The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World - Edward Dolnick (2011)

Part III. Into the Light

Chapter 44. Battle’s End

From its earliest days, science has been a dueling ground. Disputes are guaranteed, because good ideas are “in the air,” not dreamed up out of nowhere. Nearly every breakthrough—the telescope, calculus, the theory of evolution, the telephone, the double helix—has multiple parents, all with serious claims. But ownership is all, and scientists turn purple with rage at the thought that someone has won praise for stolen insights. The greats battle as fiercely as the mediocre. Galileo wrote furiously of rivals who claimed that they, not he, had been first to see sunspots. They had, he fumed, “attempted to rob me of that glory which was mine.” Even the peaceable Darwin admitted, in a letter to a colleague urging him to write up his work on evolution before he was scooped, that “I certainly should be vexed if anyone were to publish my doctrines before me.”

What vexed the mild Darwin sent Newton and Leibniz into apoplectic rages. The reasons had partly to do with mathematics itself. All scientific feuds tend toward the nasty; feuds between mathematicians drip with extra venom. Higher mathematics is a peculiarly frustrating field. So difficult is it that even the best mathematicians often feel that the challenge is just too much, as if a golden retriever had taken on the task of understanding the workings of the internal combustion engine. The rationalizations so helpful elsewhere in science—she had a bigger lab, a larger budget, better colleagues—are no use here. Wealth, connections, charm make no difference. Brainpower is all.

“Almost no one is capable of doing significant mathematics,” the American mathematician Alfred W. Adler wrote a few decades ago. “There are no acceptably good mathematicians. Each generation has its few great mathematicians, and mathematics would not even notice the absence of the others. They are useful as teachers, and their research harms no one, but it is of no importance at all. A mathematician is great or he is nothing.”

That is a romantic view and probably overstated, but mathematicians take a perverse pride in great-man theories, and they tend to see such doctrines as simple facts. The result is that mathematicians’ egos are both strong and brittle, like ceramics. Where they focus their gaze makes all the difference. If someone compares himself with his neighbors, then he might preen himself on his membership in an arcane priesthood. But if he judges himself not by whether he knows more mathematics than most people but by whether he has made any real headway at exploring the immense and dark mathematical woods, then all thoughts of vanity flee, and only puniness remains.

In the case of calculus, the moment of confrontation between Newton and Leibniz was delayed for a time, essentially by incredulity. Neither genius could quite believe that anyone else could have seen as far as he had. Newton enjoyed his discoveries all the more because they were his to savor in solitude, as if he were a reclusive art collector free to commune with his masterpieces behind closed doors. But Newton’s retreat from the world was not complete. He could abide adulation but not confrontation, and he had shared some of his mathematical triumphs with a tiny number of appreciative insiders. He ignored their pleas that he tell everyone what he had told them. The notion that his discoveries would speed the advance of science, if only the world knew of them, moved Newton not at all.

For Leibniz, on the other hand, his discoveries had value precisely because they put his merits on display. He never tired of gulping down compliments, but his eagerness for praise had a practical side, too. Each new achievement served as a golden entry on the résumé that Leibniz was perpetually thrusting before would-be patrons.

In Newton’s view, to unveil a discovery meant to offer the unworthy a chance to paw at it. In Leibniz’s view, to proclaim a discovery meant to offer the world a chance to shout its hurrahs.

In history’s long view, the battle ended in a stalemate. Historians of mathematics have scoured the private papers of both men and found clear evidence that Newton and Leibniz discovered calculus independently, each man working on his own. Newton was first, in 1666, but he only published decades later, in 1704. Leibniz’s discovery followed Newton’s by nine years, but he published his findings first, in 1684. And Leibniz, who had a gift for devising useful notations, wrote up his discoveries in a way that other mathematicians found easy to understand and build upon. (Finding the right notation to convey a new concept sounds insignificant, like choosing the right typeface for a book, but in mathematics the choice of symbols can save an idea or doom it. A child can multiply 17 by 19. The greatest scholars in Rome would have struggled with XVII times XIX.)47

The symbols and language that Leibniz devised are still the ones that students learn today. Newton’s discovery was identical, at its heart, and in his masterly hands it could be turned to nearly any task. But Newton’s calculus is a museum piece today, while a buffed and honed version of Leibniz’s remains in universal use. Newton insisted that because he had found calculus before anyone else, there was nothing to debate. Leibniz countered that by casting his ideas in a form that others could follow, and then by telling the world what he had found, he had thrown open a door to a new intellectual kingdom.

So he had, and throughout the 1700s and into the 1800s, European mathematicians inspired by Leibniz ran far in front of their English counterparts. But in their lifetimes, Newton seemed to have won the victory. To stand up to Newton at his peak of fame was nearly hopeless. The awe that Alexander Pope would later encapsulate—“Nature and nature’s laws lay hid in night, / God said ‘Let Newton be!’ and all was light”—had already become common wisdom.

The battle between the two men smoldered for years before it burst into open flames. In 1711, after about a decade of mutual abuse, Leibniz made a crucial tactical blunder. He sent the Royal Society a letter—both he and Newton were members—complaining of the insults he had endured and asking the Society to sort out the calculus quarrel once and for all. “I throw myself on your sense of justice,” he wrote.

He should have chosen a different target. Newton, who was president of the Royal Society, appointed an investigatory committee “numerous and skilful and composed of Gentlemen of several Nations.” In fact, the committee was a rubber stamp for Newton himself, who carried out its inquiry single-handedly and then issued his findings in the committee’s name. The report came down decisively in Newton’s favor. With the Royal Society’s imprimatur, the long, damning report was distributed to men of learning across Europe. “We take the Proper Question to be not who Invented this or that Method but who was the first Inventor,” Newton declared, for the committee.

The report went further. Years before, it charged, Leibniz had been offered surreptitious peeks at Newton’s mathematical papers. There calculus was “Sufficiently Described” to enable “any Intelligent Person” to grasp its secrets. Leibniz had not only lagged years behind Newton in finding calculus, in other words, but he was a sneak and a plagiarist as well.

Next the Philosophical Transactions, the Royal Society’s scientific journal, ran a long article reviewing the committee report and repeating its anti-Leibniz charges. The article was unsigned, but Newton was the author. Page after page spelled out the ways in which “Mr. Leibniz” had taken advantage of “Mr. Newton.” Naturally Mr. Leibniz had his own version of events, but the anonymous author would have none of it. “Mr. Leibniz cannot be a witness in his own Cause.”

Finally the committee report was republished in a new edition accompanied by Newton’s anonymous review. The book carried an anonymous preface, “To the Reader.” It, too, was written by Newton.

Near the end of his life Newton reminisced to a friend about his long-running feud. “He had,” he remarked contentedly, “broke Leibniz’ heart.”