Newton’s Apes - Newton, Leibniz, and the Greatest Mathematical Clash of All Time - The Calculus Wars

The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time (2006)

Chapter 9. Newton’s Apes

1696–1708

Know yee that wee for divers good causes and considerations . . . do give and grant unto Our trusty and Well beloved Subject Isaac Newton Esqr. the office of Master and Worker of all our Moneys both Gold and Silver within our Mint in our Tower of London and elsewhere in our Kingdom of England.”

—William III, king of England. Newton’s Appointment as Master of the Mint, February 3, 1700

Newton had a house at the Tower of London, in which he lived for the briefest time when he moved to the capital. By the end of the seventeenth century, when he took up residence there, the Tower was already an ancient site that was steeped in history and intrigue. Newton lived just a few short steps from where Anne of a thousand days and many other famous prisoners had been executed.

Today, Mint Street boasts a narrow row of rather unassuming black brick houses on the westernmost side of the Tower complex; they have been converted into private homes which a docent told me are inhabited by people who work at the famous tourist attraction.

Newton did not live there for very long. The din of all the coin clapping was so bad that he soon found a house in another part of town. But sleeping far away from the noise did not mean his attention was elsewhere. His mint was a government office in crisis. By decree, the mint had been charged with recoining the silver currency of the realm—something that became necessary because the old coins had smooth edges and could be easily “clipped.”

Clipping occurred when dishonest types would snip a little sliver of metal from the edge of a coin. If they did this to enough coins, they could melt the pieces into a bar of silver bullion; and because one of the intricacies of the mint was that it allowed people to exchange silver bullion for silver coin, the clippers could trade this bar for new money.

If coin clipping was a chronic problem, counterfeiting was an acute one. For most of the seventeenth century, England’s silver coins were struck by hand—a grueling piecework task involving sweat and hammered silver dyes. This method had been abandoned thirty years before Newton came to the mint; instead, the coining had become more of an industrial process whereby silver was melted in massive iron pots over coal fires and coins hammered out by machines specially designed for the task. But some of the old coins were still in circulation and, as long as they were, counterfeiters could create their own dyes and hammer out fakes made from lesser alloys.

Recoining the currency was the solution to these issues because a new invention allowed the new coins to be edged (given a distinctive rim) in a machine when they were made, which prevented them from being clipped undetected and also made counterfeiting much more difficult. So the mint, which was located on Mint Street between what was once the inner and outer walls of the Tower of London, began churning out new coins at the end of the seventeenth century. Some three hundred workers and fifty horses turned the nine minting mills from 4:00 a.m. to midnight every day, and they cranked out 100,000 pounds of coins per week. It was the largest recoinage program in England’s history—and was not going well.

When the project began, it had a number of problems. For one, there was not enough income to pay for the expense of the operation. The mint was funded by a tax on imported liquor, which was not enough to support such massive recoinings, and as a solution the government imposed a new tax on windows in the city of London. Supposedly, some of the old “blind” windowless buildings in the city survived from that time even to the twentieth century.

Moreover, the new coins were still not a guarantee against counterfeiting, and there were lots of counterfeiters clever enough to beat the new system. New silver coins were cast from 92.5 percent pure silver and 7.5 percent copper. A counterfeiter could simply buy new coin, mix it with copper or lower-grade silver, and beat out counterfeit coins, and then exchange these for more new coins. This was so easily done and so rampant that by the time Newton became warden of the mint, he estimated that a fifth of the coins the mint took in were fakes.

Newton got to know the ins and outs of counterfeiting and clipping quite well when he took his first job as warden, one of the mint’s three chief officers. As warden, he was the king’s representative at the mint, a post that had once been ostensibly its top official. He managed the mint’s finances and supervised its other officials, but really the power of the mint resided with the master of the mint, who was sort of the head contractor. The master’s contract was simple. For every pound of silver he minted, he was allowed a certain percentage as commission, and with this he subcontracted the work and took his profit. By the time Newton was hired, the functions of the warden’s office had been reduced, and the master of the mint had assumed a great deal of power and no longer played second fiddle to the warden.

