01/02/2023

In Folha: the life and contributions of D'Alembert

Crédito: Société Mathématique de France

Reproduction of Marcelo Viana's column in Folha de S. Paulo.

The Frenchman Jean Le Rond d'Alembert (1717–1783) is one of the most brilliant thinkers of the Enlightenment. A mathematician, physicist, and philosopher, he also made important contributions to astronomy: he was the first to explain the phenomenon of the precession of the equinoxes based on Newton's laws through precise calculations. One of the craters on the Moon bears his name.

His interest in music led him to the discovery of the wave equation, the mathematical formula that describes vibrating bodies, such as the strings of a guitar. This discovery created a new area of mathematics, the theory of partial differential equations, one of the most important to this day.

Another very important contribution is D'Alembert's Theorem, also called the Fundamental Theorem of Algebra: every polynomial equation of degree N has exactly N solutions in the set of complex numbers. Calculus students are also well acquainted with D'Alembert's criterion for the convergence of infinite series.

In physics, besides developing wave theory, his main contribution was the publication of the "Treatise on Dynamics," a fundamental step in the mathematical formalization of Newton's ideas, a precursor to the work of Lagrange and Laplace. At its core is the so-called d'Alembert's Principle of Equilibrium, also well-known to undergraduate students.

Outside the scientific world, d'Alembert is best known for having been, with Denis Diderot, co-editor of the "Encyclopedia," an ambitious initiative to collect the knowledge of the time and make it accessible to all. D'Alembert brought this great project, a symbol of the Enlightenment, to life from its inception until 1757, when he disagreed with Diderot.

And yet, the beginning of his life could not have been less promising. Born from a fleeting relationship between his mother, Claudine de Tencin, and an aristocrat, possibly the knight Louis-Camus Destouches, he was abandoned the day after his birth on the steps of the Saint-Jean-le-Rond chapel (from whom he received his name).

Recovered by his father, he was placed in the Hospice for Found Children and, later, with an adoptive family. Destouches left him a small annual income in his will, which ensured his survival and allowed him to pursue his studies.

In 1772, D'Alembert became perpetual secretary of the French Academy of Sciences. Nowadays, this is a position with fixed terms – the current holder is the mathematician Étienne Ghys, a great friend of Brazil – but at the time the title was taken seriously: D'Alembert remained in the position until his death.

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