Anatol Wegner

"In order to prove certain propositions about integers, the concept of set of integers is necessary. So here, in order to find out what properties we have given to certain objects of our imagination, we must first create certain other objects—a very strange situation indeed!" - Kurt Gödel

You can't make this stuff up.😂

It is about time we introduce a next phase into the circuit: the 'blind devotion/abandon' phase where mathematicians extrapolate AI capabilities into absurdity and turn into wide eyed mystics fantasizing about future machines taking us on interstellar trips to alien math planets and alternate dimensions beyond our imagination.

“I think from what I've seen of Americans since I have come here, they are not suited by temperament or tradition for existence under a totalitarian system. I think that most of them would not find life worth living so. Therefore, it is very important that they consider how these liberties that are so necessary to them may be preserved and defended.” - Albert Einstein in 1940 upon becoming a US citizen.

“I believe that America will prove that democracy is not merely a form of government bound to a good Constitution but also a way of life supported by a people who have a good tradition, a tradition of moral strength. And the fate of the human race is more than ever dependent on its moral strength today.” - Albert Einstein in 1940 upon becoming a US citizen.

"Our science, which we loved above everything, had brought us together. It appeared to us as a flowering garden. In this garden there are beaten paths where one may look around at leisure and enjoy oneself without effort, especially at the side of a congenial companion. But we also liked to seek out hidden trails and discovered many a novel view, beautiful to behold, so we thought, and when we pointed them out to one another our joy was perfect." - David Hilbert on his friendship with Hermann Minkowski

“The problems of mathematics are not isolated problems in a vacuum; there pulses in them the life of ideas which realize themselves in concreto through our human endeavors in our historical existence, but forming an indissoluble whole transcend any particular science.” - Hermann Weyl

“Dark ordinance by fate and dark number-magic are overcome in Greek thought by the glorious, lucid idea of mathematical lawfulness governing the world. Without having relation to any meaning as do the acts of the ego, the external world is thus nevertheless filled with the light of spirit, of reason.” - Hermann Weyl

“Ever since Newton, in his modesty, spoke of playing with pebbles on the shore of a wide ocean, the attitude that we mathematicians play a nice game that ought not to be taken too seriously has enjoyed considerable popularity. In my opinion it is fundamentally unsound. Whatever analogies there are between the mental activities of a mathematician and a chess player, the problems of the former are serious in the sense that they are bound up with truth, truth about the world that is and truth about our existence in the world. That the game of mathematics and physics is a harmless game, one of Hardy’s main points in defense of mathematics, nobody can claim any longer. Hardy distinguishes between the real mathematics, that of Gauss and Riemann and Ramanujan, and the dull Hogben type of Mathematics for the Million, and thinks that only the latter is useful or harmful as the case may be. I do not believe that his distinction is valid. Riemann is as respectable a mathematician in his papers on the hydrodynamics of shock waves as in his paper on the zeta function. If the progress of science is blamed for the impasse in which the world finds itself today, then the mathematician has to assume his share of responsibility.” — Hermann Weyl, Princeton Bicentennial Conference (1946)

“The task of the mathematician is to see to it that the theories in the concrete sciences satisfy this conditio sine qua non that they be formally determinate and non-contradictory.”-Hermann Weyl

“we do not possess the truth; it is not enough to open our eyes wider, for the truth is to be won by action.” - Hermann Weyl

“It pays to keep an open mind, but not so open your brains fall out.” - Carl Sagan

“So the following disjunctive conclusion is inevitable: Either mathematics is incompletable in this sense, that its evident axioms can never be comprised in a finite rule, that is to say, the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable diophantine problems of the type specified.” Kurt Gödel

"But surpassing all stupendous inventions, what sublimity of mind was his who dreamed of finding means to communicate his deepest thoughts to any other person, though distant by mighty intervals of place and time! Of talking with those who are in India; of speaking to those who are not yet born and will not be born for a thousand or ten thousand years; and with what facility, by the different arrangements of twenty characters upon a page! Let this be the seal of all the admirable inventions of mankind." - Galileo Galilei

“Many kinds of men devote themselves to Science, and not all for the sake of Science herself. There are some who come into her temple because it offers them the opportunity to display their particular talents. To this class of men science is a kind of sport in the practice of which they exult, just as an athlete exults in the exercise of his muscular prowess. There is another class of men who come into the temple to make an offering of their brain pulp in the hope of securing a profitable return. These men are scientists only by the chance of some circumstance which offered itself when making a choice of career. If the attending circumstance had been different they might have become politicians or captains of business. Should an angel of God descend and drive from the Temple of Science all those who belong to the categories I have mentioned, I fear the temple would be nearly emptied. But a few worshipers would still remain—some from former times and some from ours. To these latter belongs our Planck. And that is why we love him.” - Albert Einstein on Max Planck

“Whatever has the air of a paradox, and is contrary to the first and most unprejudiced notions of mankind is often greedily embraced by philosophers, as showing the superiority of their science, which could discover opinions so remote from vulgar conception. On the other hand, any thing proposed to us, which causes surprise and admiration, gives such a satisfaction to the mind, that it indulges itself in those agreeable emotions, and will never be persuaded that its pleasure is entirely without foundation.” David Hume

“It is not possible to mechanise mathematical reasoning, i.e., it will never be possible to replace the mathematician by a machine, even if you confine yourself to number-theoretic problems.” - Kurt Gödel

“In speaking here of "comprehensibility," the expression is used in its most modest sense. It implies: the production of some sort of order among sense impressions, this order being produced by the creation of general concepts, relations between these concepts, and by definite relations of some kind between the concepts and sense experience. It is in this sense that the world of our sense experiences is comprehensible. The fact that it is comprehensible is a miracle.” - Albert Einstein

"If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics. The fact is that in mathematics we still have the same attitude today that in former times one had toward all science, namely, we try to derive everything by cogent proofs from the definitions (that is, in ontological terminology, from the essences of things). Perhaps this method, if it claims monopoly, is as wrong in mathematics as it was in physics."- Kurt Gödel

“Let us get down to bedrock facts. The beginning of every act of knowing, and therefore the starting point of every science, must be in our own personal experiences. I am using the word, experience, here in its technical philosophical connotation, namely, our direct sensory perception of outside things. These are the immediate data of the act of knowing. They form the first and most real hook on which we fasten the thought-chain of science; because the material that furnishes, as it were, the building-stones of science is received either directly through our own perception of outer things or indirectly, through the information of others, that is to say from former researchers and teachers and publications and so on. There are no other sources of scientific knowledge.” - Max Planck