Basically, the warden was responsible almost exclusively for police and legal work. Newton’s first duty was ferreting out counterfeiters and clippers, and prosecuting them—work that held little appeal to him but which he excelled at. While the prosecution of the coiners and clippers was a duty that had been a part of the warden’s job for decades, Newton’s predecessors had left it to their clerks to carry out. Newton did it himself but is said to have been so disgusted by the work that after a while asked the treasury to relieve him of it. “’Tis the business of an Attorney and belongs properly to the King’s Attorney and Solicitor General,” he wrote. “I humbly pray that it may not be imposed on me any longer.”

This is not to say that he slacked off on the job. He took to his prosecutions with the same singular zeal that he applied to most things in life, personally taking extensive depositions from the accused counterfeiters and their lawyers, and writing something like a casebook to guide his work. He even bought a new suit for the task. He paid a significant sum of his own money to be made justice of the peace in several counties so that he could prosecute counterfeiters far and wide.

If there was any one criminal on whom Newton would sharpen his prosecutorial teeth more than any other, it was the notorious counterfeiter William Challoner. Challoner was a thief and a flimflam man of great skill and even greater bravado. A few years before Newton became warden, he had managed to collect a handsome reward through a shrewd backstabbing con involving a bounty offered by the British government for information leading to the capture of a pamphleteer who was spreading propaganda against the king. Challoner found one of the offending pamphlets, paid to have it reprinted, and turned in those printers for the reward money.

In early 1696, when Newton arrived at the mint, Challoner had an even bolder con in the works. A year earlier, he had written a pamphlet advocating a reduction of weight of silver coin to match the older, clipped coins. Presumably the reason for this was that Challoner was one of the best counterfeiters in Britain at that time, and a reduction of weight would mean more profits for him, since he could use less silver in his counterfeit coins. He approached Parliament and various members of the British government to decry the incompetence and corruption of the mint. Offering his services, Challoner claimed that he had invented a way of making counterfeit-proof coins. He tried to convince the government that he could modernize the coin-pressing machines at the mint, provided he personally supervised their operation.

A parliamentary committee that heard these offers asked Newton a few months later to give Challoner access to the mint machines. But Newton refused. Some of these machines were top secret. Newton himself had to swear out an oath not to reveal the workings of the mint operations when he assumed his post. He seems to have seen through Challoner’s ruse, and was not one to be trifled with in these matters. Newton had Challoner clapped in irons and placed under arrest. Many months later, in 1699, he had prosecuted the notorious counterfeiter so successfully that the rogue was put to death for his crimes.

For this and other displays of competence, Newton was rewarded with a promotion to master of the mint in 1699, when the master he served under, Thomas Neale, died. Newton was appointed in his place the day after Christmas. His appointment letter, in the name of King William III, granted “unto the said Isaac Newton all edifices, buildings, Gardens, and other fees, allowances, proffitts, privileges, franchises and immunities belonging to the aforesaid Office.”

Soon after this appointment, the spheres of Newton’s government and Leibniz’s would become inexorably linked. England’s King William died in 1702; and his co-regent wife, Mary, had had the bad fortune of fatally falling victim to smallpox about ten years before (and some hundred years before Jenner’s method of vaccination began the long process that would eventually lead to the eradication of the disease from the world in the 1970s). William and Mary left no heirs to the throne, and this set up something of a crisis in the years before the king died, when the British Parliament scrambled to find some solution to ensure a Protestant succession.

Next in line was Princess Anne, who was safely Protestant despite the fact that she was the daughter of the deposed King James II. In 1702, after William died, she became the ruler of Britain. Queen Anne was a stout, squat woman. In a 1705 portrait of her by the artist Michael Dahl that hangs in the National Portrait Gallery in London, she is standing impressively in a regal gold dress and a royal blue furry wrap, wearing impossibly large diamonds, one hand placed on the crown jewels. Having herself portrayed standing may have been an important statement because, when she was crowned in April 1702, she was obese, sick, and stricken with gout so severe that she could not stand or walk. She had to be carried on the backs of the yeomen of the guard into Westminster Abbey, where the crown was placed on her head.

