„The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.“

As quoted in Bigeometric Calculus: A System with a Scale-Free Derivative (1983) by Michael Grossman, and in Single Variable Calculus (1994) by James Stewart.

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

„It is upon the foundation of this general principle, that I purpose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of Mathematical Analysis,“

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

Fonte: 1840s, The Mathematical Analysis of Logic, 1847, p. iii
Contexto: That to the existing forms of Analysis a quantitative interpretation is assigned, is the result of the circumstances by which those forms were determined, and is not to be construed into a universal condition of Analysis. It is upon the foundation of this general principle, that I purpose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of Mathematical Analysis, regardless that in its object and in its instruments it must at present stand alone.

Edmund Landau photo

„I will ask of you only the ability to read English and to think logically—no high school mathematics, and certainly no higher mathematics.“

—  Edmund Landau German Jewish mathematician 1877 - 1938

Grundlagen der Analysis [Foundations of Analysis] (1930) Preface for the Student, as quoted by Eli Maor, Trigonometric Delights (2013)

John Hall photo

„We can no more have exact religious thinking without theology, than exact mensuration and astronomy without mathematics, or exact iron-making without chemistry“

—  John Hall Presbyterian pastor from Northern Ireland in New York, died 1898 1829 - 1898

Fonte: Dictionary of Burning Words of Brilliant Writers (1895), P. 580.

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.

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.

Bertrand Russell photo
Bernard Le Bovier de Fontenelle photo
Paul Karl Feyerabend photo
A. Wayne Wymore photo

„[The process of system design is]… consisting of the development of a sequence of mathematical models of systems, each one more detailed than the last.“

—  A. Wayne Wymore American mathematician 1927 - 2011

A. Wayne Wymore (1970) Systems Engineering Methodology. Department of Systems Engineering, The University of Arizona, p. 14/2; As cited in: J.C. Heckman (1973) Locating traveler support facilities along the interstate system--a simulation using general systems theory. p. 43.

Richard Courant 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

„The great advances in mathematics have not been made by logic but by creative imagination.“

—  George Frederick James Temple British mathematician 1901 - 1992

100 Years of Mathematics: a Personal Viewpoint (1981)
Contexto: Logical analysis is indispensable for an examination of the strength of a mathematical structure, but it is useless for its conception and design. The great advances in mathematics have not been made by logic but by creative imagination.

Auguste Comte photo

„Mathematical Analysis is… the true rational basis of the whole system of our positive knowledge.“

—  Auguste Comte French philosopher 1798 - 1857

Bk. 1, chap. 1; as cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book https://archive.org/stream/memorabiliamathe00moriiala#page/81/mode/2up, (1914), p. 224
System of positive polity (1852)

Bertrand Russell photo

„The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age“

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

Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 5
1900s
Contexto: The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself.

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