Erret Bishop

Mathematics belongs to man, not to God. We are not interested in properties of the positive integers that have no descriptive meaning for finite man. When a man proves a positive integer exists, he should know how to find it. If God has mathematics of his own that needs to be done, let him do it himself.

__ Erret Bishop, in the Introduction to Foundations of Constructive Analysis


I knew a mathematician who said, "I do not know as much as God, but I know as much as God did at my age."

Henri Poincaré

"I have never known a more realistic mathematician in the Platonist sense than Hermite ... He accused Cantor of creating objects instead of merely discovering them. Doubtless because of his religious convictions he considered it a kind of impiety to wish to penetrate a domain which God alone can encompass [i.e. the infinite], without waiting for Him to reveal its mysteries one by one. He compared the mathematical sciences with the physical sciences. A natural scientist who sought to divine the secret of God, instead of studying experience, would have seemed to him not only presumptuous but also lacking in respect for the divine majesty; the Cantorians seemed to him to want to act in the same way in mathematics. And this is why, a realist in theory, he was an idealist in practice. There is a reality to be known, and it is external to and independent of us; but all we can know of it depends on us, and is no more than a gradual development, a sort of stratification of successive conquests. The rest is real but eternally unknowable."

__ Henri Poincaré (Poincaré was Hermite's student)


Finally, two days ago, I succeeded - not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what was the conducting thread that connected what I previously knew with what made my success possible.

__ C. F. Gauss, ranked by most among the three best mathematicians of all time