# „Mathematics… is the set of all possible self-consistent structures“

## Citações relacionadas

### „Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick.“

— Martin Gardner recreational mathematician and philosopher 1914 - 2010

Mathematics, Magic, and Mystery https://books.google.com/books?id=-kOFBQAAQBAJ&pg=PR11#v=onepage&q=%22Mathematical%20magic%20combines%22%23v%3Dsnippet&f=false (1956), p. ix

### „Before a man can successfully plan a structure… he must study, from every possible angle, the ultimate purpose of his building. Attention must be directed to the basic structural concept before the mathematical process of calculation is undertaken.“

— Eduardo Torroja Spanish architect 1899 - 1961

Philosophy of Structures (1958), p, 125

### „The rules of logic are to mathematics what those of structure are to architecture.“

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

1900s, "The Study of Mathematics" (November 1907)

### „A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…“

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

As quoted in a review of The Fractal Geometry of Nature by J. W. Cannon in The American Mathematical Monthly, Vol. 91, No. 9 (November 1984), p. 594

### „The art of doing mathematics consists in finding that special case which contains all the germs of generality.“

— David Hilbert German prominent mathematician 1862 - 1943

Quoted in Constance Reid, "Hilbert" (1970)

### „Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition.“

— Joshua Girling Fitch British educationalist 1824 - 1903

The Fourth Dimension simply Explained. (New York, 1910), p. 58. Reported in Moritz (1914); Also cited in: Howard Eves (2012), Foundations and Fundamental Concepts of Mathematics, p. 167

### „(Game theory is) essentially a structural theory. It uncovers the logical structure of a great variety of conflict situations and describes this structure in mathematical terms. Sometimes the logical structure of a conflict situation admits rational decisions; sometimes it does not.“

— Anatol Rapoport Russian-born American mathematical psychologist 1911 - 2007

1960s, Prisoner's dilemma: A study in conflict and cooperation (1965), p. 196

### „Mathematics is merely a convenient tool by which the designer determines the physical proportions and details of a planned structure in order to transform his ideas… to the actuality of a finished structure.“

— Eduardo Torroja Spanish architect 1899 - 1961

Philosophy of Structures (1958), p, 125

### „It is simplest to think of mathematics as the catalogue of all possible patterns. …When viewed in this way, it is inevitable that the world is described by mathematics. …In many ways the search for a Theory of Everything is a manifestation of a faith that this compression goes all the way down to the bedrock of reality…“

— John D. Barrow British scientist 1952

New Theories of Everything (2007)

### „The technical literature on structural engineering abounds with theoretical works of a mathematical nature, but few publications are concerned with the various kinds of structures or the fundamental reasons for their existence.“

— Eduardo Torroja Spanish architect 1899 - 1961

Philosophy of Structures (1958), p, 125

### „The very possibility of the science of mathematics seems an insoluble contradiction.“

— Henri Poincaré, livro Science and Hypothesis

Science and Hypothesis (1901), Context: The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A!... Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive?... If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.<!--pp.5-6
Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead

### „As a mathematical object, the constitution is maximally simple, consistent, necessarily incomplete, and interpretable as a model of natural law. Political authority is allocated solely to serve the constitution. There are no authorities which are not overseen, within nonlinear structures. Constitutional language is formally constructed to eliminate all ambiguity and to be processed algorithmically. Democratic elements, along with official discretion, and legal judgment, is incorporated reluctantly, minimized in principle, and gradually eliminated through incremental formal improvement. Argument defers to mathematical expertise. Politics is a disease that the constitution is designed to cure.“

— Nick Land British philosopher 1962

"A Republic, If You Can Keep It" https://web.archive.org/web/20140327090001/http://www.thatsmags.com/shanghai/articles/12321 (2013) (original emphasis)

### „Not all the geometrical structures are "equal". It would seem that the riemannian and complex structures, with their contacts with other fields of mathematics and with their richness in results, should occupy a central position in differential geometry. A unifying idea is the notion of a G-structure, which is the modern version of an equivalence problem first emphasized and exploited in its various special cases by Elie Cartan.“

— Shiing-Shen Chern mathematician (1911–2004), born in China and later acquiring U.S. citizenship; made fundamental contributions to differ… 1911 - 2004

### „If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.“

— George Dantzig American mathematician 1914 - 2005

Linear programming and extensions (1963), p. 2

### „Let me also remind you that zero, like all of mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, mathematics is a fairyland where ideal and fictional objects are possible.“

— Doron Zeilberger Israeli mathematician 1950

" " (nothing) published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger