Chapter 1

Paris,
October 29, 1675

Progress, Optimism, and Restless Journeying

It is not good for one to spend the whole day brooding.

Thinking is bad for one's health, Metaphysicus.

Why don't you look there at the muddy ground instead, see what quivers and gurgles.

Durs Grünbein, Vom Schnee, oder Descartes in Deutschland (2003)

The Fly

It swoops down from the ceiling and buzzes around the room, darting this way and that, fitfully changing the direction of its flight. The housefly's movements aren't so quick anymore; the days have gotten shorter, and it sinks sluggishly onto the windowsill. In the chill it grows inert, but as the stove heats up, it begins once more to zip through the small room, lit by the glow of torches and candles. By the window, there is another source of warmth. On the table next to the window are the remnants of a meal and a cup of sugar-sweetened coffee. The sweet nourishment lures the fly; it flies to the table. There the dark source of warmth begins to move. A hand raised to strike casts a shadow; quick as the wind, the insect dodges out of the way. While the hand's owner has eyes that can process only about twenty frames per second, the fly perceives nearly two hundred frames in the same amount of time. To it, the hand moves incredibly slowly, as if in slow motion; by the time it reaches the fly's position, the insect has already turned and flown off toward the stove. From there, the tiny creature observes the large warm shadow that perches in its chair for what seems like an eternity-and from time to time, it flies once more toward the tempting sugar.

Coffee, a Little Wine, and Plenty of Sugar

Bent low over the table sits a man, incessantly reading and writing, occasionally raising a hand to shoo away a fly that loves sugar as much as he does. Thus can we imagine Gottfried Wilhelm Leibniz, who has likely been in this spot working without pause since late morning. It wouldn't be hard for Leibniz to imagine what is happening from the vantage point of a fly-after all, in his conception of it, the world in its totality consists of a multitude of actors, all with different perspectives. Late summer in Paris-an especially dry one this year-is long gone; the weather is slowly getting cooler.1 Without a heated stove, one could hardly bear to spend most of the day sitting. This, however, is the preferred way of life for the scholar from Saxony. Leibniz is twenty-nine years old, of medium height, and a bit skinny; his hair is brown. He describes himself as fairly well balanced, tending neither to impulsiveness nor to melancholy, a man with a quick wit and a lively sensibility. More than anything, he fears that prolonged sedentary study and too little movement could one day cause him an early death.2 During the day he drinks coffee with lots of sugar, and at night just a little wine, which to the delight of the flies he also likes to sweeten a little. In France, where the Gregorian calendar is in effect, today is Tuesday, October 29, 1675. Leibniz is living on Rue Garancière-a street just 220 meters long and straight as an arrow-in the Faubourg Saint-Germain, which at this time still lies outside the city center.

On this gloomy Tuesday in late October, Leibniz for the first time writes down on paper a symbol that will fundamentally change mathematics. What flows from his quill on this Tuesday, and what is today part of the standard curriculum in advanced math classes, is a simple symbol that gathers together the knowledge of the best mathematicians of the seventeenth century in the most splendid fashion and that its inventor will further develop into the key symbol of a new mathematical method. This symbol is the ?, an oversize s, today known as the integral symbol; with its help, both the length of a curve and the area underneath it can be elegantly calculated and succinctly notated using one and the same calculation method. October 29 marks a high point in Leibniz's years of work on infinitesimal mathematics. In the ? he creates a symbol that-as the next weeks and months will bear out-will make a crucial contribution to the development of a method of calculation that deals with infinitely small values within the framework of an easily manageable formulaic apparatus. But let's not get ahead of ourselves.

The night before this Tuesday, Leibniz probably went to bed late, as he so often does. "Stays up late and gets up later," he says of himself.3 He is used to working tirelessly, late into the night, while others are already asleep. For about a year now, he has been living on this narrow, dark street not far from the Jardin du Luxembourg. But what has brought Leibniz to Paris? The path that led him here from distant Saxony could not have been more unusual. Born in 1646 in Leipzig in an academic household-his mother was the daughter of a renowned lawyer, his father a notary and university professor-he grew up in a time of political and religious upheaval. Broad swaths of central Europe lay in rubble and ashes. The devastating Thirty Years' War was over, but it left in its wake a fractured continent and a deeply divided Christianity split into scarcely reconcilable confessions. At the same time, the unity of faith and reason threatened to break apart as the new disciplines of rationalism and empiricism started to assert themselves. At eight years old, the bright young mind taught himself-his father had died two years earlier-Greek, Latin, and Hebrew with the help of his home library. He devoured one book after another; some of them he even learned by heart.

At first, the highly gifted boy seemed to be following in his father's footsteps. He studied philosophy and law in his hometown and later in Altdorf bei Nürnberg. But he refused the professorship offered to him after completing his doctorate and postdoctorate studies, and instead-incessantly seeking and absorbing new knowledge-he went traveling. He didn't exactly have a plan, but armed with an interest in everything and everyone, he headed toward Holland, only to end up first in Frankfurt and then in Mainz in 1668. There he managed to enter into the service of Elector and Archbishop Johann Philipp von Schönborn and took part in a major project of judicial reform. Even in these early days in Mainz, he displayed what would be his typical working method, jumping between the most disparate political, religious, and scientific issues. As a child of the Thirty Years' War and its aftermath, he sought ways to reconcile a riven Europe, to reunite the continent's Christians, and to promote wide-reaching progress in all areas of human society and civilization. Spreading a Christian faith founded on reason throughout the globe, supporting the general welfare, improving life through science and technology-throughout his life, Leibniz will feel himself duty-bound to these idealistic goals.

But how to achieve all this? Leibniz needs a universal scientific concept and many allies-like-minded scholars and, above all, powerful patrons. And ideally he will find them in one of the metropolises of Europe. Thus Leibniz doesn't hesitate when, in the spring of 1673, an opportunity presents itself for him to travel to Paris as part of a diplomatic mission. He is supposed to play a role in the attempt to keep the French government from going to war against Holland and Germany. He develops a plan for Louis XIV to lead a military operation to occupy Egypt, not only to keep the power-hungry king from launching an offensive to his immediate east, but also to place France in a strategic position that would enable her to press on and gain access to the riches of India and Southeast Asia. To this end, Leibniz even proposes the construction of a canal between the Mediterranean and the Red Sea. But the "Egyptian Plan," which anticipates the idea of the Suez Canal but never reaches the ears of the French monarch, becomes moot when, soon after its drafting, France attacks the Netherlands.4

Oh well, Leibniz thinks to himself, the main thing is to be in Paris, which, alongside London, is a center of science and culture in Europe. Nearly half a million people live in France's capital; Leibniz finds himself in a modern city. Countless carriages and coaches fill the streets and allées. Even after dark the traffic doesn't let up. Oil lamps light up the streets and are relit every evening, the world's first comprehensive street lighting in a large city. Leibniz is electrified. He dives excitedly into the whirlpool of urban modernity. Filled with drive and ambition, he seeks to enter the orbit of the social and scientific elite, above all the Académie des Sciences, where the leading scientific minds conduct research. He makes contact with several members of the academy, meeting with, among others, Pierre de Carcavy, the royal librarian, and Giovanni Domenico Cassini, who works...