Mobility through Mathematics

The most pivotal of these turns on Laplace's decision to become a scientist. His first appearance on the scientific stage is in September 1769 as a teacher of elementary mathematics at the Ecole royale militaire in Paris, where for seven years he dispensed his knowledge to teenage sons of impoverished nobles. Since he received neither special praise nor blame in this occupation, one presumes he discharged his duties competently. The lectures he presented on elementary mathematics twenty-five years later at the Ecole normale—the only other teaching stint he accepted in his long career—show a solid command of the main features of mathematics and, in at least one instance, creative abilities as a mathematician probing the foundations of calculus.^[3] But one must not look to Laplace's career for major contributions to the mathematical discipline, or cast him in the role of a rival to his creative contemporaries Lagrange, Legendre, or Gauss. Lecturing on mathematics was a job he initially accepted as a means to escape the provinces where family plans would undoubtedly have taken him in a totally different direction. For Laplace, the move to Paris was a cathartic declaration of independence from his peasant origins and their social implications. Mathematics was the liberating agent that offered him a chance to begin a new life. The experience was also traumatic because mathematics constituted the philosophical antipode of the career his family had chosen for him in theology.

Laplace came from a modest family in Normandy who sent him to a local school from which he was recruited by the University of Caen for the Church. The standard career path for an intelligent youth born in a rural district in the middle of the 18th century led to administration or the clergy. His uncle, who taught him the "three R's," held a sinecure at a nearby parish that left him in a state of secure indolence. Young Pierre Simon could aspire to a similar position after completing his Master's in Theology, which he was awarded only three months before his move to Paris. In his student

days, however, Laplace had already succumbed to the lure of mathematics.

Laplace's teacher of metaphysics and natural philosophy was an unreconstructed Aristotelian who bore the distinctively primitive name of Jean Adam. Judged by the size of his classes, Adam was an enticing popular lecturer who performed divertingly on demonstration equipment he bought from the outlawed Jesuits. But he became a pathetic figure whose exploits were ridiculed in a scathing anonymous play (written by a student) ingeniously entitled Nostradamus .^[4] Whereas contemporaries were arguing about the merits of Newton over Descartes, our abbé Adam was still championing Aristotle. His printed lectures could have been written centuries earlier.^[5] They display the worst features of scholasticism, filled with hairsplitting verbal distinctions, elaborate and useless Latin terminology, and questionable principles. His attempt to modernize his manual with examples from current studies on hydraulics and electricity were so inept that his students found in it cause for mockery. The abbé Adam was also a fierce defender of the faith, particularly those values championed by Jesuits, who had been a dominant force earlier in the century at Caen. Adam took special delight in bringing before the bar of justice a fellow priest and professor at Caen named Christophe Gadbled on the grounds that he had failed in his duties as a teacher and clergyman. In his lectures, Gadbled had criticized Adam for his philosophical ineptness, had raised metaphysical questions about God's omnipotence, and had even ventured to hypothesize about a physical world operating without His immanence. The abbé Gadbled was also accused of offering flimsy excuses for failing to attend Mass, thereby setting an intolerable example for youth.

As an impressionable and curious youth, Laplace naturally took notice of Gadbled. A totally new world opened up to him. His new teacher was thoroughly versed in Newtonian physics. He substituted the succinct language of calculus for the tangled verbiage of Aristotle.

He wove a beautiful tapestry of the system of the world, using mathematical threads of gold that dazzled the youth and challenged his mind. To appreciate the new picture, Laplace quickly absorbed the calculus, probably using the new texts of Euler recommended by Gadbled. There was in the manipulation of mathematics a clarity and sharpness that could not be extracted from Adam's lectures. Gadbled was also in touch with practitioners of modern natural philosophy, incorporating the latest advances in the scientific literature, particularly from the work of Clairaut and d'Alembert. Moreover, Gadbled applied mathematics in a useful fashion to navigation in his lectures on hydrography. As one contemporary document puts it, Gadbled had "made calculation and geometry fashionable in Caen."^[6]

The critical moment in Laplace's conversion probably came when the hapless Adam, not content to squabble with Gadbled, decided to take on d'Alembert as well. The only known copy of his combative pamphlet was destroyed during the D-Day invasion. It may be assumed, however, that it accused the Newtonian coauthor of the Encyclopédie of criminal disrespect for the teachings of the Church and of Aristotle. While Laplace's Adam may have dazzled some of his students, he did not draw as much as a rejoinder from d'Alembert, who was most likely informed about the attack by his correspondent Le Canu, Gadbled's major assistant. It was this same Le Canu who apprised the high priest of the mathematical sciences about a promising twenty-year-old abbé named Laplace, and provided the young man with a letter of introduction. Pierre Simon set off for Paris armed with this letter and an audacious essay criticizing one of d'Alembert's minor writings on the law of inertia. D'Alembert had missed a mathematical point. Laplace's conversion from theology to science was completed when a properly chastened d'Alembert found him a well-paid position in mathematics at the Ecole militaire.

