The Mathematical Experience |
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Page 81
... considered a worthy goal to establish this theory without depending on the use of complex numbers . When this goal was finally achieved , then the utility of complex variable in number theory had changed . Time may bring about changes ...
... considered a worthy goal to establish this theory without depending on the use of complex numbers . When this goal was finally achieved , then the utility of complex variable in number theory had changed . Time may bring about changes ...
Page 192
... considered a high point within the framework of classical algebraized theory of numbers . 6. The difference in tone between this and the previous formulation is intense . Here we have a complete rewriting of the theorem under the ...
... considered a high point within the framework of classical algebraized theory of numbers . 6. The difference in tone between this and the previous formulation is intense . Here we have a complete rewriting of the theorem under the ...
Page 334
... considered meaningful , may not be said to exist , unless they are given by a construction , in finitely many steps , starting from the natural numbers . It is not sufficient to show that the assumption of nonexistence would lead to a ...
... considered meaningful , may not be said to exist , unless they are given by a construction , in finitely many steps , starting from the natural numbers . It is not sufficient to show that the assumption of nonexistence would lead to a ...
Other editions - View all
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience: Study Edition Philip J. Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 1995 |
Common terms and phrases
abstract aesthetic algebra algorithmic analysis analytic answer applications argument arithmetic asserts axiom of choice Bibliography calculus called century circle complex conjecture construct continuum hypothesis course definition differential equations elements ematics Euclid Euclidean geometry Euler example existence experience fact figure finite formal language formalist formula Fourier Fourier series function Further Readings G. H. Hardy Hilbert human hypercube hypersquares idea ideal infinite set infinitesimal infinity integers intuition knowledge Lakatos logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers non-Euclidean geometry non-Riemannian nonstandard notion number theory parallel postulate philosophy of mathematics physical Platonism Platonist possible postulate prime number prime number theorem problem proof proved question real numbers reason restricted set theory result rigorous sense solution square statement straight line symbols theorem thing tion triangle true truth universe words zero