Richard Courant Quotes & Sayings

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

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

Mathematical objects states "only the relationships between mathematically 'undefined objects' and the rules governing operations with them." It doesn't matter what mathematical things are: it's what they do that counts. Thus mathematics hovers uneasily between the real and the not-real; its meaning does not reside in formal abstractions, but neither is it tangible. This may cause problems for philosophers who like tidy categories, but it is the great strength of mathematics - what — 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

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

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

Calculus is the outcome of a dramatic intellectual struggle which has lasted for twenty-five hundred years. — Richard Courant

Euler - The unsurpassed master of analytic invention. — Richard Courant