„Only by a study of the development of mathematics can its contemporary significance be understood.“

100 Years of Mathematics: a Personal Viewpoint (1981)
Contexto: The professional mathematician can scarcely avoid specialization and needs to transcend his private interests and take a wide synoptic view of the whole landscape of contemporary mathematics. His scientific colleagues are continually seeking enlightenment on the relevance of mathematical abstractions. The undergraduate needs a guidebook to the topography of the immense and expanding world of mathematics. There seems to be only one way to satisfy these varied interests... a concise historical account of the main currents... Only by a study of the development of mathematics can its contemporary significance be understood.

George Temple photo
George Temple
1901 - 1992

Citações relacionadas

Freeman Dyson photo
Georg Cantor photo
Hermann Weyl photo
A. Wayne Wymore photo
Paul Dirac photo

„Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future.“

—  Paul Dirac theoretical physicist 1902 - 1984

The Evolution of the Physicist's Picture of Nature (1963)
Contexto: Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future. A good many people are working on the mathematical basis of quantum theory, trying to understand the theory better and to make it more powerful and more beautiful. If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them.

Edgar Degas photo

„I always urged my contemporaries to look for interest and inspiration to the development and study of drawing, but they would not listen. They thought the road to salvation lay by the way of colour.“

—  Edgar Degas French artist 1834 - 1917

Quote of Degas, as cited by Walter Sickert, in 'Post-Impressionism and Cubism', Pall Mall Gazette (1914-03-11).
According to Sickert, Degas had said this quote to him in 1885
1876 - 1895

Hans Reichenbach photo
Lucio Russo photo

„Euclid … manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.“

—  Lucio Russo Italian historian and scientist 1944

2.4, "Discrete Mathematics and the Notion of Infinity", p. 45
The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn (2004)

Norbert Wiener photo
Rollo May photo

„I propose that the aim of education is exactly the opposite, namely, the widening and deepening of consciousness. To the extent that education can help the student develop sensitivity, depth of perception, and above all the capacity to perceive significant forms in what he is studying, it will be developing at the same time the student's capacity to deal with anxiety constructively.“

—  Rollo May US psychiatrist 1909 - 1994

Fonte: Psychology and the Human Dilemma (1967), p. 50
Contexto: The overemphasis on the Baconian doctrine of knowledge as power, and the accompanying concern with gaining power over nature as well as over ourselves in the sense of treating ourself as objects to be manipulated rather than human beings whose aim is to expand in meaningful living, have resulted in the invalidation of the self. This tends to shrink the individual's consciousness, to block off his awareness, and thus play into … unconstructive anxiety … I propose that the aim of education is exactly the opposite, namely, the widening and deepening of consciousness. To the extent that education can help the student develop sensitivity, depth of perception, and above all the capacity to perceive significant forms in what he is studying, it will be developing at the same time the student's capacity to deal with anxiety constructively.

Bertrand Russell photo

„Only mathematics and mathematical logic can say as little as the physicist means to say.“

—  Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970

The Scientific Outlook (1931)
1930s
Contexto: Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

Paul A. Samuelson photo
Alfred North Whitehead photo
Carl Friedrich Gauss photo

„The study of Euler's works will remain the best school for the different fields of mathematics and nothing else can replace it.“

—  Carl Friedrich Gauss German mathematician and physical scientist 1777 - 1855

As quoted by Louise Grinstein, Sally I. Lipsey, Encyclopedia of Mathematics Education (2001) p. 235.

Martin David Kruskal photo

„Origami helps in the study of mathematics and science in many ways. … Using origami anyone can become a scientific experimenter with no fuss.“

—  Martin David Kruskal American mathematician 1925 - 2006

at the AAAS meeting: Mathematics and Science of Origami: Visualize the Possibilities, February 15, 2002, as quoted by Science Daily Origami Helps Scientists Solve Problems http://www.sciencedaily.com/releases/2002/02/020219080203.htm, February 21, 2002.

Kwame Nkrumah photo
John Von Neumann photo
Norbert Elias photo
Vladimir I. Arnold photo

„At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering.“

—  Vladimir I. Arnold Russian mathematician 1937 - 2010

"Will Mathematics Survive? Report on the Zurich Congress" in The Mathematical Intelligencer, Vol. 17, no. 3 (1995), pp. 6–10.
Contexto: At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering. This principle quickly led mathematicians to break from physics and to separate from all other sciences. In the eyes of all normal people, they were transformed into a sinister priestly caste... Bizarre questions like Fermat's problem or problems on sums of prime numbers were elevated to supposedly central problems of mathematics.

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