I don't believe in natural science.
[Said to physicist John Bahcall.]
Quoted in Ed Regis, Who Got Einstein's Office? 1987.
The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.
Opening of the paper introducing the Undecidability theorem (1931).
...a consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the system ... itself.
Gödel gave a formal demonstration of the inadequacy of formal demonstrations. [An anonymous quotation]
Nothing new had been done in Logic since Aristotle!