Primordial Seeds

La fin de siècle, la belle epoque. Paris was abuzz with progress. In the west, Gustave Eiffel's new tower — still considered a controversial eyesore by Parisians living in its shadow — shot up over the site of the 1889 World's Fair. In the north, at the foot of Montmartre, a new cabaret called the Moulin Rouge had just opened to such fanfare that the Prince of Wales came over from Britain to see the show. Closer to the center of town, word had begun to spread of certain unexplained accidents at the magnificent and still-new home of the city's opera, the Palais Garnier — accidents that would lead to at least one death when part of a chandelier fell. Rumor had it that a phantom haunted the building.

Just a few blocks east from the Palais Garnier lay the beating heart of the French empire: the Paris Bourse, the capital's principal financial exchange. It was housed in a palace built by Napoleon as a temple to money, the Palais Brongniart. Its outside steps were flanked by statues of its idols: Justice, Commerce, Agriculture, Industry. Majestic neoclassical columns guarded its doors. Inside, its cavernous main hall was large enough to fit hundreds of brokers and staff members. For an hour each day they met beneath ornately carved reliefs and a massive skylight to trade the permanent government bonds, called rentes, that had funded France's global ambitions for a century. Imperial and imposing, it was the center of the city at the center of the world.

Or so it would have seemed to Louis Bachelier as he approached it for the first time, in 1892. He was in his early twenties, an orphan from the provinces. He had just arrived in Paris, fresh from his mandatory military service, to resume his education at the University of Paris. He was determined to be a mathematician or a physicist, whatever the odds — and yet, he had a sister and a baby brother to support back home. He had recently sold the family business, which had provided sufficient money for the moment, but it wouldn't last forever. And so, while his classmates threw themselves into their studies, Bachelier would have to work. Fortunately, with a head for numbers and some hard-won business experience, he had been able to secure a position at the Bourse. He assured himself it was only temporary. Finance would have his days, but his nights were saved for physics. Nervously, Bachelier forced himself to walk up the stairs toward the columns of the Bourse.

Inside, it was total bedlam. The Bourse was based on an open outcry system for executing trades: traders and brokers would meet in the main hall of the Palais Brongniart and communicate information about orders to buy or sell by yelling or, when that failed, by using hand signals. The halls were filled with men running back and forth executing trades, transferring contracts and bills, bidding on and selling stocks and rentes. Bachelier knew the rudiments of the French financial system, but little more. The Bourse did not seem like the right place for a quiet boy, a mathematician with a scholar's temperament. But there was no turning back. It's just a game, he told himself. Bachelier had always been fascinated by probability theory, the mathematics of chance (and, by extension, gambling). If he could just imagine the French financial markets as a glorified casino, a game whose rules he was about to learn, it might not seem so scary.

He repeated the mantra — just an elaborate game of chance — as he pushed forward into the throng.

"Who is this guy?" Paul Samuelson asked himself, for the second time in as many minutes. He was sitting in his office, in the economics department at MIT. The year was 1955, or thereabouts. Laid out in front of him was a half-century-old PhD dissertation, written by a Frenchman whom Samuelson was quite sure he had never heard of. Bachelor, Bacheler. Something like that. He looked at the front of the document again. Louis Bachelier. It didn't ring any bells.

Its author's anonymity notwithstanding, the document open on Samuelson's desk was astounding. Here, fifty-five years previously, Bachelier had laid out the mathematics of financial markets. Samuelson's first thought was that his own work on the subject over the past several years — the work that was supposed to form one of his students' dissertation — had lost its claim to originality. But it was more striking even than that. By 1900, this Bachelier character had apparently worked out much of the mathematics that Samuelson and his students were only now adapting for use in economics — mathematics that Samuelson thought had been developed far more recently, by mathematicians whose names Samuelson knew by heart because they were tied to the concepts they had supposedly invented. Weiner processes. Kolmogorov's equations. Doob's martingales. Samuelson thought this was cutting-edge stuff, twenty years old at the most. But there it all was, in Bachelier's thesis. How come Samuelson had never heard of him?

Samuelson's interest in Bachelier had begun a few days before, when he received a postcard from his friend Leonard "Jimmie" Savage, then a professor of statistics at the University of Chicago. Savage had just finished writing a textbook on probability and statistics and had developed an interest in the history of probability theory along the way. He had been poking around the university library for early-twentieth- century work on probability when he came across a textbook from 1914 that he had never seen before. When he flipped through it, Savage realized that, in addition to some pioneering work on probability, the book had a few chapters dedicated to what the author called "speculation" — literally, probability theory as applied to market speculation. Savage guessed (correctly) that if he had never come across this work before, his friends in economics departments likely hadn't either, and so he sent out a series of postcards asking if anyone knew of Bachelier.

Samuelson had never heard the name. But he was interested in mathematical finance — a field he believed he was in the process of inventing — and so he was curious to see what this Frenchman had done. MIT's mathematics library, despite its enormous holdings, did not have a copy of the obscure 1914 textbook. But Samuelson did find something else by Bachelier that piqued his interest: Bachelier's dissertation, published under the title A Theory of Speculation. He checked it out of the library and brought it back to his office.

Bachelier was not, of course, the first person to take a mathematical interest in games of chance. That distinction goes to the Italian Renaissance man Gerolamo Cardano. Born in Milan around the turn of the sixteenth century, Cardano was the...