Hers was not an easy rule. She inherited a war, which began in 1702 when a new alliance—the “Grand Alliance” of Denmark, Prussia, Hanover, the Palatinate, England, and Holland—was formed against France; and her reign also coincided in almost its entirety with the war of Spanish succession, which was not concluded until the Treaty of Ultrecht the year before Anne died in 1713. The real tragedy of Anne’s life, though, was that she was unable to raise a child, despite half a lifetime of trying. Queen Anne had eighteen pregnancies and seven children, but the last one died before she even took the throne.

Even before she became Queen, however, the British parliament passed in 1701 the Act of Settlement, which explicitly named the descendants of Leibniz’s good friend Queen Sophia as being in line for the British crown. This meant that Sophia’s son George Ludwig was slated to become king of England after Anne died. George was in an odd position to be in line for the throne. Proper succession would have had Queen Anne’s brother, James (the would-be James III), become the king. Instead, because of the Act of Settlement, the crown passed to their distant cousin, whose sole claim was that his great-grandfather on his mother’s side was King James I. James’s daughter Elizabeth Stuart had married Frederick, an elector in Germany, and they had had one child. She was the Sophia who wound up marrying Ernst August, the Duke of Hanover. Sophia and Ernst had six children, one of who was George Ludwig. When Ernst August died in 1698, he was succeeded as duke by George. The cause for George’s ascension to the English throne would not have looked good were he subjected to rules of inheritance that were not based on the fear of another Catholic king.

After George Ludwig became elector of Hanover, he changed the good-natured mood of the court. One witness to this change, the Duchess of Orleans, described it in a letter: “It is no wonder that pleasure is no longer to be seen in Hanover, for this Elector is so cold he turns everything to ice.”

There was some friction between Queen Anne and the duke in Hanover years before. George Ludwig traveled to England and was presented to Anne as a potential husband, but nothing came of the meeting. Rumors at the time attributed this to the fact that the fit and fierce young duke was not attracted to the squat, square Anne.

There was also friction between George Ludwig and Leibniz after the former became duke. George was probably willing to put up with more from Leibniz than he would have from one of his other courtiers, since Leibniz was a living legend—an illustrious thinker who was a leading intellect. Besides, Leibniz did provide valuable advice and faithful service. However, George never really took Leibniz into his confidence, and his respect often took a mocking tone. He once referred to Leibniz, for instance, as his “living dictionary,” and complained of his frequent absences and inability to finish the Brunswick history.

Leibniz took these things in stride. He was, indeed, a living legend by the time George Ludwig became duke in 1698. His record of service to the House of Hanover was solid and his list of accomplishments, quite aside from his work for the two previous dukes, George Ludwig’s father and his uncle, was immense. Despite the fact that he had not finished the history on which he had already been working nearly ten years, Leibniz assumed his court position at the end of the seventeenth century was as secure as his being the grandmaster champion of calculus—unassailable.

Hardly!

Out of nowhere, Fatio de Duiller popped back into the picture, when he was moved to champion Newton in 1699 after writing an article, “A Two-Fold Geometrical Investigation of the Line of Briefest Descent,” which made the startling public accusation that not only was Newton the first to discover calculus, but that Leibniz had actually stolen it from Fatio’s mentor and friend.

“The celebrated Leibniz may perhaps inquire how I became acquainted with the calculus which I may use,” Fatio wrote. “I recognize that Newton was the first and by many years the most senior inventor of calculus, being driven thereto by the factual evidence on this point. As to whether Leibniz, its second inventor, borrowed anything from him, I prefer to let those judge who have seen Newton’s letters and other manuscript papers, not myself.”

Why did Fatio suddenly jump in where there didn’t seem to be any ongoing dispute, and champion Newton after they had, for the previous several years, drifted apart? One possibility is that perhaps he was seeking to renew his friendship with Newton. But equally compelling as an explanation is that he may have been driven by feelings of resentment toward Leibniz.

Fatio had his own personal history with Leibniz, and he disliked the German immensely. Just as Leibniz had done a decade earlier, Fatio had made a connection with Huygens. Fatio was younger than Leibniz had been when he was in the same position, and Huygens was much older, but Fatio nevertheless saw himself as something of a peer of Leibniz because they were now both disciples of Huygens. For his part, Huygens wanted to promote an exchange between Fatio and Leibniz because he thought that it would be productive, and so Fatio wrote to Leibniz on several occasions, asking him to share his mathematical tools and techniques. Leibniz refused to become involved, failing to see what he stood to gain from the exchange. He still had the greatest respect for his old mentor but apparently not enough for Huygens’s new protégé.

