Below are several quotes suggesting that Newton's notation had the effect of retarding English mathematics by 50 years, 100 years, or even centuries.
Here is my simplistic two-sentence historical account of what happened (based on my reading of the various writers below):
After Newton, English mathematics was in a dark hole years behind the Continent. Then circa 1820, Englishmen adopted Leibnizian notation and by 1830, had mostly caught up and could once again contribute to mathematics.
As a layperson who isn't too familiar with this history, it seems rather incredible that notation alone cost 50+ years of progress.
My questions:
- Was English mathematics ever significantly behind — by say 50 years, 100 years, or even centuries?
- If so, to what extent can this be attributed to Newton's poor notation?
Arturo Magidin on Math.SE (2011):
In fact, Leibniz's notation is so good, so superior to the prime notation and to Newton's notation, that England fell behind all of Europe for centuries in mathematics and science because, due to the fight between Newton's and Leibniz's camp over who had invented Calculus and who stole it from whom (consensus is that they each discovered it independently), England's scientific establishment decided to ignore what was being done in Europe with Leibniz notation and stuck to Newton's... and got stuck in the mud in large part because of it.
Noah Kennedy, The Industrialization of Intelligence: Mind and Machine in the Modern Age (1989):
Disastrously for English mathematics, there was an easy way for an English mathematician to affirm his national allegiance to Newton's claim, a way that seemed innocuous enough but was actually destined virtually to cripple mathematical inquiry in England for more than a century. The two men had quite naturally arrived at two entirely different systems of notation for denoting the central concept of differentiation, and quite naturally the English adopted Newton's and the Germans favoured Leibniz's. The problem for the English was that Leibniz's notation was a far more elegant and evocative expression of the concept and lent itself much more easily to various innovations that rippled through mathematics in the wake of the discovery of the calculus. Primarily because of its utility, Leibniz's notation was in general use throughout Europe and precipitated significant innovation, particularly by the French, while in England, mathematical progress was tortuously slow, in part because of the burden of Newton's notation and in part because English mathematicians had effectively isolated themselves from the common language of continental mathematics.
Morris Kline, Mathematical Thought From Ancient to Modern Times (1972):
England too languished. Brook Taylor, Matthew Stewart (1717–85), and Colin Maclaurin were the only prominent mathematicians. England's poor performance in view of its great activity in the seventeenth century may be surprising, but the explanation is readily found. The English mathematicians had not only isolated themselves personally from the Continentals as a consequence of the controversy between Newton and Leibniz, but also suffered by following the geometrical methods of Newton. The English settled down to study Newton instead of nature. Even in their analytical work they used Newton's notation for fluxions and fluents and refused to read anything written in the notation of Leibniz.
In the first quarter of the nineteenth century the British mathematicians began to take interest in the work on the calculus and its extensions, which had proceeded apace on the Continent. The Analytical Society was formed at Cambridge in 1813 to study this work. George Peacock (1791–1858), John Herschel (1792–1871), Charles Babbage and others undertook to study the principles of "d-ism"—that is, the Leibnizian notation in the calculus, as against those of "dot-age," or the Newtonian notation. Soon the quotient $dy/dx$ replaced $\dot{y}$, and the Continental texts and papers became accessible to English students. Babbage, Peacock, and Herschel translated a one-volume edition of Lacroix's Traité and published it in 1816. By 1830 the English were able to join in the work of the Continentals. Analysis in England did prove to be largely mathematical physics, though some entirely new directions of work, algebraic invariant theory and symbolic logic, were also initiated in that country.
Jason Bardi, The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time (2006):
Nor was Newton's notation as useful as the superior notation that Leibniz had invented and the advanced calculus that Johann Bernoulli and the other European mathematicians developed throughout the century. Leibniz had correctly surmised that his symbols would make for the easy development of calculus, and these symbols, which he first penned in his notebooks in Paris in 1675, can still be found to this day in every calculus textbook.
In this sense, the high esteem in which Newton was held in Britain was not always a good thing, because, many of the mathematicians and scientists living there in the eighteenth century were behind the iron curtain of Newton's fame and glory. Ironically, as much as Leibniz's reputation suffered in Great Britain, the whole country may have suffered a self-inflicted wound by so underappreciating him. After the calculus wars, British mathematicians were prevented from learning calculus using Leibniz's notations, which were largely in use elsewhere, and they were not finally accepted in that country until the early nineteenth century.
Christopher D. Green, "Charles Babbage, the Analytical Engine, and the Possibility of a 19th-Century Cognitive Science" (2001):
The upholding of the Newtonian notation was a matter of some national pride for the British, for the nasty priority dispute between Newton's and Leibniz's partisans over the discovery of calculus still echoed in the very traditional halls of Cambridge. Unfortunately for the British, Newton's notation was difficult to manipulate algebraically, and they were now some 50 years behind the mathematical developments of their Continental colleagues, who had of course used Leibniz's notation from the first. Babbage, Herschel, and Peacock aimed to put a stop to what they called the "dot-age" of Cambridge (a satirical reference to the dots used to indicate derivatives in the Newtonian notation) and replace it with the "pure d-ism" of Leibniz (who used the letter "d" to indicate the same).
Gerald L. Alexanderson, "About the Cover - Voltaire, du Châtelet, and Newton" (2014):
Newton’s clumsy notation may have hampered progress in England.
