David Hilbert

If a man is a good mathematician, he will be a good lawyer, a good doctor, a good engineer.

The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than it.

Mathematics is the queen of the sciences and number theory is the queen of mathematics. She often deigns to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned by the connection of its parts.

The further a mathematical theory is developed, the more beautiful and elegant it becomes.

The object of mathematics is the discovery of the laws of the universe.

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.

Mathematics is a venture of the human spirit which has been more successful than any other.

The problems are not solved, but they are soluble.

If you want to be a mathematician, you must learn to be a good swimmer.

Mathematical rigor is a method of proof, not a definition of truth.

The only way to learn mathematics is to do mathematics.

The problems of mathematics are not isolated, but are connected with each other and with the problems of other sciences.

Logic is not a theory but a reflection of the world.

The value of a mathematical theory is not measured by its practical applications, but by its beauty and elegance.

The most important thing in mathematics is to ask the right questions.

If I had to choose between truth and beauty, I would choose beauty.

The future of mathematics lies in the hands of the young.

The problems of mathematics are not solved by force, but by thought.

The mathematician's world is a world of ideas, not of things.