"The integral along two different paths will always have the same value if it is never the case that φ(x) = ∞ in the space between the curves representing the paths. This is a beautiful theorem, whose not-too-difficult proof I will give at a suitable opportunity." (Carl F Gauss, [letter to Bessel] 1811)
"It is characteristic of higher arithmetic that many of its most beautiful theorems can be discovered by induction with the greatest of ease but have proofs that lie anywhere but near at hand and are often found only after many fruitless investigations with the aid of deep analysis and lucky combinations." (Carl F Gauss, 1817)
"Up to now, one as has not succeeded to find a rigourous proof of that truth [Euclid’s axiom on parallels]. Those which were given may be named only explanations, but do not deserve to be considered, in the full sense, mathematical proofs. " (Nikolai I Lobachevsky, 1823)
"Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning." (John Locke, 1824)
"Mathematics in gross, it is plain, are a grievance in natural philosophy, and with reason. […] Mathematical proofs are out of the reach of topical arguments, and are not to be attacked by the equivocal use of words or declamation, that make so great a part of other discourses; nay, even of controversies." (John Locke, 1824)
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