MicroscopyPioneers
Pioneers in Optics: Pierre de Fermat
and Sir George Biddell Airy
Michael W. Davidson
National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32306
davidson@magnet.fsu.edu
Pierre de Fermat
ideas of diff erential calculus in a paper entitled the “Method for
(1601-1665)
Determining Maxima and Minima and Tangents to Curved
Pierre de Fermat was a lawyer by occupation but possessed
Lines.”
one of the greatest mathematical minds of the seventeenth
Th ough brilliant, Fermat was oft en at odds with other
century. He made major contributions to geometric optics,
mathematicians, most notably René Descartes. Th e two almost
modern number theory, probability theory, analytic geometry,
simultaneously developed the principles of analytical geometry,
and is generally considered the father of diff erential calculus.
and a dispute of priority ensued. Th ough Fermat prevailed,
Th ough there is some doubt as to the date of his birth, Fermat
many members of the Paris group remained disgruntled
was baptized on August 20, 1601 in Beaumont-de-Lomagne,
because of his partial submittal of work and his competitive
France. His father was
approach. From his reluctance to publish, Fermat would suff er
a successful merchant,
similar criticism throughout his life and never achieved the
and his mother hailed
notoriety he deserved. His work, primarily circulated in letter
from a well-to-do family.
and manuscript format, oft en did not fully reveal his methods
Fermat most likely
and proofs.
received his primary
Fermat also diff ered from Descartes in his views on optics.
education from a local
In 1637 Descartes published “Dioptrics” as an appendix to his
Franciscan monastery
Discourse on Method. Within the work he examined the law of
and later studied at the
refraction, claiming that light travels faster in the denser of the
University of Toulouse.
two mediums involved. Many years later, Fermat noticed that
Fermat moved to
the claim was contradictory to the Aristotelian notion that in
Bordeaux, France for a
nature, the shortest path is always taken. Th us, with this idea
few years in the 1620s,
in mind and through the use of his method for determining
where he undertook
minima and maxima, Fermat established in 1658 what is
an informal study
usually described as “the principle of least time.” According
of mathematics but
to the tenet, a beam of light traveling between two points
ultimately settled on
will follow the path that takes the shortest amount of time to
law as a profession, receiving his Bachelor’s degree in Civil
complete. From the principle of least time, the law of refraction
Law from the University of Orleans. In 1631 Fermat formally
and the law of refl ection could be deduced. Future scientists,
entered the legal profession, serving in the local Parliament at
however, demonstrated that Fermat’s principle was incomplete
Toulouse. Th at same year he married his fourth cousin, Louise
or only partially true. In reality, a beam of light may also follow
de Long, with whom he would have fi ve children. Over time,
a trajectory of maximum duration.
Fermat gradually attained legal positions with increasing
Fermat’s health suff ered greatly in his later years due to a
responsibility and prestige, becoming a member of the criminal
bout with the plague in 1651. He cut off correspondence with
court in 1638 and a king’s councilor in 1648, a post he retained
other members of the scientifi c community periodically, though
for the rest of his life.
he carried on his own studies. By 1662, his mathematical
In addition to his professional duties, Fermat carried on an
communications ended altogether and he died on January
extensive correspondence with a number of prominent Parisian
12, 1665. Subsequently, Fermat’s eldest son, Clement-
mathematicians, sometimes proposing analytical problems
Samuel, assembled what he could fi nd of his father’s work for
to them that he had already solved. Some of his earliest
publication. In the margin of a Latin translation of Diophantus
work examined the experiments of Galileo and the paths of
of Alexandria’s Arithmetic, Clement-Samuel found what is
freefalling objects. During his eff orts to disprove several of the known as Fermat’s last theorem, which would also serve as the
postulates made by Galileo, Fermat developed a new method great mathematician’s fi nal challenge to other mathematicians.
of quadrature for curves. Th en, when attempting to explain his A brief note explained that he had discovered a remarkable
techniques to his correspondents, he laid down the fundamental proof of the complex theorem that was too long to fi t into the
52 doi: 10.1017/S1551929509000388
www.microscopy-today.com • 2009 September
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