Perhaps it was this earlier snub that led Fatio to take up Newton’s cause in 1699 and accuse Leibniz of plagiarism. Or perhaps he felt slighted by Leibniz because of Bernoulli’s challenge problem, which Fatio also solved but didn’t get it in on time. Fatio was offended when he read what Leibniz wrote about this problem—the gloating boasts about how only Newton and Leibniz’s exclusive clique of followers could solve it. Fatio saw this as a direct snub and was driven, therefore, to counter by throwing sand in Leibniz’s face in the form of a major accusation of plagiarism.

“Neither the silence of the more modest Newton nor the eager zeal of Leibniz in ubiquitously attributing the invention of this calculus to himself will impose on any who have perused those documents which I myself have examined,” Fatio wrote in his paper. There is no question that he was uniquely positioned to make such a spirited defense of Newton and attack of Leibniz. Fatio was one of the few people in Europe who were sufficiently versed in calculus to understand the documents, plus he had been given more access to Newton’s inner sanctum, with all its rich papers, than nearly any other human in the Englishman’s lifetime.

Nevertheless, Fatio’s attack was ill timed. While he did not out-rightly accuse Leibniz of plagiarism, he definitely implied it. A substantive case against Leibniz would eventually be made, and in time many others would also take up the accusation and attack Leibniz on Newton’s behalf much as Fatio did in 1699. But that would have to wait until later. In 1699, Newton was just a few years into his tenure at England’s mint, and overseeing this institution consumed much of his time and attention. He offered no help to Fatio.

Operating alone, Fatio was very far out of his league. Leibniz was, after all, hailed in Europe as the foremost mathematician of his day—a position that Leibniz himself was ever vigorous in asserting. In England, too, his reputation was stellar, and he was a long-time member of the Royal Society. And the foremost mathematician of his day was furious. He showed amazing restraint by not losing his cool; instead, he replied directly in the pages of the Acta Eruditorum.

In May 1700, Leibniz published his response to Fatio’s accusation, defending his position vigorously and dismissing the young man as having been perverted by a thirst for recognition. In an almost psychoanalytical attack, he wrote, “Mistrust is a feeling of hostility.” And he followed this statement with the eloquent zeal of a brilliant lawyer: “We can readily conceal under a zeal for justice sentiments which, plainly acknowledged, would disgust us. In truth, the more I understand the defects of the human mind, the less I grow angry at any aspect of human behavior.”

In his article, he defended himself by implying that Fatio did not have the support of even Newton in his accusation. For Leibniz, even though his relationship with Newton had always more or less been at a great distance, theirs had all the outward signs of one of mutual respect and the highest admiration. Newton’s silence on the issue was deafening to Leibniz’s ears. “At least the excellent man appeared, in several conversations with friends of mine,” wrote Leibniz, referring to Newton, “to manifest a kind disposition towards me, and made to them no complaints, so far as I know. In public, also, he has spoken of me in terms which it would be most unjust to find fault with. I, too, have acknowledged his great service on appropriate occasions.”

Leibniz was willing to give Newton his due as a mathematician on more than one occasion, and this was certainly one of them. At this point, the German still had no quarrel with his British rival, and he did not waste the opportunity to give adequate if not overabundant praise to Newton, setting themselves out as mathematical equals. But he maintained that theirs were parallel greatnesses—that he had gleaned little of Newton’s original discoveries from their exchange of letters. He claimed that he had no idea how advanced Newton’s mathematics were until he read the Principia, but that it was not until the 1690s that he realized that Newton’s methods were “a calculus so similar” to his own. In his article, Leibniz pointed out that the Englishman, in the Principia, established that they respectively invented their mathematical methods independently: “As in his Principia he has also explicitly and publicly testified, that neither of us is indebted, for the geometrical discoveries made common by us both, to any light kindled by the other, but to his own meditations.”

