Richard Courant Quotes

7 Sourced Quotes

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

Richard Courant
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.

Richard Courant
Starting in the seventeenth century, the general theory of extreme values - maxima and minima - has become one of the systematic integrating principles of science.

Richard Courant
With an absurd oversimplification, the 'invention' of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part.

Richard Courant
Empirical evidence can never establish mathematical existence—nor can the mathematician's demand for existence be dismissed by the physicist as useless rigor. Only a mathematical existence proof can ensure that the mathematical description of a physical phenomenon is meaningful.

Richard Courant
It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together.

Richard Courant
Mathematics must take its motivation from concrete specific substance and aim again at some layer of "reality." The flight into abstraction must be something more than a mere escape; start from the ground and reentry are both indispensable, even if the same pilot cannot handle all phases of the trajectory.

Richard Courant