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.
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