Leibniz also explicitly stated his innocence in the matter. “When I published my elements of the differential calculus, in 1684, I knew nothing of his discoveries in this department, except what he himself had told me in one of his letters, wherein he stated that he could draw tangents. . . .” The drawing of tangents that Leibniz drew attention to in this paper (an operation that is greatly simplified by the use of calculus) was hardly unique to Newton. Likewise, elsewhere Leibniz explicitly pointed out that nobody knew better than Newton how their discoveries were truly independent “without either receiving any enlightenment from the other.”

Leibniz did not merely write a rebuke of Fatio’s paper in his own favorite journal. For good measure, he also reviewed his own letter anonymously, giving it a favorable review of course. In addition, he sought vindication by complaining formally in a letter that was presented to the Royal Society on January 31, 1700. Without Newton’s backing, Fatio was easily shot down by Leibniz, and the mathematicians of note in those days backed Leibniz.

John Wallis, for instance, was said to have been most distressed by the accusations and sympathetic toward Leibniz. He assured him that Fatio’s attack had not been sanctioned by the Royal Society and that Leibniz’s reputation was safe. And Newton? . . . Newton remained silent on the matter.

The dispute could have ended here, and the calculus wars could have fizzled out with Leibniz, the victor of sorts, allowing that Newton was his equal in original discovery, demonstrating that Fatio was out of line, and going on with his business. To Leibniz, this was a simple matter that had been simply resolved. In his worldview, the invention of calculus belonged to him more than it did to Newton. Had they not discovered it independently, and had not Leibniz published his work first? “When I published the elements of my calculus in 1684,” Leibniz wrote, “there was assuredly nothing known to me of Newton’s discoveries in this area, beyond what he had formerly signified to me by letter.” The material he was referring to, he added, was not calculus but rather some preliminary methods.

Moreover, Leibniz had published calculus in a journal that was then being circulated among the top mathematicians in Europe. His methods were long established and well known throughout the Continent, not squirreled away as if some guilty secret. And, most important, had he not invented the notation of calculus that allowed its further development? In 1700, his calculus was successful in various applications used by others with Leibniz’s blessing, and the fact that it continued to be developed was strong testimony to Leibniz’s methods. Newton, on the other hand, did nothing to publish his version of calculus until he was a relatively old man, and he seemed less interested in promoting his fluxions and fluents than in securing the rights of their invention for himself; moreover, his notation was inferior to Leibniz’s.

Solidifying his mathematical reputation, Leibniz published another paper in 1701 under the French title, “Essay d’une nouvelle science des nombres.” The essay was in honor of his being made a member of the French Academy of Sciences, and it described a new science of numbers called binary mathematics, which he had developed in 1679. Binary (literally, “two numerals”) is a system whereby all values are represented as sequences of only two digits—one and zero. Leibniz thought that binary numbers would reveal properties of ordinary numbers that would not otherwise be apparent, and in fact binary numbers, as established by Leibniz, became the basis of electronic circuitry.

Following Leibniz’s well-presented series of rebuttals, Fatio did not fare so well. In 1704, he was the secretary to a group of fanatics called the Camisard prophets—a sort of doomsday cult from France who were obsessed with the imminent fulfillment of prophecy from the Bible’s revelations and who claimed that they could raise the dead. The group was ostracized for their beliefs, and Fatio himself was pilloried at Charing Cross on December 2, 1707. His head and hands were stuck through the holes of the wooden frame of the pillory, and a hat was placed on his head that read, “Nicolas Fatio convicted for abetting Elias Moner in his wicked and counterfeit prophesies and causing them to be printed and published to terrify the queen’s people.”

Interestingly, Leibniz never seemed personally vindictive toward Fatio even after the accusations came out. Several times after the events of 1700, he addressed kind words about Fatio in writing to his friend Thomas Burnet. And when Fatio was pilloried in 1708, Leibniz wrote of how appalled he was by the treatment though also at how Fatio, “a man excellent in mathematics,” could have been involved with the Camisard prophets.

The dispute with Fatio portended a different sort of doomsday for Leibniz. Fatio’s attack was isolated and little came of it. But it was a signal of what was to come.

The next time the fires flared up was when they were stoked by a minor character named George Cheyne, whose main claim to fame other than his role in the calculus wars seems to be his strange new theory of fevers, which he based on Newtonian physics.

