The best way to guide the mental development of the individual is to let him retrace the mental development of the race – retrace its great lines, of course, and not the thousand errors of detail.
– Bers Kline Polya Schiffer
I look at the burning question of the foundations of infinitesimal analysis without sorrow, anger or irritation. What Weierstrass - Cantor - did was very good. That’s the way it had to be done. But whether this corresponds to what is in the depths of our consciousness is a very different question. I cannot but see a stark contradiction between the intuitively clear fundamental formulas of the integral calculus and the incomparably artificial and complex work of the “justification” and their “proofs”. One must be quite stupid not to see this at once, and quite careless if, after having seen this, one can get used to this artificial, logical atmosphere, and can later on forget this stark contradiction.
– Nikolai Lusin