The Mathematical Experience |
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Page 40
... thing is a proof , I have to decide who the experts are . What does that have to do with proving things ? I.M .: Student : I.M .: No , no . There's nothing subjective about it ! Everybody knows what a proof is . Just read some books ...
... thing is a proof , I have to decide who the experts are . What does that have to do with proving things ? I.M .: Student : I.M .: No , no . There's nothing subjective about it ! Everybody knows what a proof is . Just read some books ...
Page 358
... thing . In an analogous way , mathematics is one single thing . The Platonist , formalist and constructivist views of it are believed because each corresponds to a certain view of it , a view from a certain angle , or an examination ...
... thing . In an analogous way , mathematics is one single thing . The Platonist , formalist and constructivist views of it are believed because each corresponds to a certain view of it , a view from a certain angle , or an examination ...
Page 407
... thing to the most ancient . Arithmetic and geometry came from the same place as ho- motopy theory — from the human brain . Every day , mil- lions of us labor to instil these into other human brains . Fact 2 is that these things we bring ...
... thing to the most ancient . Arithmetic and geometry came from the same place as ho- motopy theory — from the human brain . Every day , mil- lions of us labor to instil these into other human brains . Fact 2 is that these things we bring ...
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