The Laplacian is a scalar (not a vector) differential operator that appears in important equations in physics and chemistry, such as Schrodinger's wave equation.
The operator, and the quintessential equation it appears in are named for Pierre-Simon Laplace, an 18th century French mathematician, who made critical contributions to the development of calculus and classical mechanics. The Laplace equation
appears in Laplace's Treatise on Celestial Mechanics, however, it was not original to Laplace, having been known for almost a half century.
Chemists typically write the Laplacian using the symbol ∇, however, some mathematicians will use Δ instead. Since chemists associate Δ with "change in" or "heat", depending on context, the source of the preference is obvious! The Laplacian can be constructed for higher dimensional spaces. The symbol used for the operator in 4-dimensions (called the d'Alembertia after another French mathematician of the 18th century, the quarrelsome Jean Le Rond d'Alembert) is . I presume the symbol for the Laplacian in 5-D would involve a pentagon?
What do Laplace and d'Alembert have to do with Napoleon Bonaparte? Laplace was appointed by Napoleon to the Ministry of the Interior, but removed from his post in less than a year for what Napoleon later wrote was his habit of bringing "the spirit of the infinitely small into the government." Napoleon was 14 when d'Alembert died, as far as I know, there is no direct connection.
13 hours ago in Variety of Life