Proof Quotes - page 3
The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind. Similar proofs may be encountered in the theory of infinitely many simultaneous linear equations and in the theory of integral and differential equations. Consideration of semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form.
Leonid Kantorovich
Where the preamble declares, that coercion is a departure from the plan of the holy author of our religion, an amendment was proposed by inserting "Jesus Christ," so that it would read "A departure from the plan of Jesus Christ, the holy author of our religion;" the insertion was rejected by the great majority, in proof that they meant to comprehend, within the mantle of its protection, the Jew and the Gentile, the Christian and Mohammedan, the Hindoo and Infidel of every denomination.
Thomas Jefferson
There is a sort of enthusiasm in all projectors, absolutely necessary for their affairs, which makes them proof against the most fatiguing delays, the most mortifying disappointments, the most shocking insults; and, what is severer than all, the presumptuous judgement of the ignorant upon their designs.
Edmund Burke
I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.
G. H. Hardy