- Paperback: 368 pages
- Publisher: Oxford University Press; 1 edition (July 8, 1999)
- Language: English
- ISBN-10: 0195130871
- ISBN-13: 978-0195130874
- Product Dimensions: 9 x 1.1 x 6.1 inches
- Shipping Weight: 1.4 pounds (View shipping rates and policies)
- Average Customer Review: 4.1 out of 5 stars See all reviews (14 customer reviews)
- Amazon Best Sellers Rank: #697,627 in Books (See Top 100 in Books)
Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
To get the free app, enter your mobile phone number.
What Is Mathematics, Really? 1st Edition
Use the Amazon App to scan ISBNs and compare prices.
Frequently bought together
Customers who bought this item also bought
In What Is Mathematics, Really?, author Reuben Hersh proposes a philosophy of mathematics that he calls "humanism" and uses this philosophy to analyze age-old questions of proof, certainty, and invention versus discovery. He also surveys the history of the philosophy of math. Readers of all levels of mathematical experience will be stimulated by the fascinating and perspicacious discussions Hersh has to offer. --This text refers to an out of print or unavailable edition of this title.
From Library Journal
Hersh, mathematician and coauthor of The Mathematical Experience (1983), attempts to answer here the philosophical question, "What is mathematics?" Many practitioners think of themselves as "platonists," discovering truths about ideal, eternally existing, abstract objects. The principal alternative to this concept is the "formalist" notion that mathematics is a game in which theorems are developed logically, starting from a set of axioms chosen almost arbitrarily. Hersh's humanistic position is, in essence, that mathematics is what mathematicians do. This is hard to disagree with but does not really explain how the subject evolves. Many feel that all mathematics begins with real-world applications, from which we try to extract the common properties and thence create a universe of abstract objects that can reveal unexpected beauty. In this somewhat disjointed book, Hersh reviews the history of the philosophy of mathematics, discusses the major players, and convincingly sets forth his thesis while undermining those of the competitors. For academic collections.?Harold D. Shane, Baruch Coll., CUNY
Copyright 1997 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.
Browse award-winning titles. See more
If you are a seller for this product, would you like to suggest updates through seller support?
Top Customer Reviews
There are basically three philosophies of mathematics: Platonism, Formalism and Constructivism. Reuben Hersh proposes an alternative: Humanism. The three basic philosophies deal mainly with the problem of foundations and view mathematics as a source of indubitable truth. The problems with foundations (the paradoxes), the failure of Hilbert's program (Gödel's theorem) and recent controversial proofs, such as the Four Colour Theorem, breathe air to this new kind of philosophy, perhaps not so new, since we can find its origins already in Aristotle. The humanist philosophy looks at what mathematicians do. It is no so different from what other scientists do. Mathematics is fallible and corrigible and mathematical rigour varies with the ages(remember A. Wiles first proof of Fermat's conjecture, classical calculus infinitesimals or Pasch missing gap in Euclid's axioms). Mathematics is not so different from music. Music exists by some biological or physical manifestation, but it makes sense only as a mental and cultural entity. RH defines mathematics as "the study of the lawful, predictable, parts of the socio-conceptual world". Mathematics is part of our culture and history and mathematical ideas match our world for the same reason that our lungs match earth's atmosphere.
Solving problems and making up new ones is the essence of mathematics. It is the questions that drive mathematics. It is a pity that math teachers forget about this when they teach and professional mathematicians often forget it when they write their papers.
Is mathematics invented or discovered? It has been a long standing controversy subject of discussions such as Alain Connes and a French neurologist. Hersh thinks both. After you invent a new theory (example group theory) you must discover its properties (find, for example, how many simple finite groups exist). And you may have to invent a trick to discover the solution of a problem.
To sum up: this book a "dimythization" of mathematics. Mathematics is just a human endeavour,but a highly beautiful, interesting, sophisticated and applicable human endeavour.
"What Is Mathematics, Really?" is one of the most though-provoking books I've ever read. It has helped me to make progress on jurisprudential problems that I had formerly been attacking in largely fruitless ways.
The book thus filled a particular need for me. But I think anyone interested in intellectual history or the placing of math in context with other fields will find this book fascinating.
Most Recent Customer Reviews
and philosophical ideas are very well described and put in perspective especially on foundations of...Read more