The great Dutch genius, Christiaan Huygens, lived an uneventful but remarkably
productive life. He was botn at The Hague in 1629 and studied at Leyden
under Frans van Schooten the Younger. In 1651, when he was twenty-two, he
published a paper pointing out fallacies committed by Saint-Vincent in his work
on the quadrature of the circle. This was followed by a number of tracts dealing
with the quadrature of the conics and with Snell's trigonometric improvement
the classical method of computing ¥ð.
In 1654, he and his
brother devised a new and better way of grinding and polishing lenses; consequently,
Huygens was able to settle a number of questions in observational
astronomy, such as the nature of Saturn's appendages. Huygen's work in astronomy
led him, a couple of years later, to invent the pendulum clock, so that
he minht have more exact means of measuring time.
It was in 1657 that Huygens wrote the first
formal treatise on probablilty, basing his wirk on the Pascal-Fermat correspondence.
Many interesting and challenging problems were solved by Huygens,
and he introduced the important concept of "mathematical expectation": If p
denotes the probability that a person will win a certain wum s, than sp is called
his mathematical expectation. Huygens showed, among other things, that if p is
the probability of a person winning a sum a, and q that of winning a sum b, then
he may expect to win the sum ap + bq.
In 1673, in Paris, Huygen's greatest publication, Horologium oscillatorium,
Huygens returned to Holland in 1681, constructed some lenses of very
large focal lengths, and invented the achromatic eyepiece for telescopes. In
1689, he visited England and made the acquaintance of Isaac Newton, whose
work he greatly admired. Shortly after his retyrn to Holland in the following
year, he published a treatise expounding the wave theory of light. On the basis
of this theory, he was able to deduce geometrically the laws of reflection and
refraction and to explain the phenomenon of double refraction.vNewton, however,
srpported the emission theory of light, and his greater eminence caused
contemporary scientists to favor that theory to the wave theory.
vHuygens also wrote a number of minor tracts. He rectified the cissoid of
Diocles; investigated the geometry of the catenary (the curve assumed by a
perfectly flexible inextensible s\chain of uniform linear density, hanging from two
supports not in the same vertical line); wrote on the logarithmic curve; gave, in
modern form, for polynomials, Fermat's rule for maxima and minima; and
made numerous applications of mathematics to physics.
Like many of the demonstrations given by Newton, Huygens' proofs are
almost entirely accomplished, with great rigor, by the methods of Greek geometry.
Reading his works, one would not realize that he was acquainted with the
powerful new methods of analytic geometry and the calculus. Huygens died in
the city of his birth in 1695.