John Napier (NAY-peer) was a Scottish Baron, thus he could afford to pursue
the unprofitable career of a mathematician. He is responsible for the
development of Logarithms. Napier laboured for twenty years on his
theories and in 1614 published them in a book Mirifici Logarithmorum
canonis descriptio or A Description of the Wonderful Law of
Logarithms. The discovery was enthusiastically adopted by
mathematicians throughout Europe as a method for shortening the labours
of the astronomer thereby doubling his life (free time).
Logorithms make mathematical operations simpler by converting the more
complex multiplication and division processes into the simpler addition
and subtraction processes.
René Decartes (REN-ay DAY-cart) was born in 1596 in France, in
1617 he joined
the Dutch Army and upon his discharge moved to Holland to study.
Just before his death in 1650 Decartes was studying in Sweden,
in about 1637 he wrote a Discourse on mathematical methods which
contained the first publishing of Snell's Law of Refraction and the
rainbow effect.
Galois (gull-WAH) was born in France in 1811, he was educated at his home
until he was 12 years old when he entered a boarding school, the
Louis-le-Grand. Galois twice tried to enter the leading
French school for mathematicians, the École Polytechnique,
but was rejected both times. He submitted three papers to the Academy
of Sciences, these were either lost or so incomprehensible that they
were rejected.
Next Galois turned to political activism and was arrested and imprisoned
for his outspoken rebublican convictions. Shortly before his dead in 1832
he jotted down some of his algebraic theories, these manuscripts were
later found and published in 1846 and 1870. It was only after these
printings that Galois was recognised for his mathematical genius and
became widely recognised within the mathematical community.
Today some of his constructs such as the Galois Group, Galois Field and
Galois Theory are fundamental concepts within modern algebra.
Galois proved that it is impossible to solve algebraically the general
equation of degree greater than four (Abel also proved this at about the
same time independently of Galois) using Group Theory. He established the
following theorem :
An algebraic equation is algebraically solvable if and only if its group is solvable.