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Название: How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Автор: William Byers
Mathematics is a fascinating subject. I am not a mathematician, but deal enough with it in my chosen profession to be constantly amazed by how logical the application of mathematics to proving a theorem or analyzing an algorithm turns out to be. But wait ... is it really logical? Or does it merely seems so and what is actually happening is that the author of the said proof is using creative tricks and techniques from the mathematical tool box to somehow tie everything up with a nice red bow-tie? In this book, the author argues that mathematics is creative more than algorithmic, and that mathematicians use a good dose of ambiguity mixed with equal parts of contradiction and paradox to create mathematics. Now, I shall point out that the term "ambiguity" here does not mean vagueness, rather it refers to a central truth that is perceived in two self-consistent but mutually incompatible contexts. The author takes the reader on this journey of ambiguity, paradox and contradiction on the way to discovering a lot of interesting mathematics. There is a section on counting numbers and cardinality, complete with Hilbert's Infinity Hotel; there is an interesting section on how to approach geometry through Euclid's Elements, and so on. I don't suppose that this is the sort of book you would pick up for a plane ride — contemplating the philosophy of mathematics at 35,000 feet is enough to induce stupor. But if you are interested in the field and still remember the Central Limit Theorem from Calculus-I or Series and Sequences from Calculus-II, then you will definitely enjoy this book. I know I did.