# Mathematicians and Enlightenment Society

# Mathematicians and Enlightenment Society

*Overview*

In the eighteenth century, mathematicians formed an integral part of society and culture. They exploited available avenues toward gaining patronage and prestige. Further, mathematicians such as Jean Le Rond d'Alembert (1717-1783) influenced the intellectual developments of the Enlightenment, which radiated out from France. The writers and thinkers of that time, in turn, relied upon mathematical language and logic in a unique manner.

*Background*

By 1700, the Scientific Revolution had culminated mathematically with Isaac Newton's (1642-1727) and Gottfried Wilhelm Leibniz's (1646-1716) invention of the calculus along with Newton's universal theory of gravitation and his study of optics. The next generation of mathematicians turned to finding physical confirmation of these mathematical theories and to applying new mathematical tools, such as differential equations. However, mathematicians who were not independently wealthy needed to somehow secure financial support for their work.

Professorships were not necessarily a viable option for employment at this time. European universities had declined in importance as centers of mathematical research, in part because jobs in universities were limited in number and often went to people who possessed political connections rather than intellectual ability. These professors, furthermore, often wasted time in pointless debates. Even Newton had left Cambridge University and went to work for the English Mint for thirty years, where he also gave positions to some of his scientific followers.

Mathematicians could alternatively look to scientific societies. The Royal Society of London and the Paris Academy of Sciences had been established in the seventeenth century as arbiters and promoters of scientific knowledge. Whereas the Royal Society offered little financial support beyond publishing some mathematical books for authors, mathematicians chosen for the Paris Academy were directly employed by the French state. Other European governments followed the French model of founding academies to create centralized communities of mathematicians and scientists who would devote some of their efforts to projects that would improve the state. Rulers often attached observatories to these academies as well. Installing the expensive telescopes and instruments needed to make observations further demonstrated the wealth and power of the state. Academies established by national governments provided a two-way relationship-this patronage gave legitimacy, credibility, and moral confirmation to mathematicians as well as to the state.

As these scientific societies judged and publicized new mathematical achievements, new knowledge became accessible on a popular level as never before. Eighteenth-century intellectuals studied and promoted mathematics and natural philosophy. For example, Voltaire (1694-1778) and Emilie du Châtelet (1706-1749) published a popularization of Newton's ideas in 1738 and a French translation of the *Principia* in 1759. In addition, authors adopted the rational reasoning behind the discoveries of the Scientific Revolution not only for the study of nature but also for philosophy. Their critical spirits embraced the values of toleration, freedom, reasonableness, and opposition to authoritarianism. In other words, appreciation for the powerful natural laws discovered in the seventeenth century was a driving force behind the tenets of the Enlightenment, which characterized the eighteenth century. To the philosophes, or the writers and thinkers of the Enlightenment in France, mathematics held the key to true philosophy.

While most European absolutist rulers did not adopt Enlightenment calls for governmental reform, they did covet the mathematical and scientific heroes of the Enlightenment. They became further convinced of the importance of patronizing scientific societies. Figures such as Frederick the Great of Prussia (1712-1786) and Catherine the Great of Russia (1729-1796) acquainted themselves with the mathematical members of their academies. They employed mathematicians at court, and they sponsored prizes for those who presented new results. Mathematicians, in turn, were generally willing to work on state projects or to tutor royal youths because these jobs gave them a route to wealth and prestige.

*Impact*

Thus, mathematicians and Enlightenment society were close partners in the eighteenth century. Even a gargantuan talent such as Leonhard Euler (1707-1783) had to fit in with the literary and courtly culture to prosper financially. One of the most successful exploiters of the mutual relationship between mathematics and philosophy was d'Alembert, as he and Marie-Jean de Caritat, marquis de Condorcet (1743-1794) were the only intellectuals to function both as mathematicians and as philosophes.

First, d'Alembert established a reputation as a skilled mathematician by presenting his first mathematical paper, a criticism of Charles Reyneau's ideas, to the Paris Academy in 1739. He was elected to the Academy as an astronomy member in 1741, and he moved into the mathematics section in 1746. In 1743, d'Alembert published his first book, *Traité de dynamique*, which was an attempt to formalize dynamics. He also won a prize from the Berlin Academy of Sciences in 1746.

During the 1740s, d'Alembert had spent his evenings in the Paris salons of Madame Geoffrin and Madame du Deffand, which were the breeding grounds of Enlightenment culture. Topics of discussion in these informal gatherings included scientific discoveries and political or philosophical theories. Salon attendees were generally wealthy, well-educated young men who appreciated a clever turn of phrase as much as a profound idea. Thus, d'Alembert's abilities in witty conservation and at dramatically reading his correspondence won him favor with the other intellectuals.