CHEYNE WAS SCOTTISH by birth but had settled in London around the turn of the eighteenth century as one of a growing group of Newtonians. In an unauthorized tribute to his new master, Cheyne wrote a book he called On the Inverse Method of Fluxions, in which he attempted to explain Newtonian calculus to the world.

It was an inferior, unimportant book by a man who would probably have been completely forgotten had it not been for the fact that so little had ever appeared in print on the methods of calculus that it could not have gone unnoticed. And indeed many people noticed it—not the least of them Newton.

When Cheyne’s book was published, Newton was becoming more and more important as a figure in England. Robert Hooke died in March 1703, and this freed Newton of his longtime nemesis, who had been a cantankerous gadfly to him at times. Even at the end of his life, Hooke was still menacing Newton with his public accusations. On August 16, 1699, for example, when Newton appeared before the Royal Society to present a sextant he had just invented, Hooke, always unimpressed, responded by claiming that he himself had invented the sextant thirty years before.

Shortly thereafter, on November 30, 1703, Newton was elected president of the Royal Society. This was not the only satisfaction Newton enjoyed at the turn of the eighteenth century. On April 16, 1705, he was awarded the ultimate recognition of knighthood by Queen Anne.

Now, as a knight and Royal Society president, Newton was finally about to throw off his long silence and assert his priority in the invention of calculus when he published Opticks in 1704. Cheyne’s book was part of the inspiration for this, because Cheyne got Newton’s calculus wrong enough that Newton wanted to get his own written material out there, which he did in the appendix section of Opticks, “On the Quadrature of Curves.”

This led directly to a confrontation with Leibniz, because after he became aware of Opticks, Leibniz of course leapt to publish an anonymous review of Newton’s mathematical appendix. In his review, he wrote, “Instead of the differences of Leibniz, Newton applies and has always applied fluxions . . . as also Honoratus Fabrius, in his Synopsi Geometrica, substituted progressive motion in the place of indivisibles of Calvalieri.”

What did he mean by this? It means almost nothing to modern readers, the names Honoratus Fabrius and Calvalieri being so obscure that the offending statement is completely vague—even innocuous. But to a mathematician as brilliant as Newton, who was well versed in the mathematical discoveries and controversies of his day, the meaning was instantly clear. Fabrius had borrowed the work of Calvalieri, and by comparing Newton to the former, Leibniz may have been subtly implying that Newton borrowed calculus from him. This would really be too much for Newton to endure when he found out about it.

However, it would take a few years before Newton did find out. Those years would be the last that Newton and Leibniz would spend, that weren’t clouded by the full-blown calculus wars, which exploded after 1708, when one of Newton’s supporters attacked Leibniz.

Meanwhile, the years between 1705 and 1708 were not the happiest of Leibniz’s life because of the loss of a good friend. For years he had been close to the women of the German courts. He was a perfect companion for the ladies of the court, really, since he could speak wonderfully and was well informed on a dozen topics of timeless importance and probably twice that many topics of contemporary or trivial interest.

Particularly endeared to Leibniz was Sophie Charlotte, the daughter of Queen Sophia and Ernst August, who had an extraordinary affection for the older philospopher. She once expressed this in the over-the-top superlative praise that was the fashion of that time. “Think not that I prefer this greatness and these crowns, about which they make such a bustle here,” she wrote to Leibniz, “to the conversations on philosophy we have had together.”

Sophie Charlotte was an important royal in Europe. Ernst August had married her to Prince Frederick of Brandenburg when she was a teenager. Sophie Charlotte was a lovely girl, beautiful, rich, intelligent, and destined for greatness. Her husband became the elector Frederick III a few years after they were married, and, a while after that, in 1701, Frederick and Sophie Charlotte became king and queen of Prussia. Their grandson was Frederick the Great.

Sophie Charlotte had been tutored by Leibniz and as queen carried on an extensive correspondence with him—on metaphysics, history, literature, and just about everything. She was apparently so clever that she sometimes complained that Leibniz oversimplified things in his discussions with her. Supposedly, according to Frederick the Great, when she complained to Leibniz about this, he said that it was a reflection of her brilliance more than his condescending attitude. “It is not possible to satisfy you,” Leibniz supposedly said. “You desire to know the wherefore of the wherefore.”

