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

Primordial Seeds 
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tuitions from finance to drive the development of new mathematics, 
was abhorrent and terrifying.
Poincaré’s influence was enough to shepherd Bachelier through 
his thesis defense, but even he was forced to conclude that Bachelier’s 
essay fell too far from the mainstream of french mathematics to be 
awarded the highest distinction. Bachelier’s dissertation received a 
grade of honorable, and not the better très honorable. the commit-
tee’s report, written by Poincaré, reflected Poincaré’s deep appreciation 
of Bachelier’s work, both for the new mathematics and for its deep 
insights into the workings of financial markets. But it was impossible 
to grant the highest grade to a mathematics dissertation that, by the 
standards of the day, was not on a topic in mathematics. And with-
out a grade of très honorable on his dissertation, Bachelier’s prospects 
as a professional mathematician vanished. With Poincaré’s continued 
support, Bachelier remained in Paris. He received a handful of small 
grants from the University of Paris and from independent foundations 
to pay for his modest lifestyle. Beginning in 1909, he was permitted to 
lecture at the University of Paris, but without drawing a salary.
the cruelest reversal of all came in 1914. early that year, the council 
of the University of Paris authorized the dean of the faculty of Science 
to create a permanent position for Bachelier. At long last, the career he 
had always dreamed of was within reach. But before the position could 
be finalized, fate threw Bachelier back down. In August of that year, 
Germany marched through Belgium and invaded france. In response, 
france mobilized for war. on the ninth of September, the forty-four-
year-old mathematician who had revolutionized finance without any-
one noticing was drafted into the french army.
Imagine the sun shining through a window in a dusty attic. If you 
focus your eyes in the right way, you can see minute dust particles 
dancing in the column of light. they seem suspended in the air. If you 
watch carefully, you can see them occasionally twitching and changing 
directions, drifting upward as often as down. If you were able to look 
closely enough, with a microscope, say, you would be able to see that 
the particles were constantly jittering. this seemingly random mo-
tion, according to the roman poet titus Lucretius (writing in about 

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60 b.c.), shows that there must be tiny, invisible particles—he called 
them “primordial bits” — buffeting the specks of dust from all direc-
tions and pushing them first in one direction and then another.
two thousand years later, Albert einstein made a similar argument 
in favor of the existence of atoms. only he did Lucretius one better: he 
developed a mathematical framework that allowed him to precisely 
describe the trajectories a particle would take if its twitches and jit-
ters were really caused by collisions with still-smaller particles. over 
the course of the next six years, french physicist Jean-Baptiste Perrin 
developed an experimental method to track particles suspended in a 
fluid with enough precision to show that they indeed followed paths 
of the sort einstein predicted. these experiments were enough to per-
suade the remaining skeptics that atoms did indeed exist. Lucretius’s 
contribution, meanwhile, went largely unappreciated.
the kind of paths that einstein was interested in are examples of 
Brownian motion, named after Scottish botanist robert Brown, who 
noted the random movement of pollen grains suspended in water in 
1826. the mathematical treatment of Brownian motion is often called 
a random walk — or sometimes, more evocatively, a drunkard’s walk. 
Imagine a man coming out of a bar in cancun, an open bottle of sun-
screen dribbling from his back pocket. He walks forward for a few 
steps, and then there’s a good chance that he will stumble in one di-
rection or another. He steadies himself, takes another step, and then 
stumbles once again. the direction in which the man stumbles is basi-
cally random, at least insofar as it has nothing to do with his purported 
destination. If the man stumbles often enough, the path traced by the 
sunscreen dripping on the ground as he weaves his way back to his 
hotel (or just as likely in another direction entirely) will look like the 
path of a dust particle floating in the sunlight.
In the physics and chemistry communities, einstein gets all the 
credit for explaining Brownian motion mathematically, because it was 
his 1905 paper that caught Perrin’s eye. But in fact, einstein was five 
years too late. Bachelier had already described the mathematics of ran-
dom walks in 1900, in his dissertation. Unlike einstein, Bachelier had 
little interest in the random motion of dust particles as they bumped 
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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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