@BalarkaSen Well the kid was joking
mathoverflow.net/a/153606/38721 not sure if Arnold knew that but he was making a solid point, a point illustrated via the supposed inability to calculate $\frac{\partial}{\partial r}(x^2 \vec{e}_x + y^2 \vec{e}_y)$ brute force, accompanied by actual comments this is wrong or a bad style of mathematics & that I'm crazy etc... though you find it in good vector calculus books, why? Well a bunch of abstract manifolds concepts 'imply' it's not possible :\