On Impossibility (Unsourced)

"Anytime new insight replaces an old assumption, or a fossilized perception is the spring. New understandings sprout, new tolerances appear, and new curiosity draws you to previously dark places. Just as the sun shines earlier and longer in the spring, changes that seemed impossible appear to be possible with each new insight into your own health." (Gary Zukav)

"I did not understand how such a quantity could be real, when imaginary or impossible numbers were used to express it." (Gottfried W Leibniz)

"I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible." (Carl Friedrich Gauss)

"In the world of human thought generally, and in physical science particularly, the most important and fruitful concepts are those to which it is impossible to attach a well-defined meaning." (Hendrik A Kramers)

"Indeed, when in the course of a mathematical investigation we encounter a problem or conjecture a theorem, our minds will not rest until the problem is exhaustively solved and the theorem rigorously proved; or else, until we have found the reasons which made success impossible and, hence, failure unavoidable. Thus, the proofs of the impossibility of certain solutions plays a predominant role in modern mathematics; the search for an answer to such questions has often led to the discovery of newer and more fruitful fields of endeavour." (David Hilbert)

"It often happens that understanding of the mathematical nature of an equation is impossible without a detailed understanding of its solution. (Freeman J Dyson)

"It is impossible to overstate the importance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps. […] Every new discovery in mathematics, results from an attempt to solve some problem." (Howard W Eves)

"It is impossible to transcend the laws of nature. You can only determine that your understanding of nature has changed." (Nick Powers)

"It is impossible to trap modern physics into predicting anything with perfect determinism because it deals with probabilities from the outset." (Sir Arthur S Eddington)

"Mathematical language, precise and adequate, nay, absolutely convertible with mathematical thought, can afford us no example of those fallacies which so easily arise from the ambiguities of ordinary language; its study cannot, therefore, it is evident, supply us with any means of obviating those illusions from which it is itself exempt. The contrast of mathematics and philosophy, in this respect, is an interesting object of speculation; tut, as imitation is impossible, one of no practical result." (Sir William R Hamilton)

"String theory is extremely attractive because gravity is forced upon us. All known consistent string theories include gravity, so while gravity is impossible in quantum field theory as we have known it, it is obligatory in string theory."(Edward Witten)

"That this subject [imaginary numbers] has hitherto been surrounded by mysterious obscurity, is to be attributed largely to an ill adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question." (Carl Friedrich Gauss)

"The universe has no circumference, for if it had a center and a circumference there would be some and some thing beyond the world, suppositions which are wholly lacking in truth. Since, therefore, it is impossible that the universe should be enclosed within a corporeal center and corporeal boundary, it is not within our power to understand the universe, whose center and circumference are God. And though the universe." (Nicholas of Cusa)