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The Ancient world saw many advances (or were they discoveries?) in the
field of mathematics, the major contributor was Greece, or to be more
precise Greek mathematicians spread around the Mediterranean.
The real start to the story of mathematics would be much to hard to
pinpoint, so I think a good place to start would be with Thales in the late 7th century BC. Although
Thales only made a few contributions to what could be called pure
mathematics, he was more concerned with practical applications of what he
had learned.
Everyone knows of Pythagoras and his triangle theorem, and since this is
supposed to be an informative page I'll avoid regurgitating that
information again. I'll just mention that he made his appearance
in about 572 BC and founded a mathematical brotherhood named the
Pythagoreans who continued his work long after he died.
From 500 BC to around 300 BC advances were made by the Athenian
mathematicians Anaxagoras, Democrates and Hippocrates. Anaxagoras
was known for his objections to the Zenoist school of thought,
Democrates for his studies with Conics and Cylinders
and Hippocrates for being a Pythagorean and working out the Quadrature of
various Lunes, he also wrote a precursor to Euclid's Elements.
Various great minds came onto the scene in this ensuing Golden Age, such
people as Plato, Aristotle, Euclid and Archimedes
wandered the academic landscape beginning to sculpt it into what we know
today. At this time Eratosthenes roughly
calculated the circumference of the Earth and the distance to the moon
and Eudoxus worked with areas and volumes,
eventually coming up with the Method of Exhaustion.
The collapse of Rome and the general chaos that followed has no great advancements in the mathematical community in it. The Dark ages and then the Middle Ages were upon the land and civilisation let alone the science of mathematics was having trouble surviving the times. Repelling the barbarian hordes from northern Europe was taking up all the energy and time of the civilised world. A few methods for restoring civilisation were tried by the Catholic Church and Byzantium, these helped the learning in general and hence gave mathematics a basis in education. To read further on this meagre boon to the sciences have a look at my Medieval Mathematics Essay.
The period after the Late Middle Ages saw the rise of maths again as a
science worth a second glance and many educated men throughout Europe
took up the challenge of relearning the "Wisdom of the Ancients".
In about 1614 Baron John Napier of Scotland
published his book on Logarithms, this caused a stir in the scienctific
world for it reduced the amount of sheer number-crunching that a
mathematician or statistician needed to do in a day's work.
Later in 1637 René Descartes
wrote a discourse on mathematical methods which contained many rules,
laws and facts used today in what is knows as Physics.
A mechanistic view of nature was adopted by many scientists, but this
openly opposed the Church's views and was therefore unpopular with the
general populace. It was also difficult for these mostly Aetheistic
scientists to explain how the world came about using their knowledge of
how the world worked. There were also the Deistic scientists who took the
view that although God was responsible for creation the world now ran in
it's own 'fashion'.
When the Napoleonic Wars started around 1790 there was a mighty upheaval
as the armies of France went to great lengths to destroy the power of the
Church in France and Europe in general. In 1815 the Battle of Waterloo
saw the start of a new era, Aetheists and Republicans became very
unpopular and many of their discoveries in mathematics had no audience.
At about this time a Frenchman named Evariste
Galois was active within the scientific community, his contributions
to group theory laid a solid basis for todays algebra.
These prejudices against Aethiests and Republicans ended around the time
of Darwin, Faraday and Lyell in 1850.
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