The Mathematical Experience |
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Page 114
... abstract . This is certainly spoken like a modern scientist , and one wonders whether this spirit is the imposition of a modern translator who renders " big " as " concrete " and " fine " as " abstract . " But I think not , for in the ...
... abstract . This is certainly spoken like a modern scientist , and one wonders whether this spirit is the imposition of a modern translator who renders " big " as " concrete " and " fine " as " abstract . " But I think not , for in the ...
Page 116
... abstract graph . ( See Chapter 4 , Abstraction as Ex- traction . ) With respect to the current trend of extreme abstrac- tion , the mathematical world finds itself divided . Some say that while abstraction is very useful , indeed ...
... abstract graph . ( See Chapter 4 , Abstraction as Ex- traction . ) With respect to the current trend of extreme abstrac- tion , the mathematical world finds itself divided . Some say that while abstraction is very useful , indeed ...
Page 130
... abstract numbers , existing , apparently , in isola- tion from birds or oranges . " Arithmetic , " says Plato ( Republic VII.525 ) , “ has a very great and elevating effect , compelling the soul to reason about abstract number , and ...
... abstract numbers , existing , apparently , in isola- tion from birds or oranges . " Arithmetic , " says Plato ( Republic VII.525 ) , “ has a very great and elevating effect , compelling the soul to reason about abstract number , and ...
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