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Philosophy of Mathematics: A Contemporary Introduction to the World of…

av James Robert Brown

MedlemmarRecensionerPopularitetGenomsnittligt betygDiskussioner
793255,487 (4)Ingen/inga
In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?   This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.… (mer)
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    Bevis och motbevis : matematiska upptäckters logik av Imre Lakatos (freetrader)
    freetrader: Showing how the experimental view on mathematics works
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Visar 3 av 3
Fantastic book. Fascinating questions are raised and addressed, in an easy to read and convincing style. If the topic interests you, this is a good place to start. ( )
  aront | Apr 14, 2018 |
A nice read and rather in line with some of the stuff i lately read about it. Brown argues for a more experimental view of mathematics, where mathematicians are not the people rigorously proofing everything, but the ones who contribute to our understanding of mathematics. Pictures, conjectures, intuition etc playing an essential role. The nice thing is that a lot of great mathematicians seem to agree with this view. It is contrary to the 'proofs only' approach that i encountered when studying math, and which at that time felt like a mathematicians form of machismo.
Interesting read in this perspective is Ulam's Adventures of a mathematician. ( )
  freetrader | Jan 29, 2010 |
A rather unusual account of the foundations of mathematics; Brown covers all of the traditional schools (platonism, logicism, formalism, constructivism, intuitionism), but stands out by taking a stand for a modified form of platonism that's quite attractive. One of his concerns is the status of diagrams in proofs, and he makes interesting observations. It seems he does not know Peirce very well (he's consistently misspelt Pierce); Brown could have found some helpful tools and concepts in Peirce's writing. ( )
  mschaefer | Sep 3, 2008 |
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In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?   This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.

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