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

“Louis Bachelier. It didn’t ring any bells”: Samuelson told the story of his re-
discovery of Bachelier’s work in numerous places, including his preface to davis and 
etheridge (2006) and in Samuelson (2000). In this latter reference, Samuelson suggests 
that he might have heard of Bachelier at least once before Savage’s postcard arrived. note 
that although the version of the story I tell here, in which Bachelier was forgotten until 
Savage happened upon his 1914 textbook, is the standard one, there are some who have 
argued that Bachelier was never really as obscure, even in the english-speaking world, 
as this standard story suggests. See Jovanovic (2000).
3
“. . . a textbook from 1914 . . .”: Savage had found Bachelier (1914).
4 “That distinction goes to the Italian . . .”: Much of what is known about car-
dano comes from his own autobiography, cardano (1929 [1576]). Several other biog-
raphies have been written, including Morley (1854), ore (1953), and Siraisi (1997), that 
seek to put his work (both in mathematics and in medicine) in context. for more on the 
history of probability generally, see Bernstein (1998), Hacking (1975, 1990), david (1962), 
Stigler (1986), and Hald (2003).
4
“Cardano wrote a book . . .”: the “book” I have in mind is much of what later 
became the posthumous Liber de ludo aleæ (cardano 1961 [1565]).
5 “. . . a French writer who went by . . .”: for more on de Méré, Pascal, and 
fermat, see devlin (2008), in addition to the works cited above on the history of prob-
ability.
7 “. . . a deep philosophical question at stake”: for sophisticated but readable 
overviews of the philosophical difficulties associated with interpreting probability the-
ory, see Hájek (2012), Skyrms (1999), or Hacking (1990).
8 “This result is known as the law of large numbers”: for more on the law of large 
numbers, see casella and Berger (2002) and Billingsley (1995). See also Bachelier (1937).
9 “Poincaré was an ideal person to mentor Bachelier”: for more on Poincaré, see 
Mahwin (2005) or Galison (2003), as well as references therein.
11 “. . . even he was forced to conclude . . .”: Poincaré’s report on Bachelier’s thesis 
can be found in courtault and Kabanov (2002), and in translated form in davis and 
etheridge (2006).
12 “. . . according to the Roman poet Titus Lucretius . . .”: See Lucretius (2008 
[60b.c.], p. 25).
12
“These experiments were enough . . .”: the history of the “atomic theory” and 
its detractors through the beginning of the twentieth century is fascinating and plays an 
important role in present debates concerning how mathematical and physical theories 
can be understood to represent the unobservable world. for instance, see Maddy (1997, 
2001, 2007), chalmers (2009, 2011), and van fraassen (2009). Although discussing such 
debates is far from the scope of this book, I should note that the arguments offered here 
for how one should think of the status of mathematical models in finance are closely 
connected to more general discussions concerning the status of mathematical or physi-
cal theories quite generally.

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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
12
“. . . named after Scottish botanist Robert Brown . . .”: Brown’s observations 
were published as Brown (1828).
12
“The mathematical treatment of Brownian motion . . .”: More generally, Brown-
ian motion is an example of a random or “stochastic” process. for an overview of the 
mathematics of stochastic processes, see Karlin and taylor (1975, 1981).
12
“. . . it was his 1905 paper that caught Perrin’s eye”: einstein published four 
papers in 1905. one of them was the one I refer to here (einstein 1905b), but the other 
three were equally remarkable. In einstein (1905a), he first suggests that light comes in 
discrete packets, now called quanta or photons; in einstein (1905c), he introduces his 
special theory of relativity; and in einstein (1905d), he proposes the famous equation e