, Newton's delay is suspect. |