“If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.”

As quoted in Proportions, Prices, and Planning (1970) by András Bródy

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely…" by John Von Neumann?
John Von Neumann photo
John Von Neumann 19
Hungarian-American mathematician and polymath 1903–1957

Related quotes

Frank P. Ramsey photo
Benjamin Peirce photo

“The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics.”

§ 2.
Linear Associative Algebra (1882)
Context: The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.

Louisa May Alcott photo
Jean Piaget photo

“If a baby really has no awareness of himself and is totally thing-directed and at the same time all his states of mind are projected onto things, our second paradox makes sense: on the one hand, thought in babies can be viewed as pure accommodation or exploratory movements, but on the other this very same thought is only one, long, completely autistic waking dream.”

Jean Piaget (1896–1980) Swiss psychologist, biologist, logician, philosopher & academic

The First Year of Life of the Child (1927), "The Egocentrism of the Child and the Solipsism of the Baby", as translated by Howard E. Gruber and J. Jacques Vonèche

“During this century mathematics has been transformed…”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

John D. Barrow photo

“Mathematics became an experimental subject. Individuals could follow previously intractable problems by simply watching what happened when they were programmed into a personal computer.”

John D. Barrow (1952–2020) British scientist

Introduction
Cosmic Imagery: Key Images in the History of Science (2008)
Context: Mathematics became an experimental subject. Individuals could follow previously intractable problems by simply watching what happened when they were programmed into a personal computer.... The PC revolution has made science more visual and more immediate.... by creating films of imaginary experiences of mathematical worlds.... Words are no longer enough.

“Since there is no such thing as complete knowledge of a subject, one is always working to improve one's reading, writing, etc., of a subject.”

Neil Postman (1931–2003) American writer and academic

Language Education in a Knowledge Context (1980)
Context: Since there is no such thing as complete knowledge of a subject, one is always working to improve one's reading, writing, etc., of a subject. As Thomas Henry Huxley said, "If a little knowledge is a dangerous thing, is there anyone who knows so much as to be out of danger?" …. The problems of learning to read or write are inexhaustible.

Nima Arkani-Hamed photo

“Whether in physics and mathematics or in the humanities, when something really finally works, it has a certain perfection to it, a feeling of inevitability, like it was so completely obvious all along, and it couldn't be any other way.”

Nima Arkani-Hamed (1972) American-Canadian physicist

[#qotd #quote of the day #IASIdeas, twitter.com, 12 July 2018, https://twitter.com/the_ias/status/1017439929985634304?lang=en] (9:05 AM)

Emil M. Cioran photo

“You really should come to the house — one of these days we might die without having seen each other again.”

Emil M. Cioran (1911–1995) Romanian philosopher and essayist

"Since we have to die in any case, what's the use of seeing each other again?"
Drawn and Quartered (1983)

Related topics