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prime number theorem, which would remain unpublished for many
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