Title
The Nature Of Infinitesimals,Used
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This cerebral text seeks understanding of the mysteries at the heart of mathematics.At a certain level, math is a mystery. For example, what exactly is a line? Is it a series oftiny dots in a row? Is it the length from one dot to another? These are the types of questions that author Peter F. Erikson seeks to answer in The Nature of Infinitesimals. But though The Nature of Infinitesimals focuses on number theory, its discussion of the philosophical bents of mathematicians in history is just as revealing.As the book details number theorists of old, it becomes clear that math is at least asprone to interpretation as art or music. Richard Dedekind, for example, believed that math could not be based on human perception but strictly on imaginary numbers. The book cites Ayn Rand as believing that infinity is potential only. As a result, the cold numbers of mathematics seem much more mutable and subjective than most college textbooks would imply.The book can be construed as the authors conversation with several generations oftheorists. From Aristotle to Leibniz, each one seems to have different ideas about the concept of infinity and the way to define a real number. Drawing so many philosophies together in one text allows for a dialogue of sorts between past theories and the one presented in the book. This not only puts the various thinkers and ideas into perspective, but it also showcases the rich history of mathematical thought.The time and effort that the author put into this book is clear. It is well edited andorganized in a useful manner. Multiple appendixes and visuals do a great deal to illuminate thedense subject matter. However, the intensity with which the book critically examines thecomponent theories and assumptions of calculus will surely constitute a brainbusting workout even for advanced math users. Nonmembers of the math club may find it hard to determine whats so important about the concept of infinity in the first place.Any book on math will be heavy mental lifting, but the philosophical context presentedhere raises a different question: if the laws of math are so open to debate, then how canmathematicians truly know that two and two really do equal four? If a number continuesindefinitely after its decimal point, its value so exact that it defies geometrical measurement,then does that number even really exist? Whatever the answer is today, it seems like a sure bet that it will change. Humankind might never completely understand the mystery of mathematics, but we may be thinking about it until the end of time.
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