The Physics of Wall Street: a brief History of Predicting the Unpredictable

partment at MIt. the year was 1955, or thereabouts. Laid out in front 
of him was a half-century-old Phd dissertation, written by a french-
man 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. Samu-
elson’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 — mathe-
matics 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 de-
veloped 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 “specula-
tion” — 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.

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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 disser-
tation, 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 renais-
sance man Gerolamo cardano. Born in Milan around the turn of the 
sixteenth century, cardano was the most accomplished physician of 
his day, with popes and kings clamoring for his medical advice. He au-
thored hundreds of essays on topics ranging from medicine to math-
ematics to mysticism. But his real passion was gambling. He gambled 
constantly, on dice, cards, and chess — indeed, in his autobiography he 
admitted to passing years in which he gambled every day. Gambling 
during the Middle Ages and the renaissance was built around a rough 
notion of odds and payoffs, similar to how modern horseraces are 
constructed. If you were a bookie offering someone a bet, you might 
advertise odds in the form of a pair of numbers, such as “10 to 1” or “3 
to 2,” which would reflect how unlikely the thing you were betting on 
was. (odds of 10 to 1 would mean that if you bet 1 dollar, or pound, or 
guilder, and you won, you would receive 10 dollars, pounds, or guil-
ders in winnings, plus your original bet; if you lost, you would lose the 
dollar, etc.) But these numbers were based largely on a bookie’s gut 
feeling about how the bet would turn out. cardano believed there was 
a more rigorous way to understand betting, at least for some simple 
games. In the spirit of his times, he wanted to bring modern math-
ematics to bear on his favorite subject.
In 1526, while still in his twenties, cardano wrote a book that out-
lined the first attempts at a systematic theory of probability. He focused 
on games involving dice. His basic insight was that, if one assumed a 
die was just as likely to land with one face showing as another, one 
could work out the precise likelihoods of all sorts of combinations oc-
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t h e p h y s i c s o f wa l l s t r e e t

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