20th-century Mathematician Quotes

Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.

Harold Davenport

Rationality of thought imposes a limit on a person's concept of his relation to the cosmos.

John Forbes Nash, Jr.

In planning the idea of decentralization must be connected with routines of linking plans of rather autonomous parts of the whole system. Here one can use a conditional separation of the system by means of fixing values of flows and parameters transmitted from one part to another. One can use an idea of sequential recomputation of the parameters, which was successfully developed by many authors for the scheme of Dantzig-Wolfe and for aggregative linear models.

Leonid Kantorovich

On foundations we believe in the reality of mathematics, but of course when philosophers attack us with their paradoxes we rush to hide behind formalism and say: "Mathematics is just a combination of meaningless symbols..."

Jean Dieudonné

Lately there have been complaints that the use of the magnitude scale is confusing, or at least the reporting of magnitudes in the newspapers 'confuses the public.

Charles Francis Richter

This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.

An idea is nothing, its implementation everything.

Alexander Kronrod

They used Akbar's principles to formulate a version of Islam that could peacefully co-exist with other religions (or so they claimed). An Emperor's Bequest to Islam, their joint 1,300-page doorstopper, spent twenty weeks on the New York Times bestseller list in hardcover alone. The fact that they remained practicing Muslims (albeit the liberal, wine-guzzling kind) put their message in high international demand.

Probably no branch of mathematics has experienced a more surprising growth than has... topology... Considered as a most specialized and abstract subject in the early 1920's, it is today [1938] an indispensable equipment for the investigation of modern mathematical theories.

Raymond Louis Wilder

A growing number of respectable scientists are defecting from the evolutionist camp.....moreover, for the most part these "experts" have abandoned Darwinism, not on the basis of religious faith or biblical persuasions, but on strictly scientific grounds, and in some instances, regretfully.

Papers should include more side remarks, open questions, and such. Very often, these are more interesting than the theorems actually proved. Alas, most people are afraid to admit that they don't know the answer to some question, and as a consequence they refrain from mentioning the question, even if it is a very natural one. What a pity! As for myself, I enjoy saying 'I do not know'.

Jean-Pierre Serre

They could but make the best of it, and went around with woebegone faces sadly complaining that on Mondays, Wednesdays and Fridays they must look on light as a wave; on Tuesdays, Thursdays and Saturdays, as a particle. On Sundays they simply prayed.

Banesh Hoffmann

At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate.

Faith is a response to evidence, not a rejoicing in the absence of evidence.

I do support direct action. I do not advocate or support violence.… Elections are not a viable means of ensuring democratic change in Russia. Therefore I do support using other methods to push for a change back towards democracy

Boris Berezovsky

The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.

What you do on a dinosaur expedition is you hike and look at the ground. You find bones sticking out of the dirt and, once you see something, you dig.

Nathan Myhrvold

In the history of the concept of number, number has been adjective (three cows, three monads) and noun (three, pure and simple), and now.... number seems to be more like a verb (to triple).

Axiomatization is what one does last, it's rubbish. It's the hygiene of mathematics, axiomatization.

Cybernetics is the study of systems and processes that interact with themselves and produce themselves from themselves.

Alekhine is a poet who creates a work of art out of something that would hardly inspire another man to send home a picture post card.

First they said my [cyclol] structure [of proteins] couldn't exist. Then when it was found in Nature they said it couldn't be synthesized in a laboratory. Then when it was synthesized they said it wasn't important anyway.

Dorothy Maud Wrinch

Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?

A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.

Mathematics is a product - a discovery - of the human mind. It enables us to see the incredible, simple, elegant, beautiful, ordered structure that lies beneath the universe we live in. It is one of the greatest creations of mankind - if it is not indeed the greatest.