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by Phillip J. Davis,Reuben Hersh
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Mathematics
  • Author:
    Phillip J. Davis,Reuben Hersh
  • ISBN:
    0395929687
  • ISBN13:
    978-0395929681
  • Genre:
  • Publisher:
    Mariner Books; Reprint edition (January 14, 1999)
  • Pages:
    464 pages
  • Subcategory:
    Mathematics
  • Language:
  • FB2 format
    1108 kb
  • ePUB format
    1847 kb
  • DJVU format
    1827 kb
  • Rating:
    4.6
  • Votes:
    976
  • Formats:
    txt doc lit azw


Philip Davis and Reuben Hersh discuss everything from the nature of proof to the Euclid myth, and mathematical aesthetics to non-Cantorian set theory.

Philip Davis and Reuben Hersh discuss everything from the nature of proof to the Euclid myth, and mathematical aesthetics to non-Cantorian set theory. They make a convincing case for the idea that mathematics is not about eternal reality, but comprises "true facts about imaginary objects" and belongs among the human sciences.

Philip J Davis, Reuben Hersh. This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities. Издательство: Birkhäuser.

The Mathematical Experience (1981) is a book by Philip J. Davis and Reuben Hersh that discusses the practice of modern mathematics from a historical and philosophical perspective. The book discusses the psychology of mathematicians, and gives examples of famous proofs and outstanding problems. It goes on to speculate about what a proof really means, in relationship to actual truth. Other topics include mathematics in education and some of the math that occurs in computer science.

The Mathematical Experience is a very interesting read – it provides a highly personal tour through aspects of mathematics, its history, its philosophy, and its relationship with the ‘real’ world. Winner of the 1983 National Book Award, The Mathematical Experience presented a highly insightful overview of mathematics that effectively conveyed its power and beauty to a large audience of mathematicians and non-mathematicians alike.

Authors: Davis, Philip, Hersh, Reuben, Marchisotto, Elena Anne. This is an unusual book, being more a book about mathematics than a mathematics book. I really enjoyed reading The Mathematical Experience and would recommend it for college and personal libraries

Authors: Davis, Philip, Hersh, Reuben, Marchisotto, Elena Anne. I really enjoyed reading The Mathematical Experience and would recommend it for college and personal libraries. Richard J. Wilders, The Mathematical Association of America, March, 2012).

Philip Davis and Reuben Hersh discuss everything from the nature of proof to the Euclid myth, and mathematical . In his introduction to The Mathematical Experience, Gian-Carlo Rota notes that instead, "a mathematician's work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof. is more often than not a way of making sure that our minds are not playing tricks.

The Mathematical Experience book. Am heavily into "The Prime Number Theorem" chapter. Am getting some new insights.

Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations

Where is Mathematics? The Mathematical Community. The Ideal Mathematician. 1868 and 1979 Compared. Varieties of Mathematical Experience. The Current Individual and Collective Consciousness.

Where is Mathematics? The Mathematical Community. A Physicist Looks at Mathematics.

This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

AnnyMars
This is ultimately a book on the philosophy of mathematics. Rather than a tedious and dry slog though, the authors use a very broad array of mathematical vignettes - often only a page or two long - to probe into various aspects of mathematics and the activity of doing mathematics in order to illuminate to the reader the position they ultimately present; namely, that mathematics occupies a third philosophical category alongside those of physical reality and subjective reality. For them, "mathematics is an objective reality that is neither subjective nor physical. It is an ideal (i.e., nonphysical) reality that is objective (external to the consciousness of any one person)." This is explicitly not Platonism ("mathematics is not the study of an ideal, preexisting nontemporal reality"); instead, mathematics is a free creation of the mind, and they consider the meaning of mathematics "is to be found in the shared understanding of human beings, not in an external nonhuman reality", and go on to say "in this respect, mathematics is similar to an ideology, a religion, or an art form". What makes mathematics unique from these other areas is "its science-like quality", whereby the ideal nature of the objects of study in mathematics render its conclusions "compelling" and creating "facts" about this third philosophical category.

Wherever one stands on this this particular philosophy, the book can be read on multiple levels without agreeing with the philosophy. The short vignettes can be read as enjoyable interesting mathematical and historical snippets, each independent of the other. It can be read as an exposition of the human activity which comprises mathematical investigations and discoveries (or are they creations?). Finally, it can be read as probes into the philosophy and foundations of mathematics.

A fair bit of mathematical knowledge (undergrad/grad-level) and some history of mathematics is recommended, and an understanding of philosophy of mathematics and FOM would be helpful if one wants to get the most out of this book. However, anyone with a motivated interest in mathematics should find this book worthwhile.
Malahelm
As an aspiring mathematican I found this book both very inspiring and ......... I had, like many mathematicians, a view on mathematics as just a formalist game with symbols and abstract concepts before I read this book. However, the book challenges this view, and portraits Mathematics as a fallible science, in which the mathematician's role is not only the toying with symbols, but also the invention of mathematics. And that's a hard process: guessing, wishful thinking, and so on.

After I read this book, I have been trying to be a little more Platonist than I used to.
Gelgen
This is a book I read through and return to again and again. It is truly illuminating about mathematics and the philosophy of mathematics (at least for this chemist).
asAS
A very inytoduction to mathematics field,easy and interesting to read for anybody who likes to know the relations of mathematics with his history,developments,and other related fields.And over all to know what is the mathematics in itself.
Painshade
The perfect book
WtePSeLNaGAyko
:)
Water
This book was recommended to me by my boyfriend. I teach high school math, so it seems like an ideal book for me. I haven't had a chance to read it yet, but maybe I can get to it during spring break.
This book is now fairly old, but overall it has aged well. This is written at an intermediate level--meaning too difficult for some novices and too simple for some mathematicians, but hopefully there is a takeaway for everyone. The book consists of somewhat loosely connected chapters, examining the purpose of modern mathematics and the underlying philosophical issues. In my experience most laymen have virtually no conception of what higher math is about--some vague (and incorrect) conception that it must be like their high school algebra classes, only bigger or harder. This is a book designed to fill the gap, though deeper (and a bit more philosophical) than many other books in the genre.

The highlight of the book in my opinion is the chapter "The Ideal Mathematician". This, taken alone, might be the best short piece I've read about the philosophy of mathematics. It describes the life of an imagined "Ideal Mathematician" specializing in "non-Riemannian hypersquares", and his struggles communicating his work to outsiders. The conversations are somewhat contrived for comic effect, but deep down it is close to the truth--most of our Ideal Mathematician's responses are what a typical competent math professor might say in the same situation. It's quite entertaining--as long as us mathematicians feel comfortable making fun of ourselves a bit.