Proofs Quotes

“The first and most important field of philosophy is the application of principles such as “Do not lie.” Next come the proofs, such as why we should not lie. The third field supports and articulates the proofs, by asking, for example, “How does this prove it? What exactly is a proof, what is logical inference, what is contradiction, what is truth, what is falsehood?” Thus, the third field is necessary because of the second, and the second because of the first. The most important, though, the one that should occupy most of our time, is the first. But we do just the opposite. We are preoccupied with the third field and give that all our attention, passing the first by altogether. The result is that we lie – but have no difficulty proving why we shouldn’t.”

“Actually, the “leap of faith”—to give it the memorable name that Soren Kierkegaard bestowed upon it—is an imposture. As he himself pointed out, it is not a “leap” that can be made once and for all. It is a leap that has to go on and on being performed, in spite of mounting evidence to the contrary. This effort is actually too much for the human mind, and leads to delusions and manias. Religion understands perfectly well that the “leap” is subject to sharply diminishing returns, which is why it often doesn’t in fact rely on “faith” at all but instead corrupts faith and insults reason by offering evidence and pointing to confected “proofs.” This evidence and these proofs include arguments from design, revelations, punishments, and miracles. Now that religion’s monopoly has been broken, it is within the compass of any human being to see these evidences and proofs as the feeble-minded inventions that they are.”

“There are no proofs. There are only agreements”

“One can be enlightened about proofs as well as theorems. Without enlightenment, one is merely reduced to memorizing proofs. With enlightenment about a proof, its flow becomes clear and it can become an item of astonishing beauty. In addition, the need to memorize disappears because the proof has become part of your soul.”

“It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true.”

“Our photographs are our best proof to others that we lived the things we lived in the past!”

“Proofs are to mathematics what spelling (or even calligraphy) is to poetry. Mathematical works do consist of proofs, just as poems do consist of words.”

“Man is a social being; it’s not surprising we love social proofs, it sells brands fast”

“I am not qualified to say whether or not God exists. I kind of doubt He does. Nevertheless I'm always saying that the SF( The SF is the supreme Fascist, the Number-One guy up there) has this transfinite book-transfinite being a concept in mathematics that is larger than infinite-that contains the best proofs of all mathematical theorems, proofs that are elegant and perfect.”