D'Alembert had additional reasons to empathize with Laplace, since he had in his youth experienced a similar transition from theological studies to the sciences. Recruitment into a mathematical occupation for most of the century often involved painful shifts from

parental expectations or initial career paths.^[7] La Caille, for example, renounced a life as a priest once he "discovered" Euclid for himself. Condorcet, Laplace's elder by six years, and tired of his traditional Jesuit education, turned his back on his uncle the bishop of Auxerre and a military life, embracing instead the uncertainties of a mathematical career, supported at first only by a gifted teacher at the Collège de Navarre. Others fortunate to be in Paris—like Coulomb, Legendre, and Lacroix—took to mathematics because of inspiring lecturers, while still others including Borda, Monge, and Carnot were drawn to the subject through military schooling. The individual paths may each have been different, but they all signaled a break from the security of established patterns for bright youths. In Paris especially, mathematics was an exciting and burgeoning activity that captivated many risk-takers.^[8]

As the central feature of Laplace's new life, mathematics came to be quite naturally the symbol of emancipation from the errors of the past and the agent of personal success. In his first three years in Paris, Laplace wrote sixteen original papers on a variety of topics that immediately established him as a leading contributor to the mathematical sciences of his era.^[9] He was twenty-three when he took his seat in the Academy of Sciences on a bench behind d'Alembert, following the same path as his elders Condorcet, Vandermonde, and Cousin.

Once in Paris, Laplace's professional life until the French Revolution was entirely centered on the Academy of Sciences. As an academician, he was called upon to review a host of papers and projects submitted for approval to the learned body. On the average, he sat on over a dozen review committees annually and wrote many of the reports, the texts of which still survive in good numbers. His membership in the Academy's section on mechanics and his mathe-

matical abilities brought him the tedious task of reporting on eccentric projects for the making of mechanical devices to douse fires, to float on water, or to erect perpetual-motion wheels. Most of them were rejected, often with scathing comments that reveal the mathematical illiteracy of the projectors. The task consumed so much time that in 1775 the Academy accepted d'Alembert's proposal to refuse outright to consider papers on squaring the circle, trisecting an angle, or perpetual motion schemes. Several years later, Laplace sought to use elementary mathematics tests to screen out artisan crackpots who did not deserve serious attention, much to the chagrin of amateurs like Marat and Brissot. A mathematics test was already in use by examiners of military and naval schools to rank aspiring officers. In effect, Laplace had already been practicing what he preached for artisans since 1783 in his capacity as entrance examiner of artillery and naval engineering schools.^[10] Next to proof of noble origin, mathematical competence was the only means adopted for separating the wheat from the chaff in the officer corps of the Old Regime. The extension of this practice to artisans seemed natural to Laplace; it also reveals in a pointed way the great importance he attached to this kind of literacy. There was a threshold of learning beneath which one could not be considered as a serious contributor to science.

Equally instructive were his positive reactions as a referee. Laplace was asked to comment on several projects on demography, life insurance schemes, and tables of amortization, all involving mathematical counts and statistics. In these instances, he was either an enthusiastic supporter or found ways to criticize the projects constructively. Laplace was constantly called upon to examine new scientific devices, particularly scales to record numerical data, techniques of interpolation, or other means to improve thermometers, barometers, microscopes, pyrometers, and other apparatus. The reports invariably focused on the improvements the new instruments provided for measuring. He hailed each device leading to more precise and reliable data as a progressive step.

Laplace's voice was heard and respected even before he made a name for himself in this line of work. In 1781 he devised a telescopic pyrometer to assist Lavoisier in experiments on thermal expansion of solids.^[11] A year later, he invented the ice calorimeter, whose sole purpose was to turn qualitative arguments about exothermic reactions into measurable data that could be used to test hypotheses. Lavoisier had enlisted Laplace in his experimental work as a keen critic of instrument-making and as a scientist endowed with a sharp mind trained to uncover errors and to devise methods to turn them. Despite its design limitations, the calorimeter was evidence that they appreciated the critical role instruments must play in a developing science still encumbered with vague principles. We know that later during the Revolution, Laplace participated with singular attachment in every phase of the establishment of the meter and the gram as national standards, and that he continued to promote the diffusion of the metric system in France and its conquered territories as Minister of Interior and later, as Senator.^[12] His public service included calling the first international congress of weights and measures in 1798 and laboring at the implementation of its decisions.^[13] His correspondence is replete with details about techniques of measurement, sources of error, and the consistency yielded by repeated measurement.

