10 1. A Baker’s Dozen

Most of his colleagues smiled at the abstruse numbers game played

by the aging scientist.

One who did not smile was Eddington’s compatriot and fellow

scientist, the physicist and Nobel Prize winner Paul Dirac. Quite en-

amored by the beauty of mathematics, he justified the Pythagorean

world view with the claim that if there is a choice between two

theories—one ugly, the other beautiful—the beautiful one would al-

ways win out, even if the ugly one fits the experimental data better.

While Dirac thus threw the scientific method overboard, his quest to

express nature in beautiful equations would nevertheless prove very

useful. Seeking esthetically pleasing formulations, he came across an

equation that neatly combined the theory of relativity with quantum

mechanics. Unfortunately, the equation had two separate solutions,

one of which seemed to be quite meaningless at first glance. But

it was too beautiful for Dirac to just let go. His persistence paid

off. The nonsensical, but beautiful solution was the first indication

of the existence of anti-matter. “God used beautiful mathematics in

creating the world,” he stated with reverence. Meanwhile, Einstein

thought he could detect human traits in God’s universe which led him

to conclude that “God is subtle, but malicious he is not.”

Beauty in mathematics was also of high importance to the philoso-

pher and Nobel laureate in literature Bertrand Russell. “Mathemat-

ics, rightly viewed, possesses not only truth, but supreme beauty—

a beauty cold and austere, like that of sculpture,” he wrote. G. H.

Hardy, the Cambridge number theorist, resolutely claimed that

“Beauty is the first test; there is no permanent place in the world for

ugly mathematics.” With this as standard, the most sublime expres-

sion of esthetics in mathematics must surely lie in the extraordinary

formula which the Swiss mathematician Leonhard Euler proved in

1748:

−eiπ

+ 1 = 0. In a sequence of symbols it links five fundamen-

tal mathematical constants through addition, subtraction, multiplica-

tion, and potentiation—namely, e, the base of the natural logarithms,

i, the square root of −1, π, the ratio of the circumference of a circle

to its diameter, 1, and 0—into one slim formula.