8 1. A Baker’s Dozen

convinced that he had not actually invented the binary system but

merely discovered it. Hugely impressed by the binary system, he

thought that with its help he could convert the Chinese—who already

possessed the binary symbols Yin and Yang—to Catholicism.

The Pythagorean world view once again came into its own in

1869, when Dmitri Ivanovich Mendeleev presented his suggestion of a

periodic table of chemical elements, arranged in order of their atomic

mass. With wise foresight, Mendeleev left some spaces in his table

empty for elements that were as yet undiscovered although very little

hinted, at the time, that further chemical elements existed. In the gap

between the elements zinc with the atomic mass of 30, and arsenic

with the atomic mass of 33—both known since antiquity—there just

had to exist elements with the atomic masses of 31 and 32. Mendeleev

remained firmly convinced that these empty spots would be filled

at some time. Only a few years later, he was proved correct when

gallium and germanium were discovered and their masses matched

his predictions.

Around the same time, in 1885, a Swiss school teacher by the

name Johann Jakob Balmer was fascinated by the Kabbalah. Just

by studying numerology he discovered a simple formula for the wave-

lengths of the spectral lines of hydrogen. It was left to Niels Bohr,

thirty years later, to properly explain the causes for this phenomenon

by means of quantum mechanics.

Carl Friedrich Gauss, the leading mathematical light of the late

eighteenth and early nineteenth century, the Prince of Mathematics

as he was later called, had been fascinated by numbers since his early

childhood. Many anecdotes are known about the mathematical abil-

ities of the young Gauss. He was able to do calculations well before

he could even talk. As a three-year old, he corrected an error in his

father’s wage calculations and, at the age of eight he astonished his

teacher by instantly solving a busy-work problem: to find the sum

of the first 100 integers. As an adult he, of course, did much more

serious work. With his masterful book Disquisitiones Arithmeticae,

published in 1798, he single-handedly brought the study of number

theory, then called higher arithmetic, to new heights. His famous

prime number theorem, which would remain unpublished for many