D'Alembert and another philosophe, Denis Diderot (1713-1784), were also hired by a French publisher to oversee the development of an encyclopedia of all knowledge. D'Alembert wrote the scientific articles for the *Encyclopédie*, the first volume of which appeared in 1751. In addition, he prepared a "Preliminary discourse" which described how the history of the sciences might have been if they had been discovered in logical order. This paper helped to explain that the *Encyclopédie* was meant to lay down the principles of the Enlightenment; it also made d'Alembert well known as a literary talent. Still, d'Alembert left the project in 1758 due to the political difficulties caused by opponents of the *Encyclopédie*, while Diderot continued on and finished the final volume in 1772.

Furthermore, d'Alembert exerted his influence as a mathematician and philosophe in the academies. Although a scientific rivalry with Alexis Clairaut (1713-1765) hindered his personal advancement in the Paris Academy after his ally, Pierre-Louis Maupertuis (1698-1759), departed for the Berlin Academy in 1745, d'Alembert's enthusiastic campaign in favor of philosophy was one factor which flavored scientific societies across Europe with the cosmopolitan character of the French Enlightenment. More directly, d'Alembert was elected to the literary Académie Française in 1754 and became that society's perpetual secretary in 1772, a position that allowed him to see to the election of enough philosophes to form a majority of the members.

Prominence in the academies also provided d'Alembert with opportunities to make connections with and on behalf of other mathematicians. His friendship with Euler was rocky over the years, and after disagreeing over the definition of mathematical functions in 1749, the two did not reconcile until 1763, when d'Alembert was no longer an active mathematician. Still, d'Alembert's contacts did enable him to support younger mathematicians. He secured Pierre-Simon, marquis de de Laplace's (1749-1827) first teaching position at the Ecole Militaire. D'Alembert also mentored Joseph Lagrange (1736-1813) and Condorcet.

While d'Alembert's own mathematical research had no direct impact on Enlightenment philosophy, the discipline of mathematics was a major aspect of Enlightenment culture. The philosophes were inspired by the mathematization of natural philosophy to carry the rationalization of their subject even further in the later French Enlightenment. Condorcet and the Abbé de Condillac were two of the most notable figures in this regard. They argued that mathematical laws could be adapted to human reasoning and that algebra was an unambiguous language that should be the model for all communication. During the French Revolution, the former philosophes who gained control of the government instituted programs to decimalize all units of measurement and to rationalize education based on the mathematical approach to philosophy.

Laplace was one of the later eighteenth-century mathematicians who gained financially by adapting to shifting political situations during his lifetime. He had become one of the senior members of the Paris Academy by 1789, and he managed to remain friendly to each of the groups that gained political control over the course of the French Revolution. Around 1800, Napoleon Bonaparte (1769-1821) awarded Laplace the Grand Cross of the Imperial Order and put him in the Senate; but Laplace shifted his allegiances to Louis XVIII in 1814, just in time to benefit from the restoration of the French monarchy. One property Laplace purchased with his Senate salary was his house at Arcueil, where he and his protégés conducted research during the last two decades of his life.

In the nineteenth century, many mathematicians retreated from social, political, and philosophical involvements, partly because the status of academies and prizes became subordinate to that of research universities. Göttingen University, founded in the late eighteenth century, was one of the first to be oriented toward mathematical and scientific research. Simultaneously, internal developments in mathematics became increasingly specialized, and it was no longer possible for a person to know everything there was to know about mathematics. Thus, mathematicians turned to technical pursuits and away from the general intellectual culture.

In summary, eighteenth-century mathematicians were interconnected with Enlightenment society. The new mathematics impressed not only mathematicians, but also rulers who established academies to bring prestigious mathematicians to their courts, and the philosophes popularized mathematics and applied it to general human reasoning. Mathematicians benefited financially from the academies either directly or through contacts with new patrons; academy involvement also encouraged mathematicians to share their research openly. While d'Alembert was an archetype for a mathematician who was a proponent of Enlightenment philosophy, all of the most talented mathematicians on the European Continent during that time had to function within Enlightenment society.

**AMY ACKERBERG-HASTINGS**

*Further Reading*

Frängsmyr, Tore, J. L. Heilbron, and Robin E. Rider, ed.*The Quantifying Spirit in the 18th Century. *Berkeley: University of California Press, 1990.

Gillispie, Charles Coulston. *Science and Polity in France at the End of the Old Regime. *Princeton: Princeton University Press, 1980.

Hahn, Roger. *Anatomy of a Scientific Institution: The Paris Academy of Science, 1666-1803. *Berkeley: University of California Press, 1971.

Hankins, Thomas L. *Jean d'Alembert: Science and the Enlightenment. *Oxford: Clarendon Press, 1970.

Spielvogel, Jackson J. *Western Civilization.* 2d ed.*Minneapolis/St. Paul: West Publishing Company, 1994.*

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