Such axioms, together with other unmotivated definitions, serve mathematicians mainly by making it difficult for the uninitiated to master their subj… - Vladimir Arnold

In the middle of the twentieth century it was attempted to divide physics and mathematics. The consequences turned out to be catastrophic. Whole generations of mathematicians grew up without knowing half of their science and, of course, in total ignorance of any other sciences. They first began teaching their ugly scholastic pseudo-mathematics to their students, then to schoolchildren (forgetting Hardy's warning that ugly mathematics has no permanent place under the Sun).

It is almost impossible for me to read contemporary mathematicians who, instead of saying “Petya washed his hands,” write simply: “There is a <math>t_1<0</math> such that the image of <math>t_1</math> under the natural mapping <math>t_1 \mapsto {\rm Petya}(t_1)</math> belongs to the set of dirty hands, and a <math>t_2</math>, <math>t_1<t_2 \leq 0</math>, such that the image of <math>t_2</math> under the above-mentioned mapping belongs to the complement of the set defined in the preceding sentence.”

"In almost all textbooks, even the best, this principle is presented so that it is impossible to understand." (K. Jacobi, Lectures on Dynamics, 1842-1843). I have not chosen to break with tradition.