„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.“

Origine: Linear programming and extensions (1963), p. 2

Estratto da Wikiquote. Ultimo aggiornamento 03 Giugno 2021. Storia
George Dantzig
matematico e statistico statunitense 1914 - 2005

Citazioni simili

„Simulation is the use of models and/or the actual conditions of either the thing being modeled or the environment in which it operates, with the models or conditions in physical, mathematical, or some other form. The purpose of simulation is to explore the various results which might be obtained from the real system by subjecting the model to representative environments which are equivalent to, or in some way representative of, the situations it is desired to understand or investigate. Simulation may involve system hardware and the actual physical environment, or it may involve mathematical models subjected to mathematical forcing or disturbance functions representative of the systems conditions to be studied.“

—  Harold Chestnut American engineer 1917 - 2001

Origine: Systems Engineering Tools, (1965), p. 111 as cited in

„The Mathematical School; Although mathematical methods can be used by any school of management theory, and have been, I have chosen to group under a school those theorists who see management as a system of mathematical models and processes. Perhaps the most widely known group I arbitrarily so lump are the operations researchers or operations analysts, who have sometimes anointed themselves with the rather pretentious name of "management scientists." The abiding belief of this group is that, if management, or organization, or planning, or decision making is a logical process, it can be expressed in terms of mathematical symbols and relationships. The central approach of this school is the model, for it is through these devices that the problem is expressed in its basic relationships and in terms of selected goals or objectives.“

—  Harold Koontz 1909 - 1984

Origine: "The Management Theory Jungle," 1961, p. 181

„The accounting methods based on mathematical models, the use of computers for computations and information data processing make up only one part of the control mechanism, another part is the control structure.“

—  Leonid Kantorovich Russian mathematician 1912 - 1986

"Mathematics in Economics: Achievements, Difficulties, Perspectives," 1975

„Classical mechanics is mathematical not only in the sense that it makes use of mathematical terms and methods for abbreviating arguments which might, if necessary, also be expressed in the language of everyday speech; it is so also in the much more stringent sense that its basic concepts are mathematical concepts, that mechanics itself is a mathematics.“

—  Eduard Jan Dijksterhuis Dutch historian 1892 - 1965

Origine: The mechanization of the world picture, 1961, p. 499

„Only if mathematical rigor is adhered to, can systems problems be dealt with effectively, and so it is that the systems engineer must, at least, develop an appreciation for mathematical rigor if not also considerable mathematical competence.“

—  A. Wayne Wymore American mathematician 1927 - 2011

Origine: A Mathematical Theory of Systems Engineering (1967), p. 3.

„With the computer and programming languages, mathematics has newly-acquired tools, and its notation should be reviewed in the light of them. The computer may, in effect, be used as a patient, precise, and knowledgeable "native speaker" of mathematical notation.“

—  Kenneth E. Iverson Canadian computer scientist 1920 - 2004

Origine: Math for the Layman (1999), Ch. 10, §D

„The use of practically any computing technique itself raises a number of mathematical problems. There is thus a very considerable impact of computation on mathematics itself, and this may be expected to influence mathematical research to an increasing degree.“

—  George Forsythe Stanford University computer scientist 1917 - 1972

George Forsythe (1958) cited in: Computers and people Vol 23. (1974). p. 11 Pagina 11

„[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.

„There is no problem in all mathematics that cannot be solved by direct counting. But with the present implements of mathematics many operations can be performed in a few minutes which without mathematical methods would take a lifetime.“

—  Ernst Mach Austrian physicist and university educator 1838 - 1916

Origine: 19th century, Popular Scientific Lectures [McCormack] (Chicago, 1898), p. 197; On mathematics and counting.

„Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.“

—  David Deutsch, libro The Fabric of Reality

The Fabric of Reality (1997)

„Johann Herbart’s work on education and particularly mathematical psychology influenced me. I think mathematics is the pure instance of construct functioning—the model of human behaviour.“

—  George Kelly (psychologist) American psychologist and therapist 1905 - 1967

Attributed to George A. Kelly in Hinkle (1970, p. 91), as cited in: Fay Fransella and Robert A. Neimeyer. "George Alexander Kelly: The man and his theory." International handbook of personal construct psychology (2003): 21-31.

„A model may be pictorial, descriptive, qualitative, or generally approximate in nature, or it may be mathematical and quantitative in nature and reasonably precise.“

—  Harold Chestnut American engineer 1917 - 2001

Origine: Systems Engineering Tools, (1965), p. 108

„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

„If economic reality is actually so complex that it can only be described by complicated mathematical models that add epicycles to epicycles and externalities to externalities, then the reality should be simplified.“

—  Herman E. Daly American economist 1938

Origine: Steady-State Economics, 1977, p. 4

„The methods of mathematics are the main topic of the course, not a long list of finished mathematical results with such highly polished proofs that the poor student can only marvel at the results, with no hope of understanding how mathematics is actually created by practicing mathematicians.“

—  Richard Hamming American mathematician and information theorist 1915 - 1998

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

„We distinguish diagrammatic from sentential paper-and-pencil representations of information by developing alternative models of information-processing systems that are informationally equivalent and that can be characterized as sentential or diagrammatic. Sentential representations are sequential, like the propositions in a text. Diagrammatic representations are indexed by location in a plane. Diagrammatic representations also typically display information that is only implicit in sentential representations and that therefore has to be computed, sometimes at great cost, to make it explicit for use. We then contrast the computational efficiency of these representations for solving several. illustrative problems in mathematics and physics.“

—  Herbert A. Simon American political scientist, economist, sociologist, and psychologist 1916 - 2001

Origine: 1980s and later, "Why a diagram is (sometimes) worth ten thousand words," (1987), p. 65

„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
Contesto: 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.

„Computer Algebra Systems are NOT the Devil but the new MESSIAH that will take us out of the current utterly trivial phase of human-made mathematics into the much deeper semi-trivial computer-generated phase of future mathematics. Even more important, Computer Algebra Systems will turn out to be much more than just a `tool', since the methodology of computer-assisted and computer-generated research will rule in the future, and will make past mathematics seem like alchemy and astrology, or, at best, theology.“

—  Doron Zeilberger Israeli mathematician 1950

„Angling may be said to be so like the mathematics that it can never be fully learnt.“

—  Izaak Walton, libro The Compleat Angler