David Hilbert

"To understand a proof, one must first understand the problem."

"The solution of a problem consists in the finding of a conception which defines the points."

"Every mathematical truth must eventually appear simple and self-evident."

"Rigor is the morality of mathematics."

"The axis of the solution curves must be determined by means of the proper selection of axes."

"Nature speaks to us in the language of mathematics."

"We are not interested in properties of the physical world for their own sake but in their mathematical essence."

"The profound study of nature is the most fertile source of mathematical discovery."

"In mathematics, we discover rather than invent."

"The beauty of a mathematical proof lies in its necessity."

"A problem is solved completely when it ceases to trouble the mind."

"The principles of mathematics are so broad that they encompass the whole universe."

"The truth of a theorem depends on its logical structure, not on its creator."

"In the realm of mathematics, there are no unrealistic expectations."

"Every problem in mathematics is essentially a problem of definition."

"The mathematician is a maker of patterns and those patterns, like the artist's, must be beautiful."

"We can learn more from a single counterexample than from ten proofs."

"The essential feature of the mathematical creation is that it does not depend on any external stimulus."

"To think in abstract terms requires the highest human faculty."

"A theorem is important if it contains unexpected connections between distant ideas."

"The mind of the mathematician must be precise yet imaginative, concrete yet abstract."

"The truth of mathematics is not subject to opinion or convention."

"To penetrate into that world of abstract ideas requires philosophical depth."

"A mathematician who has not felt the sense of adventure in research is not a true mathematician."

"The path to mathematical understanding is paved with curiosity and persistence."

"In mathematics, every truth is ultimately simple and elegant."

"The power of mathematics lies in its universality."

"To solve a difficult problem, first solve an easier one."

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

"The creative mathematician must have the courage to follow where the logic leads."