Knowledge Quotes

"Logic is the anatomy of thought."

"I think that it is a remarkable fact that all the fundamental theorems of analysis can be derived from the concept of the derivative."

"What we know is a mere fraction of what we might know."

"The pursuit of knowledge is never complete."

"Every answer generates new questions."

"Mathematical truths are not discovered; they are invented by the human mind."

"Numbers are the alphabet in which the book of nature is written."

"In mathematics, he who does not work with symbols is like a musician without an instrument."

"In the orchestra of knowledge, mathematics plays the fundamental melody."

"Knowledge without application is merely collecting beautiful facts."

"A philosopher's ultimate aim is to construct a coherent, logical system that accounts for the apparent facts of experience."

"Abstractness is the glory of the human mind; it is also the source of human error."

"If a machine is expected to be infallible, it cannot also be intelligent."

"Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity."

"To those who do not know mathematics it is hard to feel the reality of the abstract world."

"All the evidence we have suggests that it is the explanation of intellectual process in terms of mechanical processes that has hitherto been avoided."

"It can also be maintained that any sufficiently powerful formal system is, if consistent, incomplete."

"Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding."

"To understand the infinite, one must first understand the limitations of finite thought."

"What we perceive as abstract is often more fundamental than what appears concrete."

"To understand is to see how everything connects in patterns of necessity."

"We must know, we will know."

"The axiomatic method is the highest expression of the mathematical spirit."

"To create new mathematics, one must first exhaust the old."

"To understand a proof is to stand upon the shoulders of giants."

"The infinite presents not a barrier to knowledge, but an invitation to deeper understanding."

"A paradox resolved is a theorem born."

"Mathematics is the most democratic of all sciences: its truths belong to all."

"Semantics is the study of the relationship between language and reality."

"To understand language is to understand the nature of human thought."