The Euler equation, specifying the dynamical constraint for optimality of an intertemporal optimization problem, is widely used in modern economics. But where does it get its name from? What did Euler have to do with it?
It appears, like a lot of other math economics uses, this one was lifted from fluid dynamics. From Wikipedia:
The Euler equations first appeared in published form in Euler's article "Principes généraux du mouvement des fluides", published in Mémoires de l'Academie des Sciences de Berlin in 1757 (in this article Euler actually published only the general form of the continuity equation and the momentum equation; the energy balance equation would be obtained a century later). They were among the first partial differential equations to be written down.