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for shares, as people flocked from all over the country and abroad to take part in the economic miracle of Law's system. With all this money circulating around at a ferocious rate, the economy boomed. The word “millionaire” came into use for the first time. In 1719 alone, the Company share price vaulted from 500 livres to over 10,000 livres. The dropping of the dead-weight connection to metal also released any restraints on Law's bounding ambitions. In no time he was arranging for the Company to buy the national debt, and have the right to collect taxes. This required issuing many more shares, and many more paper notes to buy them with. Which is when Law's system started to reveal its flaws.

      While Law was certainly correct that money serves as a “Sign of Transmission,” its value also depends on the confidence and trust of the community, and he had made the same mistake that he had made as a gambler in Paris, which was to fail to arrange buy-in from all the relevant players. Then it was the Chief of Police, d'Argenson, now it was the business and banking community (which included d'Argenson, who had become a prominent businessman). Rumors began to circulate that Louisiana was not quite the wealth generator it was cracked up to be, and Mississippi Company shareholders began to suspect they were being sold down the river.

      The trip down was just as brief and thrilling as the way up. Suffice to say that, as the Company's share price drained away, and the value of the bank's paper notes approached zero, Law was again drummed out of Paris, and the country, and ended up near destitute in Venice. The story ought to serve as a cautionary tale for present-day central bankers. Oh, except that these days no bankers, central or otherwise, ever end up destitute.

Gold Standard

      While Law was introducing the French to the benefits, perils, and general excitement of fiat currencies and financial innovation, Isaac Newton was serving as Warden of the Mint in England. Newton is of course best known for his famous contributions to physics, but he worked at the Mint from 1696 until his death in 1727. It is safe to say that his approach to finance was the opposite of Law's. At exactly the same time that Law was arranging to delink the livre from gold or silver, Newton was putting the pound on the gold standard, where it would remain for the next couple of hundred years.3 While Law was issuing what some considered to be fake money, Newton was sending counterfeiters to their death. One wonders what he would have said about the situation in France, from his position at the Tower of London. Perhaps he felt some sympathy with Law's fall from grace; he did manage to lose £20,000 himself (over £2 million in today's money) on his investment in the South Sea Company, the British version of the Mississippi Company.

      The two certainly had completely different personalities. Here is a portrait of the young John Law by journalist John Flynn: “He got access to the smartest circles. He was a young man of education and culture, handsome, quick-witted, a good athlete excelling at tennis, a graceful dancer, and a redoubtable talker. He spent his mornings in the city, where he got a reputation for skill in speculating in government paper. He passed his afternoons in the parks, his evenings at the opera or theater, and the later hours at the routs, balls, masquerades, and gaming houses. He played for high stakes and won large sums. He was a man with a system. Had he lived in our time he would have been in Wall Street with an infallible formula for beating the market.”4 Perhaps he would have launched a hedge fund, or penned a bestseller about his “system.”

      Isaac Newton, in contrast, was a decidedly more solitary type. As a child, he showed great talent at making models, such as a working windmill. This skill later came in useful while constructing his own experimental apparatus, including a new design of telescope. He attended Cambridge University, but his most creative period came when the university was closed for two years because of the advancing plague, and Newton returned to his home in Lincolnshire to work alone. It was there that he claimed to have been prompted to discover the law of gravity after seeing an apple fall from a tree. Throughout his life he had a passion for alchemy and mysticism; in fact, most of his output consisted of religious writings, including a 300,000-word tract on the Book of Revelation.5 He was famously anti-social and incommunicative; if no one showed up for his lectures, he just gave them to the empty room. There is no record of him being an expert dancer, or really fun at parties. As economist John Maynard Keynes wrote, he became instead the “Sage and Monarch of the Age of Reason.”6

      Researchers at Oxford and Cambridge have suggested that Isaac Newton may have had Asperger's Syndrome.7 There is quite a business in such historical psych evaluations nowadays (see Box 1.1), but this one has a ring of truth about it. Often those with Asperger's Syndrome have a very narrow field of interest, with little curiosity in or appreciation of the bigger picture. They can exhibit intense concentration and understanding, and in many cases there is increased intelligence in areas such as mathematics. Which perhaps would explain why Newton was better with celestial mechanics than the financial sort.

      These two contemporaries, Law and Newton, represent two aspects of the relationship between mathematics and finance. Mathematical finance is about using objective, rational, Newtonian models to simulate markets and make predictions about their future evolution. Quants are often described as modern-day wizards, hidden away in secret laboratories, who use mind-bending techniques inspired by areas such as quantum physics and string theory, coupled with the power of massive computers, to find hidden patterns in the markets. As Scott Patterson puts it in his book The Quants: “Think of white-coated scientists building ever more powerful devices to replicate conditions at the moment of the Big Bang to understand the forces at the root of creation.”8

      However, these scientists are trying to make money, not discover the next Higgs boson. (Juan Maldacena, Professor of Theoretical Physics at the Institute for Advanced Studies at Princeton and winner of many prizes for his work on such things as black holes, has said that finance is harder than physics. However, he has also given a public lecture in which he uses exchange rates as an analogy to explain the very same boson.) Mathematicians, like Law, are attracted to practical finance because they think they can use a system to beat the market, or even create an entirely new one. As seen later, their financial innovations often amount to creating new forms of credit, which like Law's scheme boost the money supply, at least for a while. In place of paper money, they invent credit default swaps or collateralized debt obligations. (“Make your very own ‘credit default swap’ and find out how to create money out of thin air!” as guides in a bus tour around the City of London now shout.9) They see the markets, with their rhythms and patterns, as a kind of music, which they can shape and control – and would agree with former CitiGroup CEO Chuck Prince who famously said, in the midst of the credit crunch, that “As long as the music is playing, you've got to get up and dance.”

      As we will see, it is the tension between these two aspects that drives mathematical finance, in both its inventiveness and creativity, and its tendency toward self-destruction.

The Systems of Nature

      After his losses in the South Sea debacle, Newton famously said: “I can calculate the movement of the stars, but not the madness of men.” While Newton may not have tried to calculate the markets, and preferred chemical alchemy to the financial kind, he probably did more to shape the world of mathematical finance than any other scientist. His law of gravity, coupled with his three laws of motion, provided an archetype for a successful mathematical model that would influence not just areas such as physics and chemistry, but also social sciences including economics, and serve as an inspiration for quants to the present day.

      One person who appreciated the power of Newton's approach was Adam Smith. He is of course best known for his book The Wealth of Nations,10 which was the first to present economics as an objective, rational science, separate from areas such as ethics and political science. Some insight into his motivations is provided, however, by an earlier work on astronomy, written around 1758 but not published until after his death, in which his examination of “all the different systems of nature” culminates in a celebration of “The superior genius and sagacity of Sir Isaac Newton.” He was less impressed by John Law. As he wrote in The

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