LAPLACE, P.S.(1749-1827) and LEGENDRE, A.M.(1752-1833)

    Pierre-Simon Laplace was born of poor parents in 1749.  His mathematical ability early won him good teaching posts;as a political opportunist, he ingratiated himself with whichever party happened to be in power during the uncertain days of the French Revolution.  His most outstanding work was done in the fields of celestial mechanics, probavility, differential equations, and geodesy.  He published two monumental works, Traite de mecanique celeste (five volumes, 1799-1825) and Theorie analytique des probabilites (1812), each of which was preceded by an extensive nontechnical exposition.

    The five-volume Traite de mecanique celeste, which earned him the title of "the Newton of France," embraced all previous discoveries in this field along with Laplace's own contributions, and marked the author as the unrivaled master in the subject.  it may be of interest to repeat a couple of anecdotes often told in connection with this word.  When Mapoleon teasingly remarked that God was not mentioned in his treatise, Laplace replied, "sire, I did not need that hypothesis." The American astronomer, Nathaniel Bowditch, when he translated Laplace's treatise into English, remarked, "I never come across on of Laplace's 'Thus it plainly appears' whithout feeling sure that I have hours of hard work before me to fill up the chasm and find out and show how it plainly appears. "Laplace's name is connected with the nebular hypothesis of cosmeogony and with the so-called Laplace equation of potential theory (though neither of these contributions orighinated with Laplace), with the so-called Laplace transfor that later became the key to the operational calculus of Heaviside, and with the Laplace expansion of a determinant.  Laplace died in 1827, exactly one hundred years after the death of Isaac Newton.  According to one report, his last words were :"What we know is slight;what we don't know is immense. "
    The following story about Laplace is of interest and offers a valuable suggestion to one applying for a position.  When Laplace arrived as a young man in paris seeking a professorship of mathematics.  he submitted his recommendations by prominent people to d'Alembert, but he was not received.  Returning to his lodgings, Laplace wrote d'Alembert a brilliant letter on the general principles of mechanics.  This opened the door.  and d'Alembert replied: "Sir, you notice that I paid little attention to your recommendations.  You don't need any; you have introduced yourself better. " A few days later, Laplace was appointed professor of mathematics at the Military School of Paris. 
    Lagrange and Laplace have often beem contrasted with one another.  First of all, there is a marked contrast in their styles, summed up as follows by W.W.Rouse Ball."Lagrange is perfect both in form and amtter, he is carefeu to explain his procedure, and though his arguments are general they are easy to follow.  Laplace on the other hand explains nothing is indifferent to style, and if satisfied that his results are correct, is content to leave them either with no proof or with a faulty on. "There is also a marked contrast in the viewpoints of mathematics held by the tow men.  For laplace, mathematics was merely a kit of tools used to explain nature.  To Lagrange, mathemaics was a sublime art and was its own exuse for being.

  Adrien-Marie Legendre(1752-1833) is known in the history of elementary methematics principally for his very popular Elements de geometrie, in which he attempted a pedagogical improvement of Euclid's Elements by considerably rearranging and simplifying many of the propositions. This work was very favorably received in America and became the prototype of the geometry textbooks in this country. In fact, the first English translation of Legendre's geometry was made in 1819 by John Farrar of Harvard University.

    Legendre's chief work in higher mathematics centered about number theory, elliptic functions, the method of least squares, and integrals; this work is too advanced to be discussed here. He was also an assiduous computer of mathematical tables.   In addition to his Elements de geometrie, which appeared in 1794, legendre published a two-volume 859-page work, Essai sur la theorie des nombres (1797-1798), which, for comprehensiveness and authoritativeness, rivaled the similar work of Euler. In geodesy, Legendre achieved considerable fame for his triangulation of France.