I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible. ↗
It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation. ↗
In a few decades of reconstruction, even the mathematical natural sciences, the ancient archetypes of theoretical perfection, have changed habit completely! ↗
Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it. ↗
