Provocative Riemann quotations
If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?
The greatest problem for mathematicians now is probably the Riemann Hypothesis.
I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.
It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.'
In Riemann, Hilbert or in Banach space Let superscripts and subscripts go their ways. Our symptotes no longer out of phase, We shall encounter, counting, face to face.
The best that Gauss has given us was likewise an exclusive production.
If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.
Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.