20th-century Mathematician Quotes

Proof, being the highest level of reproduction activity, has an important interiorization aspect: as Yuri Manin stresses in his book Provable and Unprovable, a proof becomes such only after it is accepted (as the result of a highly rigorous process)... Manin describes the act of acceptance as a social act; however, the importance of its personal, psychological component can hardly be overestimated.

The unity of mathematics... is often invoked in a rather imprecise way.

Science is reasoning; reasoning is mathematics; and, therefore, science is mathematics.

Mathematicians makes natural questions precise.

Richard E. Bellman
Richard E. Bellman
A quadratic function, ambitious, Said, "It's not only wrong, but it vicious. It's surely no sin To have max. and min.; To limit me so is malicious."

In dealing with academics, it is absolutely superb to be able to say you're a mathematician! Nobody dares to say mathematics is not important or not significant... No discipline surpasses mathematics in pure academic prestige.

There is an explicit way to define what explicit is.

Noga Alon
Noga Alon
It is a paradox in mathematics and physics that we have no good model for the teaching of models.

Any applied mathematicians — any engineer using mathematics — works sometimes more and sometimes less mathematically. When he is most mathematical he makes least appeal to experience.

Chandler Davis
Chandler Davis
In retrospect all great ideas take on a certain simplicity and inevitability, partly because they shape the whole subsequent development of the subject.

Three shifts can be detected over time in the understanding of mathematics itself. One is a shift from completeness to incompleteness, another from certainty to conjecture, and a third from absolutism to relativity.

The Riemann Hypothesis (RH) has been around for more than 140 years, and yet now is arguably the most exciting time in its history to be working on RH. Recent years have seen an explosion of research stemming from the confluence of several areas of mathematics and physics.

I am always surprised when a young man tells me he wants to work at cosmology; I think of cosmology as something that happens to one, not something one can choose.

Everybody knows that mathematics is about Miracles, only mathematicians have a name for them: Theorems.

Mathematics belongs to man, not to God. We are not interested in properties of the positive integers that have no descriptive meaning for finite man. When a man proves a positive integer to exist, he should show how to find it. If God has mathematics of his own that need to be done, let him do it himself.