FOURIER, J.(1768-1830) and POINSSON, S.D.(1781-1840)

    Fourier was vborn in Auxerre in 1768 and died in Paris in 1830.  The son of a tailor, he was orphaned at the age of eight and educated in a military school conducted by the Bendictines, where he was given a lectureship in mathematics.   He assisted in the promotion of the Frnch Revolution and was rewarded by a chair at the Ecole Polytechnique.  He resigned from this position so that he, along with Monge, could accompany Napoleon on the Egyptuab expedition.   In

1798, he was appointedgovernor of Lower Ehypt.  Fourier returned to france victories and the capitulation of the French in 1801, Fourier returned to France and was made prefect of Grenoble.  It was while at Grenoble the he started his experiments on heat.     In 1807, Fourier presented a paper before the French Academy of Sciences that initiated a new and highly fruitful chapter in the history of mathematics.   The paper dealt with the practical problem of the flow of heat in metallic rods, plates, and solid bodies.  In the course of the presentation of the paper, Fourier made the startling claim that any function, defined in a finite closed interval by an arbitrarily drawn graph, can be resolved into a sum of sine and cosine functions.  To be more explicit, he claimed that any function whatever, no n\matter how capriciously it is defined in the interval (-¥ð,¥ð), can be represented in that interval by where the a's and the b's are suitable real numbers.  Such a series is known as a trigonometric series, and was not new to the mathematicians of the time.  Indeed, a number of more ofr less well behaved functions had been shown to be representable by such a series.  But Fourier claimed that any function defined in (-¥ð,¥ð) can be so represented.  The savants at the Academy were very skeptical of Fourier's claim, and the paper, which was judged by Lagrange, Laplace, and Legendre, was rejedted.  However, to encourage Fourier to develop his ideas more carefully, the French Academy made the problem of heat propagation the subject of a grand prize to be awarded in 1812.  Fourier submitted a revised paper in 1811, which was judged by a group containing, among others, the former three judges, and the paper won the prize, though it was criticized for lack of rigor and so was not recommended for publication in the Acakemy's Memoies.
    An amusing story is tild about Fourier and his interest in heat.  It seems that from his experience in Egypt, and maybe his work on heat, he became convinced that desert heat is the ideal condition for good health.  He accordingly clothed himself in many layers of garments and lived in rooms of unbearably high temperature.  It has been said by some that this obsession with heat hastened his death, by heart disease, so that he died, thoroughly cooked, in his sixty-third year.
    Perhaps fourier's most quoted sentende (it appeared in his early work on the mathematical theory of heat) is: "The deep study of nature is the nost fruitful source of mathematical discovery."

    Poisson was born in Pithiviers in 1781 and died in Paris in 1840.  He was educated by his father, a private soldier who on retirement received a small administrative post in his village and, when the French Revolution broke out, assumed the governing of the place.  Relatives wished to press the young Poisson, much against his own wishes, onto medicine. The education was undertaken by an uncle, who started the boy off with pricking veins in cabbage leaves with

a lancet.   When he had perfected himself in this, he was graduated to puting on blisters.  But in almost the first case in which he did this by himself, his patient died sithin a few hours.  Although the docters assured hom that "The event was a very common one," he vowed to have nothing more to do with the profession.
    Strong mathematical interests led Poisson in 1798 to enter the Ecole Polytechnique to study the subject, where his abilities impressed Lagrange and Laplace.  Upon graduation, he was made a lecturer at the Ecole Polytechnique.
    The rest of his life was spent in various government posts and professorships.   Somewhat of a socialist, he remained a staunch republican until 1815, when he joined the legitimists.
    Poisson's mathematical publications were numerous, numbering between 300 and 400.  His chief treatises are his two-volume Traite de mecanique, published in 1811 and 1833, his Theorie nouvelle de l'action capillaire of 1831, his Theorie mathematique de la chaleur of 1835, and his Recherches sur la probablilte des jugements of 1837.
    A droll story links Poisson to one of his professional interests.  When a boy, he was put in the care of a nurse.  One day, when his father came to see him, the nurse had none out and ldrt the youngster suspended by his srtaps to a nali in the wall-to protect the boy, the nurse said, from the disease and dirt of the floor.  Pilsson said that his gymnstic efforts when thus suspended caused him to swing back and forth, and it was in this way that he early became familiar with the pendulum, the study of which occupied much of his later life.
    Poisson once remarked: "Life in good for only two thing, discovering mathematics and teaching mathematics."  He excelled in both pursuits.