Yuri Manin > Quotes

“A proof becomes a proof after the social act of accepting it as a proof. This is true of mathematics as it is of physics, linguistics, and biology.”
― Yuri Manin

“I am pretty strongly convinced that there is an ongoing reversal in the collective consciousness of mathematicians: the right hemispherical and homotopical picture of the world becomes the basic intuition, and if you want to get a discrete set, then you pass to the set of connected components of a space defined only up to homotopy.”
― Yuri Manin

“A successfully chosen name is a bridge between scientific knowledge and common sense, between new experience and old habits. The conceptual foundation of any science consists of a complicated network of names of things, names of ideas, and names of names. It evolves itself, and its projection on reality changes.”
― Yu. I. Manin, A Course in Mathematical Logic for Mathematicians

“There is a story about how a certain well-known mathematician would begin his sophomore course in logic. "Logic is the science of laws of thought," he would declaim. "Now I must tell you what science is, what law is, and what thought is. But I will not explain what 'of' means.”
― Yuri Manin, Mathematics and Physics

“When Poincaré said that there are no solved problems, there are only problems which are more or less solved, he was implying that any question formulated in a yes/no fashion is an expression of narrow-mindedness.”
― Yuri Manin, Mathematics as Metaphor

“In reality the biological function of thought is not to provoke but rather to prevent automatic action.”
― Yuri Manin, Mathematics as Metaphor

“Pure mathematics is an immense organism built entirely and exclusively of ideas that emerge in the minds of mathematicians and live within these minds.”
― Yuri Manin, Mathematics as Metaphor

“I am pretty strongly convinced that there is an ongoing reversal in the collective consciousness of mathematicians: the homotopical picture of the world becomes the basic intuition, and if you want to get a discrete set, then you pass to the set of connected components of a space defined only up to homotopy … Cantor’s problems of the infinite recede to the background: from the very start, our images are so infinite that if you want to make something finite out of them, you must divide them by another infinity.”
― Yuri Manin