In every piece there is a number -- maybe several numbers, but if
so there is also a base-number, and that is the true one. That is
something that affects us all, and links us all together.

ARVO PÄRT (composer) ¹

Number and pattern have always held a fascination, and the
true origins of mathematics and astronomy are certainly
ancient. The earliest form of organised mathematics, in
which numbers were meaningfully manipulated and patterns
recorded, is credited to the Babylonians of around 4000 BC, who
recorded star patterns and named constellations. They had also
developed a surprisingly advanced set of mathematical rules, includ-
ing a sophisticated method of counting -- a skill employed by the
record-keeper, the farmer and the architect. It is thought that the
last of these professions may also have employed simple forms of
algebra and geometry.

Modern research, such as John North's work on ancient stone
circles, has demonstrated that the ancient Britons must also have
possessed some knowledge of geometry in order to build such struc-
tures as Stonehenge, started about 3500 BC, ² and the ancient Egyp-
tians had highly developed mathematical and engineering skills which
they employed in the building of the Great Pyramid at Giza some
1,000 years later. In these ancient civilisations, mathematics and
astronomy were blended together intimately and had rich associations
with mysticism and the occult. Astronomy and astrology were viewed
as one and the same, and mathematics gained an almost spiritual
status as a tool for the astrologer/astronomer. It was not until Greek
times that mathematics and, to a lesser extent, astronomy were separ-

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