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The meaning of pure mathematics

Journal of Philosophical Logic, 1989
There are two classical answers to the question what is the meaning of pure mathematics: (1) Formalism. Pure mathematics is a symbolic construction; it becomes meaningful only when it is applied to describe physical reality. (2) Platonism. Pure mathematics describes an ideal reality which exists independently of man.
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The Halting Probability Omega: Irreducible Complexity in Pure Mathematics

, 2006
.Some Gödel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information.
G. Chaitin
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Mathematical Models in Pure and Applied Mathematics

2020
The concepts of the mathematical model in pure and applied mathematics are analyzed, as well as the concepts of rigor proof and degree of confidence. The role of asymptotic estimations as basis for mathematical modeling is analyzed.
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On Pure and Applied Mathematics

2000
THE BASELINE between pure mathematics and applied mathematics was a feature of the work of the Los Alamos Laboratory from the very beginning. It was often necessary to introduce concepts and procedures that went beyond methods that had been used previously in engineering and technology. Some new things emerged: for one, the concepts and basic relations
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Algorithms in Pure Mathematics

2001
In this article, we will discuss algorithmic group theory from the point of view of pure mathematics. We will investigate some of the problems and show why many problems are accessible just for a few years. In algebra there are many problems, which are easy to state, sometimes even easy to prove, and where one might be surprised that there is no ...
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The Conception of Pure Mathematics as an Instrument in the Professionalization of Mathematics [PDF]

, 1981
J.D. Bernal characterized the growth of science during the first half of the 19th century by the following paradox: “At the time when science should have been most obviously connected with the development of the machine age, arose the idea of pure science”.
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Formal Conceptual Blending in the (Co-)Invention of (Pure) Mathematics

Concept Invention, 2018
D. Gómez-Ramírez, A. Smaill
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Areas, anti-derivatives, and adding up pieces: Definite integrals in pure mathematics and applied science contexts

, 2015
S. Jones
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Applied Versus Pure Mathematics

2019
This chapter is about the conflictual relations among pure and applied mathematical disciplines in the century from circa 1850 to 1950. It shows the historical variations associated with the ways in which boundaries were drawn in this period, and how, often under the influence of the political orientations of China in a global context, the focus upon ...
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Goethe’s Views on Pure Mathematics

The Germanic Review: Literature, Culture, Theory, 1956
(1956). Goethe’s Views on Pure Mathematics. The Germanic Review: Literature, Culture, Theory: Vol. 31, No. 1, pp. 49-69.
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