„When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.“

As quoted in John von Neumann, 1903-1957 (1958) by John C. Oxtoby and B. J. Pettis, p. 128

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

Citações relacionadas

Richard Feynman photo

„Mathematics is not just a language. Mathematics is a language plus reasoning.“

—  Richard Feynman, livro The Character of Physical Law

Fonte: The Character of Physical Law (1965), chapter 2, “The Relation of Mathematics to Physics”
Contexto: Mathematics is not just a language. Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning. It's, in fact, a big collection of the results of some person's careful thought and reasoning. By mathematics, it is possible to connect one statement to another.

Daniel Alan Vallero photo
Josiah Willard Gibbs photo

„Mathematics is a language.“

—  Josiah Willard Gibbs physicist 1839 - 1903

At a Yale faculty meeting, during a discussion of language requirements in the undergraduate curriculum. Quoted in Muriel Rukeyser, Willard Gibbs (Garden City, NY: Doubleday, Doran & Co., 1942), p. 280.

Albert Einstein photo
Thomas Merton photo

„There is a logic of language and a logic of mathematics.“

—  Thomas Merton Priest and author 1915 - 1968

Contexto: There is a logic of language and a logic of mathematics. The former is supple and lifelike, it follows our experience. The latter is abstract and rigid, more ideal. The latter is perfectly necessary, perfectly reliable: the former is only sometimes reliable and hardly ever systematic. But the logic of mathematics achieves necessity at the expense of living truth, it is less real than the other, although more certain. It achieves certainty by a flight from the concrete into abstraction. Doubtless, to an idealist, this would seem to be a more perfect reality. I am not an idealist. The logic of the poet — that is, the logic of language or the experience itself — develops the way a living organism grows: it spreads out towards what it loves, and is heliotropic, like a plant.

Eugene Paul Wigner photo

„The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.“

—  Eugene Paul Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences

"The Unreasonable Effectiveness of Mathematics in the Natural Sciences," Communications in Pure and Applied Mathematics, February 1960, final sentence.

R. G. Collingwood photo
Caterina Davinio photo
Benoît Mandelbrot photo

„Being a language, mathematics may be used not only to inform but also, among other things, to seduce.“

—  Benoît Mandelbrot Polish-born, French and American mathematician 1924 - 2010

Fractals : Form, chance and dimension (1977)

G. H. Hardy photo
Bertrand Russell photo

„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.“

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

Fonte: 1910s, Mysticism and Logic and Other Essays http://archive.org/stream/mysticism00russuoft/mysticism00russuoft_djvu.txt (1918), Ch. 5: Mathematics and the Metaphysicians

Kenneth E. Iverson photo
Kenneth E. Iverson photo
Robert Chambers (publisher, born 1802) photo
Giuseppe Peano photo

„Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.“

—  Giuseppe Peano Italian mathematician 1858 - 1932

Arithmetices principia, nova methodo exposita [The Principles of Arithmetic, presented by a new method] (1889)
Original: (la) Quaestiones, quae ad mathematicae fundamenta pertinent, etsi hisce temporibus a multis tractatae, satisfacienti solutione et adhuc carent. Hic difficultas maxime en sermonis ambiguitate oritur. Quare summi interest verba ipsa, quibus utimur attente perpendere.

Tópicos relacionados