„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

Última atualização 22 de Maio de 2020. História
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John von Neumann
1903 - 1957
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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.“

—  Benjamin Peirce, Linear Associative Algebra

§ 2.
Linear Associative Algebra (1882)
Contexto: 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.

„During this century mathematics has been transformed…“

—  George Frederick James Temple British mathematician 1901 - 1992

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 British scientist 1952

Introduction
Cosmic Imagery: Key Images in the History of Science (2008)
Contexto: 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.

Louisa May Alcott photo
Frank P. Ramsey photo
Robert Musil photo
Augustus De Morgan photo
George Boole photo

„You will feel interested to know the fate of my mathematical speculations in Cambridge. One of the papers is already printed in the Mathematical Journal. Another, which I sent a short time ago, has been very favourably received, and will shortly be printed together with one I had previously sent.“

—  George Boole English mathematician, philosopher and logician 1815 - 1864

George Boole in letter to a friend, 1840, cited in: R. H. Hutton, " Professor Boole http://books.google.com/books?id=pfMEAAAAQAAJ&pg=PA147," in: The British Quarterly Review. (1866), p. 147; Cited in Des MacHale. George Boole: his life and work, Boole Press, 1985. p. 52
1840s

G. H. Hardy photo
Novalis photo

„Pure mathematics is religion.“

—  Novalis, livro Blüthenstaub

Reine Mathematik ist Religion.
Blüthenstaub (1798), Unsequenced

Johannes Kepler photo
G. H. Hardy photo
Stanislaw Ulam photo

„What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else.“

—  Stanislaw Ulam Polish-American mathematician 1909 - 1984

Fonte: Adventures of a Mathematician - Third Edition (1991), Chapter 15, Random Reflections on Mathematics and Science, p. 273-274

Bertrand Russell photo

„Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing.“

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

Recent Work on the Principles of Mathematics, published in International Monthly, Vol. 4 (1901), later published as "Mathematics and the Metaphysicians" in Mysticism and Logic and Other Essays (1917)
1900s
Contexto: Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. Both these points would belong to applied mathematics. We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.

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„Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established.“

—  Georg Cantor mathematician, inventor of set theory 1845 - 1918

From Kant to Hilbert (1996)
Contexto: Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established. In particular, in the introduction of new numbers, it is only obligated to give definitions of them which will bestow such a determinacy and, in certain circumstances, such a relationship to the other numbers that they can in any given instance be precisely distinguished. As soon as a number satisfies all these conditions, it can and must be regarded in mathematics as existent and real.

Hermann Weyl photo
Albert Einstein photo

„Pure mathematics is in its way the poetry of logical ideas.“

—  Albert Einstein German-born physicist and founder of the theory of relativity 1879 - 1955

1930s, Obituary for Emmy Noether (1935)
Contexto: Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

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