- Series: Very Short Introductions
- Paperback: 160 pages
- Publisher: Oxford University Press; 1st edition (October 2002)
- Language: English
- ISBN-10: 0192853619
- ISBN-13: 978-0192853615
- Product Dimensions: 7 x 0.4 x 4.2 inches
- Shipping Weight: 2.1 ounces (View shipping rates and policies)
- Average Customer Review: 49 customer reviews
- Amazon Best Sellers Rank: #72,342 in Books (See Top 100 in Books)
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Mathematics: A Very Short Introduction 1st Edition
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About the Author
Timothy Gowers is Rouse Ball Professor of Mathematics at Cambridge University and was a recipient of the Fields Medal for Mathematics, awarded for 'the most daring, profound and stimulating research done by young mathhematicians'.
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Top customer reviews
A clear explanation of how we can operate in higher dimensions; even though we can't imagine what it means to have 64 dimensions, we can still calculate similarly defined concepts as in 2 and 3 dimensions, such as lines, vertices, areas and so on. It, frankly, astonished me that we can discuss something what we can't imagine, based on strict logic ('abstract method').
I hold a belief, that a real professional in his field can explain any concept to a layman. That is what Timothy showed in his book- well structured, logically consistent presentation of the essence of mathematics. I had similar feelings after reading "A short introduction to Accounting".
For subject matter, mathematicians abstract certain features from the real world, creating simplified models that are easier to reason about. They also extend established areas to new domains, e.g. space to more than three dimensions.
Regarding epistemology, mathematicians frame conjectures that are either proved from axioms, disproved by counter-example, or remain open questions. Proofs can in theory be made rigorous enough that they establish their conclusions beyond all doubt, e.g. that the square root of 2 is irrational. Finally mathematicians are sometimes content to entertain conjectures that are only approximations, e.g. the number of prime numbers less than a certain integer.
No. Not a problem-based course. Not a history lesson. No sexy examples. Little mention of the titans. Yet the point of doing math, its constraints and pathways, would strike anyone who reads the book. Whether high school students would get it. I'm not sure. The maturity in the words and the totality of the immersion within its few pages is sublime. In knowing that exact answers are rarely found, but knowing the boundaries of the answers and their closeness to actual mimics our own lives.
This would be a must read in a non-ADHD world.
Gowers also wrote the Princeton book on Math. The professor is a Fields medal winner.
Why? The two difficulties most non-mathy folks have are infinity (that there are many) and high dimensionality.
Gowers in particular does a superb job of leading one through the understanding of a 5D "unit cube", using cartesian 5-tuple (list of 5 numbers) to discover the properties of the cube.