How the Martians Discovered Algebra: Explorations in Induction and the Philosophy of Mathematics

This exploration of induction and philosophy of mathematics is presented as a look “under the hood” at the process of mathematical theorizing, a detailed view of how the process of induction actually works. It also provides an alternative to the mind-numbing constructs of modern logic, mathematics, and set theory, explaining the true nature of zero and empty sets and revealing the flaw in Cantor’s writings on infinity.There are original ideas here, including the author’s view that zero and the empty set function as “operation blockers,” as well as his explanation of why the value of the zero power of any number is always 1. The author also offers his own discovery of a new method for generating Pythagorean triples. He lays out both the deductive validation of his method and the details of his exploration of the Pythagorean equation that uncovered the relationships underlying his method.Academics, college students, and intelligent laypersons interested in philosophy and mathematics will all find this a challenging and stimulating read. They will be rewarded with new perspectives, not only on the theoretical landscape of mathematics and logic, but also on the value in learning the mental processes involved in induction, as well as the endless opportunities for fascination and delight to be obtained from mathematical discovery.

Roger E. Bissell is a musician and writer living in Middle Tennessee. A native of Iowa, he holds a B.S. in music composition and theory, with a minor in mathematics, from Iowa State University and an M.A. in music performance and literature from the University of Iowa. Roger's 55-year career as a professional musician has included thousands of live performances and recording sessions, and his musical works have been performed by artists such as Glen Campbell, the Oak Ridge Boys, and Boots Randolph. He has also published numerous philosophical essays in Reason Papers and The Journal of Ayn Rand Studies, as well as in compilations including Free Minds and Free Markets: Twenty-Five Years of Reason and Ayn Rand's Atlas Shrugged: A Philosophical and Literary Companion.