Laplace was not the first scientist to be so concerned. No doubt he developed an appreciation for instruments from close association with observational astronomers on whom he constantly relied for his work in celestial mechanics. Though not an expert observer himself, Laplace was as keenly concerned with sighting and timing devices as Tycho Brahe had been two centuries earlier. What is particularly

noteworthy is Laplace's desire to extend this attitude to all the sciences, particularly newly emerging ones. Two examples are in order here.

The Genevan physicist Deluc was one of Laplace's favorite scientific correspondents, despite Deluc's admittedly weak grasp of mathematical theories. In his mature years, Deluc turned into an irrepressible type quite distasteful to Laplace. Nevertheless, at an earlier time, Laplace vigorously encouraged him to reorganize the field of atmospheric research by elaborating his critical history of the thermometer and barometer, published in 1772. Laplace's stated hope was that Deluc could give meteorology its proper place among the more legitimate and established physical sciences. All that meteorology needed, so he imagined, was a carefully developed theory linking altitude to heat and pressure supported by accurate data taken from Alpine climes. So encouraging did Laplace's support prove to be that Deluc originally wrote his revised treatise on modifications of gases as a series of letters to Laplace.^[14] Even though the results did not fully meet Laplace's expectations, except in hypsometry, the goal pursued for almost two decades is testimony to Laplace's commitment to an increasingly accurate quantitative approach.^[15]

A more successful sponsorship following the same lines was Laplace's advocacy of the abbé Haüy's research into crystallography. In late 1783, Laplace was on the committee assigned to examine the manuscript of an Essay on a theory of the structure of crystals . He wrote a glowing report.^[16] Haüy had discovered a theory that had all the makings of a legitimate organizing principle linked directly to observation. Moreover, the theory of lattice structure he proposed was acknowledged to stem from a conscious effort to apply mathematics to natural history, as recommended by the mathematician Bézout. Unlike Bergman and Romé de l'Isle, who had tried to

organize crystals into classes or to relate their formation to the supposedly analogous processes of the formation of the earth, Haüy sought to link the geometry of standard crystals to the geometry of elementary particles that constituted their fundamental units. He succeeded in explaining various simple, quantitative phenomena.^[17]

Laplace considered this approach so promising that he developed a close personal attachment to the abbé, seeking to appropriate his talents for the physical sciences, symbolically capturing a portion of natural history (the mineral realm) for mathematics. The strategy worked so well that Haüy's next project brought him squarely into a newly quantified portion of physics. In 1787 Haüy offered the Academy a theory of electricity and magnetism that won him overwhelming praise for combining the theories of Aepinus and the empirical laws of Coulomb.^[18] During the Revolution, Haüy was selected (probably on the recommendation of Laplace) to lecture on physics at the Ecole normale; and in 1803 he was commissioned by the government to prepare the standard textbook on physics to be used in secondary schools. In all of these works, he expressed a philosophy totally in accord with and probably inspired by Laplace. Haüy demonstrated what a well-articulated theory intimately linked to verifiable, quantified data could be. If we take the writings of the abbé as a mirror of Laplace's views, we realize that their devotion to mathematics was not an end in itself, but a powerful tool for taming nature to human understanding. In describing the significance of his work in 1792, Haüy stated:^[19]

The theory of the structure of crystals can only be furthered with the aid of calculation (calcul analytique ). Analysis has the merit of encompassing in a single formula the solution to a large number of varied problems, and it can

alone impress upon theory the mark of rigorous certitude by arriving at results completely in accord with those of observation.

Variations on this theme were repeatedly asserted in scientific literature of the early 19th century, sometimes with direct reference to the inspiration provided by Laplace. The chemist Berthollet (Laplace's neighbor in Arcueil), who shared the same attitudes in his Essai de statique chimique (1803), acknowledged that his views were shaped by prolonged exchanges with Laplace. The latter never seems to have wavered from the belief that the advancement of scientific learning depended centrally upon the intelligent and appropriate use of mathematization. The view seemed fully sanctioned by many examples of progress in the physical sciences during the late Enlightenment.