Many vital areas of mathematics rest upon some version of infinity. Philosophers and mathematiciansranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals.
Cosmologists consider sweeping questions about whether space and time are infinite. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. "synopsis" may belong to another edition of this title.Paperback. Humankind might never completely understand the mystery of mathematics, but we may be thinking about it until the end of time. Then does that number even really exist? Whatever the answer is today, it seems like a sure bet that it will change. Indefinitely after its decimal point, its value so exact that it defies geometrical measurement, Mathematicians truly know that two and two really do equal four? If a number continues Here raises a different question: if the laws of math are so open to debate, then how can
Non-members of the math club may find it hard to determine what’s so important about the concept of infinity in the first place.Īny book on math will be heavy mental lifting, but the philosophical context presented
However, the intensity with which the book critically examines theĬomponent theories and assumptions of calculus will surely constitute a brain-busting workout even for advanced math users. Multiple appendixes and visuals do a great deal to illuminate theĭense subject matter. The time and effort that the author put into this book is clear. This not only puts the various thinkers and ideas into perspective, but it also showcases the rich history of mathematical thought. Drawing so many philosophies together in one text allows for a dialogue of sorts between past theories and the one presented in the book. From Aristotle to Leibniz, each one seems to have different ideas about the concept of infinity and the way to define a real number. The book can be construed as the author’s conversation with several generations of 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. Richard Dedekind, for example, believed that math could not be based on human perception but strictly on imaginary numbers. But though The Nature of Infinitesimals focuses on number theory, its discussion of the philosophical bents of mathematicians in history is just as revealing.Īs the book details number theorists of old, it becomes clear that math is at least as Erikson seeks to answer in The Nature of Infinitesimals. Tiny dots in a row? Is it the length from one dot to another? These are the types of questions that author Peter F.
INFINITY AND INFINITESIMALS BOOK SERIES
For example, what exactly is a line? Is it a series of This cerebral text seeks understanding of the mysteries at the heart of mathematics.Īt a certain level, math is a mystery.
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