Mathematics and Logic (Paperback)

by Mark Kac (Author), Stanislaw M. Ulam (Author)

Editorial Reviews

Product Description
Fascinating study considers the origins and nature of mathematics, its development and role in the history of scientific thinking, impact of high-speed computers, 20th-century changes in the foundations of mathematics and mathematical logic, mathematization of science and technology, much more. Compelling reading for mathematicians, physicists, students—anyone interested in the evolution of mathematical thought. 34 illustrations. 1968 edition.

Product Details

• Paperback: 192 pages
• Publisher: Dover Publications (May 1, 1992)
• Language: English
• ISBN-10: 0486670856
• ISBN-13: 978-0486670850
• Product Dimensions: 8 x 5.4 x 0.5 inches
• Shipping Weight: 7.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.8 out of 5 stars See all reviews (5 customer reviews)
• Amazon.com Sales Rank: #561,571 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

20 of 20 people found the following review helpful:

4.0 out of 5 stars Important and Useful but not Engaging, March 11, 2001

By	Neal Jameson "nealwj3" (Cambridge, MA United States) - See all my reviews (REAL NAME)

The book shows what the power of mathematics is, how it changes, and how it expands to new areas. Unlike books that aim to popularize math, the book does not pontificate a mystic view of the meaning of mathematics; rather, it gives a sober perspective of what has happened in mathematics and what can be expected of the field.

The book requires somewhat serious mathematical thinking.

A great strength of the book is the diverse mathematical concepts that it presents: homology groups, group theory, Turing machines, undecidability, Monte Carlo method. In a compact book, you learn a little about some important ideas in advanced mathematics.

Important!! This book is not written to popularize its subject matter, so it is different and definitely less entertaining than most popular science books.

12 of 12 people found the following review helpful:

5.0 out of 5 stars Excellent overview by two outstanding mathematicians, June 27, 2004

By	Marvin J. Greenberg (Berkeley, CA USA) - See all my reviews (REAL NAME)

The audience for ths book is people with background in mathematics. They teach many branches briefly with their examples in Chapter 1, but the presentation is at a fairly sophisticated level.

I found the historical and philosophical remarks very valuable, coming from authorities like these two men. Examples (slightly edited by me):

The great analysts of the 18th and 19th centuries (e.g., Newton, Leibniz, Bernoulli, Euler, Lagrange ...) had an almost unerring instinct for presenting valid results and plausible proofs without a firm basis in formal systems and without strict adherence to standards of logical rigor... Mathematical intuition in the hands of people of genius has such a clarity and unity that it anticipates special formalisms.

Mathematics is a science; it is also an art. The criteria of judgment in mathematics are always aesthetic, at least in part... One looks for `usefulness,' for `interest,' and also for `beauty.' Beauty is subjective, yet it is surprising that there is usually considerable agreement among mathematicians concerning aesthetic values.

It is a distinctive feature of mathematics that it can operate effectively and efficiently without defining its objects. Points, straight lines and planes are not defined... One need not know what things are so long as one knows what statements about them one is allowed to make [the axioms]... Other statements involving these undefined words can then be deduced by logic alone. This permits geometry to be taught to a blind man and even to a computer!

7 of 8 people found the following review helpful:

5.0 out of 5 stars A Classic of Popular Mathematics, July 28, 2001

By	R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews (REAL NAME)

With new mathematics growing wild in the trees in the new century, one should review those things that have given modern mathematics direction and flavor. This classic little book sits along side of Sawyer's " Prelude to Mathematics" as the go to books for basic understanding. To these books I have added an unlikely candidate " Elliptical Curves" by McKean and Moll. If one has these three books, he will have a crack in the dam of mathematics...