https://mitpress.mit.edu/sites/default/files/titles/content/...

"Classical mechanics is deceptively simple. It is surprisingly easy to get the right answer with fallacious reasoning or without real understanding. Traditional mathematical notation contributes to this problem. Symbols have ambiguous meanings that depend on context, and often even change within a given context. For example, a fundamental result of mechanics is the Lagrange equations. ... The Lagrangian L must be interpreted as a function of the position and velocity components qi and i, so that the partial derivatives make sense, but then in order for the time derivative d/dt to make sense solution paths must have been inserted into the partial derivatives of the Lagrangian to make functions of time. The traditional use of ambiguous notation is convenient in simple situations, but in more complicated situations it can be a serious handicap to clear reasoning."

Footnote 2 is also fun to read.