Her death in 1705 was such a shock to Leibniz, that certain ambassadors and dignitaries in Berlin paid their respects to him as though he were the closest surviving family member. He later wrote one of his most famous books, Theodicy, based on conversations he had with Sophie Charlotte and on writings he did for her in French that had been based on the same conversations, as a sort of memorial to her. It addressed questions of church doctrines that he had first wrestled with in his efforts toward church reunification at the end of the seventeenth century. The book was a very influential work after it was published in 1710, especially in Germany, and is one of the most important primary texts for Leibniz scholars today because it expresses Leibniz’s philosophy. Theodicy was published anonymously in 1710, because Leibniz did not want his name to appear on a theological work.

Publishing anonymously was very common in the seventeenth century, and Leibniz had already found it a convenient way to express his mathematical opinions at certain times. This sort of anonymity complicated things immensely in the years to come because the communications that passed back and forth between Newton and Leibniz was often marked by subterfuge. Both men relied on their supporters to make their arguments and attacks for them. Leibniz had the advantage on paper, since he had a few key supporters in Europe who were themselves brilliant mathematicians. But curiously, Newton had the real advantage—perhaps because he was without equal among his supporters, as would be demonstrated by one of Newton’s key followers, a young Oxford professor named John Keill, who made prosecuting Newton’s case against Leibniz his own personal crusade.

Keill was a Scot who had followed his teacher, David Gregory, to Oxford in 1694. Though a very minor character on the stage of science, he turned out to be a major player in the calculus wars. Much as Fatio had done, Keill sought to go beyond securing Newton’s due credit as co-inventor. He wanted to secure all the credit and accompanying fame for Newton and Newton alone. In order to do this, Keill had to show that Leibniz had stolen calculus from Newton. Eventually receiving a great deal of help from Newton, Keill succeeded in issuing a serious challenge to Leibniz’s credibility.

Newton’s second “ape” after Fatio, Keill went on the offensive in 1708 and began to accuse Leibniz of plagiarism. He published a paper in the Royal Society’s Philosophical Transactions in late 1708, though it was not printed until 1710. Keill’s paper was a minor little pastiche on physics that inexplicably contained a major accusation. “The Laws of Centripetal Forces,” as it was called, is more noteworthy for what it said about the calculus dispute than for what it said about centripetal forces. In it, Keill wrote that Leibniz’s calculus was “the same arithmetic” as Newton’s fluxions, and he called Newton “beyond all doubt” the first inventor of fluxions: “The same calculus was afterward published by Leibniz, the name and mode of notation being changed.”

Keill’s claim was carefully crafted to be a blunt but indirect accusation of plagiarism against Leibniz. Nobody could dispute that Leibniz had published first. So Keill chose the next best thing. He said that Newton had invented calculus prior to Leibniz and that Leibniz did not follow Newton merely in time but also in design. Moreover, Keill modified his attack in such a way as to state that he was not accusing Leibniz of plagiarism, while at the same time suggesting that plagiarism is exactly what the German had done. Even though Newton didn’t write down his ideas and share them with his contemporaries through publication, he had nevertheless shared them with Leibniz. Keill stated that Leibniz could have gotten everything he needed to develop calculus from the two letters that Newton had sent to him way back in 1676. They contained, Keill said, what was “sufficiently intelligible to an acute mind.”

It was a clever approach, really. The case became one that was winnable for Keill—and ultimately for Newton—because they were not trying to prove historically that Leibniz had stolen anything all those years ago, but rather that he merely could have. And by coupling this argument with the even sounder evidence that Newton had developed his methods of calculus prior to Leibniz’s version, it was enough to make the case that the English mathematician was the true and sole inventor of calculus.

Such a strong challenge had not been made since the ill-fated attempt by Fatio to win credit for Newton nearly a decade earlier. But unlike Fatio’s arguments, which fell apart like a house of cards under a single wave of Leibniz’s hand, Keill’s attack was much more dangerous. It was a deliberate provocation that Leibniz had to answer—a bear trap covered with twigs and leaves.

The winter of 1709 was a terrible and miserable time in Europe. It coincided with military disaster for the French and a terrible famine in Europe, as unusually harsh conditions visited down upon the populace. And another war, several decades in the making, was finally about to explode.