dAlembert

Jean le Rond d'Alembert (1717–1783) was a French mathematician, physicist, and philosopher whose work helped shape the development of mathematical physics in the Enlightenment era. He made foundational contributions to the analysis of waves, dynamics, and differential equations, and he played a significant role in the dissemination of scientific knowledge through the Encyclopédie.

In mathematics and mathematical physics, d'Alembert is best known for the one-dimensional wave equation governing vibrating strings and for his insight that wave motion can be described as the sum of two traveling waves. This leads to the familiar d'Alembert solution, y(x,t) = f(x−ct) + g(x+ct), which illustrates how disturbances propagate as independent right- and left-moving waves. His work helped establish partial differential equations as essential tools in physics.

In dynamics, d'Alembert formulated what is now called d'Alembert's principle, a reformulation of Newton's laws that introduces inertial forces to convert dynamic problems into statics for systems with constraints. This approach influenced later developments in analytical mechanics and variational methods.

In fluid dynamics, he contributed to potential theory and is associated with d'Alembert's paradox, the result that an inviscid, incompressible, irrotational flow yields zero drag on a body moving through a fluid, a surprising outcome that spurred further study.

D'Alembert also contributed to the collaborative Enlightenment project of the Encyclopédie, helping to organize and present scientific knowledge. His legacy lies in the broad applicability of his methods to mathematics, physics, and engineering, and in his enduring influence on the study of waves, mechanics, and analytical reasoning. He died in Paris in 1783.