Prof Kalmar on the exactness of mathematics

Though most of my grandfather's work is difficult to grasp by us everyday people:-) I did find a very interesting piece he wrote on the exactness of mathematics :

“…I’ve completed the high school of mathematical exactness, and I see that exactness hasn’t got any limits.

There isn’t such a precise definition or theorem that couldn’t be found faults in by a more precise point of view; and not because of hair-splitting but with a thorough reason (because refusing a more precise point of view may lead to errors and false results).

That’s why I cannot comprehend dogmatically the precision of mathematics any more: the ones in this side aren’t precise, the ones on the other side are precise.

With this, of course, I’ve rejected the idea of mathematics as an «absolute true science».

I don’t say that I was forced to reject it, because I am convinced that the beautiful part of mathematics consists in wearing all the uncertainties of the human work.

Don’t get me wrong: a kind of precision exists for me too, however not in a static sense but in a dynamic one.

When I teach mathematics to somebody, he’s already standing at a certain degree of precision, maybe at a very low degree. He couldn’t get higher by the way that I call him idiot when he’s less precise; but I have to convince him that it’s worth coming up. Of course it’s worth only if he demands it. However, it doesn’t matter at all if one doesn’t have a demand on it; then we remain where we are…”

Source: Extract from László Kalmár’s letter to Miklós Szabó (Szeged, 19/2/1947) In: Kalmár László: Integrállevél. Matematikai írások, Gondolat, Budapest, 1986.]