David Hilbert

Mathematics is the ultimate form of abstract art.

The infinite is a concept that expands our minds.

Mathematics is the ultimate intellectual adventure.

The infinite is a concept that connects us to something larger than ourselves.

The problems of mathematics are a path to enlightenment.

The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought... The role that remains for the infinite is solely that of an idea, if one means by an idea a concept of reason which the mind can go beyond all experience and which completes the understanding of the world.

In mathematics there is no ignorabimus.

A mathematical theory is not to be considered complete until you have seen its proof.

The object of mathematics is the solution of problems.

Every mathematical problem that can be formulated is solvable.

The problems are the lifeblood of mathematics.

A mathematical proof is not a picture, but a chain of inferences.

The further a mathematical theory is developed, the more it becomes an aesthetic object.

Mathematics is not a deductive science, that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to make deductions. What you do is trial and error, experimentation, guesswork.

The finite can be understood only in terms of the infinite.

Mathematics is a game played according to certain simple rules with meaningless marks on paper, and the game is played by mathematicians.

The true method of mathematics is to make no method.

The infinite is the most powerful stimulus to the human mind.

A mathematical problem should be difficult enough to challenge us but not so difficult as to discourage us.

The whole of mathematics is nothing but a vast tautology.