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Stephenson:Neal:Quicksilver:40:The priority dispute has turned vicious (Alan Sinder)

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Stephensonia

This is the reason Daniel Waterhouse is traveling to England in 1713. Enoch Root has suggested that the Massachusetts Bay Colony Institute of Technologickal Arts is suffering birth pains because of the pan-Anglo (colonists as well as proud Britons) view Gottfried Wilhelm von Leibniz as a plagarist.

Authored entries

Who's on First? Chicken or Egg

In the early 18th century, science and mathematics had, for the first time, become available to the public. Printed books were an important factor and little more than a century old in 1600. One of the most important spectacles of the time was the battle between Newton (and the English-speaking world) and Leibniz (and everyone else in Europe) over the priority (and the glory) of having invented the calculus. The stakes were very high, at least in prestige and status and national pride, though calculus was understood by very few, inlcuding scientists of the age. It was indeed the rocket science of the time. The educated layman could recognise the importance of the discovery; it represented important new ways to calculate velocities and rates of change, useful in many things from navigation to artillery. New businesses were made and obsolete ones crumbled as the techniques of the calculus were applied to practical problems. And there was a whole new demand for scientific instuments and measurement devices.

The Priority Dispute

Although Archimedes and others had used what are essentially integral methods (eg, the method of exhaustion), and a great many (eg, Barrow, Fermat, Pascal, Wallis, and others) had previously invented the idea of a derivative, Gottfried Wilhelm von Leibniz and Sir Isaac Newton are usually credited with the invention, in the late 1600s, of differential and integral calculus as we know it today. Certainly they are the first to realize that differentiation and integration are inverse procedures; this is the fundamental theorem of the calculus. Leibniz and Newton, apparently working independently, arrived at equivalent results. Newton's discoveries were made earlier, but Leibniz' were the first to be made public.

Newton (who represented derivatives as \dot{f}, \ddot{f}, etc.) provided a host of applications in physics, but Leibniz' more flexible notation (df / dx, d2f / dx2, etc.) was eventually adopted. (The simpler f' notation is still used in some cases where it is sufficient.)

In Brief: In 1704 an anonymous pamphlet, later determined to have been written by Leibniz, accused Newton of having plagiarised Leibniz's work. That claim is easily refuted as there is ample evidence to show that Newton commenced work on the calculus long before Leibniz can possibly have done, however the resulting controversy lead to suggestions that Leibniz may not have invented the calculus independently as he claimed, but may have been influenced by reading copies of Newton's early manuscripts. This claim is not so easily dismissed and there is in fact considerable circumstantial evidence to support it. Leibnitz was not known at the time for his complete and confirmed integrity (as if Newton behaved better by using proxies), and later admitted to falsifying the dates on certain of his manuscripts in an effort to bolster his claims. Furthermore, a copy of one of Newton's very early manuscripts with annotations by Leibniz was found among Leibniz' papers after his death, although the exact date when Leibniz first acquired this is unknown. It is also interesting to note that a similar controversy exists in philosophy over whether or not Leibniz may have appropriated the ideas of Spinoza in his writings on that subject.

The truth of the matter will never be known, and in any case is unimportant to anyone alive today. Leibniz' great contribution to calculus was his notation, and this is beyond doubt purely of Leibniz's invention. The controversy was unfortunate however in that it divided the mathematicians of Britain and Europe for many years. This set back British 'analysis' (i.e. calculus-based mathematics) for a very long time. Newton's terminology and notation was clearly less flexible than that of Leibniz, yet it was retained in British usage until the early 19th century, when the work of the Analytical Society successfully saw the introduction of Leibniz's notation in Great Britain.

In 1703 Newton was elected president of the Royal Society and was re-elected each year until his death. He was knighted in 1705 by Queen Anne, the first scientist to be so honored for his work. Newton roasted those he felt criticized him, so it is not surprising that he flew into an irrational temper directed against Leibniz. Newton misused his position as President of the Royal Society to further his side of the dispute. In this capacity he appointed an "impartial" committee to decide whether he or Leibniz was the inventor of the calculus. He wrote the official report of the committee (although of course it did not appear under his name) which was published by the Royal Society, and he then wrote a review (again anonymously) which appeared in the Philosophical Transactions of the Royal Society. Newton's assistant Whiston had seen his rage at first hand. He wrote:- Newton was of the most fearful, cautious and suspicious temper that I ever knew.

Neither Newton nor Leibniz, nor any of their followers until the mid-1800s, developed calculus with the rigor needed to avoid certain problems. Calculus was (and remains) a very powerful mathematical tool, but those problems have made it a tricky one. It was not until the 19th century that mathematicians like Augustin Louis Cauchy, Bernard Bolzano, and Karl Weierstrass were able to provide a mathematically rigorous exposition, based on the epsilon-delta limit definition. In the 20th century, Abraham Robinson and others showed, in developing 'Non-standard Analysis', that it is possible to be equivalently rigorous without the complications of the epsilon-delta limits. Nevertheless, the calculus was widely used, both before and after the epsilon-delta refoundation. Some of the foundational problems encountered with calculus eventually led to deep explorations of the nature of mathematical infinity, primarily by Georg Cantor in the late 19th century.

Analytical Society: Promotion of Analytical Calculus

The father of computers Charles Babbage did weigh in. The promotion of analytical calculus is perhaps the foremost amongst them. In 1812, Babbage helped found the Analytical Society. The aim of this society, led by student George Woodhouse, was to promote Leibnizian, or analytical, calculus over the newtonian-style calculus then in use throughout the British Isles. Newton's calculus was clumsy, and was in use more for political reasons than practical. The Society included Sir John Herschel and George Peacock amongst its members. In the years 1815–1817 he contributed three papers on the "Calculus of Functions" to the Philosophical Transactions, and in 1816 was made a fellow of the Royal Society. The Analytical Society was a group of individuals in early-19th century Britain whose aim was to promote the use of Leibnizian or analytical calculus as opposed to Newtonian calculus. The latter system come into being in the 18th century as an invention of Sir Isaac Newton, and was in use throughout Great Britain for political rather than practical reasons. The Newtonian system of fluxions and fluents is cumbersome to use, and much less flexible and practical than the Leibnizian, which was used by the rest of Europe. The society still exists today.

In Conclusion

The question became so important to the scientific community at large, stalling important work as the Continent and the United Kingsom took sides. This so impacted the general public that the King George I, his capable daughter-in-law Princess Caroline, the most powerful woman in England, and many politicians and educators of the day also were involved.