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\begin{document}
\title{Some Mathematicians Like it Hot: Fourier and Descartes}%
\author{Daniel Mathews}%
\maketitle
Those of us who study mathematics are all accustomed to bandying
about mathematicians' names. We throw them around all the time
when we do mathematics, quoting their theorems, using their
methods, retracing their thoughts, imagining their genius, but
most often scratching our heads. Their mathematics is often more
than enough for anybody's brain to handle. Some mathematicians'
names are enough to make your head spin; others are enough to make
you want to scream!
Rarely, however, do we get a glimpse into the lives of great
mathematicians. Rarer still is a glimpse into the quirks and
idiosyncrasies that a life in mathematics almost invariably
produces! For every great mathematician there is a story:
sometimes heroic, sometimes controversial, sometimes romantic,
sometimes tragic. Behind most there is at least one story of gross
ineptitude.
The stories of Fourier and Descartes' demises are in a class of
their own --- flowing from gross miscalculations of elementary
properties of the temperature scale!
Jean Baptiste Fourier (1768--1830) is certainly counted amongst
the greatest mathematicians and scientists of all time. Anybody
who has studied applied mathematics will have heard of Fourier
series. Many of his discoveries came as a result of his
investigations into what is today called thermodynamics --- the
nature of heat. In his work he developed the notion of the Fourier
series, an infinite trigonometric series approximating any
periodic function. Incidentally, what is today called Fourier's
theorem, while stated by Fourier himself, was not proved properly
until 150 years later, and indeed his writings were riddled with
mistakes and inaccuracies. Nevertheless, his theorem broke new
ground in areas where other great mathematicians like Euler,
Daniel Bernoulli and Lagrange had not, and won him the Grand Prize
of the French Academy of Sciences. But it was his work as a
physicist --- in particular, his fascination with heat --- which
took his predilections in an unexpected direction. He liked it
hot!
Ren$\acute{\mbox{e}}$ Descartes (1596--1650) is, of course, a
household name in mathematics and philosophy. He signed his name
Renatus Cartesius to his works (which were in Latin), hence the
origin of the term `Cartesian' to describe his thoughts. It's
difficult now to believe that there was actually someone who
invented the Cartesian coordinate system, and the whole idea of
representing geometric points by co-ordinates. But there was a
time when these things were not invented, and before which nobody
had used them, and nobody had even thought of them --- and that
time was not so long ago in historical terms. Before that all of
geometry was in the vein of the ancient Greeks. His philosophy is
also, of course, foundational to much Western thinking.
Returning to the thermophile Fourier, he served as a soldier in
the French Revolution and under Napoleon, and accompanied Napoleon
to Egypt in 1798. There, so the story goes, he suffered a disease
of the thyroid which heat helped to relieve. And so Fourier
developed a belief in the healing power of heat --- the more heat,
the better! Not only did this spur on his work in thermodynamics,
it also gave him a much hotter lifestyle!
Fourier took to wearing layer upon layer of clothes, no matter
what the weather. He stoked up the fireplace and cranked the
heating to ever hotter temperatures. His house was unbearable for
guests to visit. Even if Fourier did find it uncomfortable, he
bathed gladly in the heat, believing it could only do him good. He
became ever more wary of leaving his house, where much more
moderate but `unhealthy' low temperatures prevailed.
But it did not do him so much good. He cooked his own goose. The
extreme heat exacerbated his heart condition and undoubtedly
accelerated his demise.
Descartes also liked it hot, though perhaps not as hot as Fourier.
He was happy enough to be snuggled under the sheets of his bed.
Indeed, bed was where he spent a lot of his time. He was part of a
wealthy family, and lived a pampered lifestyle. And despite his
incredible mind, it was trapped in a very frail body (a very
Cartesian distinction!). The story goes that his greatest
discoveries --- including, of course, the Cartesian coordinate
axes --- came to him while in bed. (Have you ever heard a better
reason to sleep through your next 9am lecture?) His family let him
sleep in as long as he liked, and his career as a gentleman
officer in the Dutch and Bavarian armies also allowed him no
shortage of rest!
Unlike Fourier, if Descartes had stayed warm, he probably would
have been fine. But if you thought nothing could tempt Descartes
out of bed, you thought wrong. Queen Christina of Sweden invited
Descartes to become her personal live-in philosophy tutor.
Descartes was offered a position in her court --- a life amongst
royalty. After some consternation, Descartes finally accepted.
Descartes had two problems.
The first problem was (and still is) that Sweden was not a very
warm place. It certainly wasn't the sort of place conducive to the
longevity of people as fragile as Ren$\acute{\mbox{e}}$ Descartes.
However, you can suppose that Descartes could have spent plenty of
time in bed and wouldn't have caught too much of a chill. Indeed,
for some time he did precisely that, as Queen Christina remained
engrossed in the frivolities of the court.
This, however, did not last for long. Problem number two was Queen
Christina of Sweden, once she regained a taste for philosophy: a
young, healthy, energetic and demanding woman with little
consideration for the frailty of her genius guest or his
proclivity for extreme somnolence. And she was a morning person.
(Not a mathematician, obviously.)
The disruption to Descartes' usually rather light morning schedule
was terminal. The queen woke him three mornings a week at 5 am,
which would be painful enough for a fit and healthy person, but
was devastating for one like Descartes. No amount of coffee could
save him; the extreme cold and early mornings ruined his health.
He contracted pneumonia and was dead within months.
The moral of the story? Beware of those cold early morning starts
- they can kill you!
\end{document}