4 out of 4 stars
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Despite its deceptively low page count, Symmetry: De Rerum Structura by Carlo Faustini is anything but a light read. The book chronicles Faustini's exploration into the world of higher-degree polynomials, as well as the development of a generic equation that can be used to solve for their roots, at least for equations raised to a prime number. To do this, he explores the symmetry of polynomial roots when manipulated as matrices and polar vectors. If that sounds like gibberish to you, I'm sure you're not alone. However, Faustini makes a challenging topic as approachable as possible with an organized structure that avoids unnecessary filler without sacrificing content.
Most people are somewhat familiar with the quadratic formula. Widely taught in high schools, it solves for the roots of a quadratic equation. Formulas like this exist for cubic and quartic equations as well, albeit extremely unwieldy ones. No equation exists, though, that applies to any polynomial, regardless of what degree its root function is raised to. Faustini's work focuses on creating a new methodology to solve for the roots of a cubic equation by manipulating symmetrical patterns, which he sees as the first step in solving this larger problem.
Throughout the book, I was required at every turn to call upon my skills in mathematics and scientific reading. The topics Faustini covers build upon themselves, so each component had to be carefully analyzed, starting with definitions and working forward to far more complex topics. This progression was laid out in a way that felt extremely challenging but natural. It's impossible to deny, though, that reading Symmetry: De Rerum Structura requires a somewhat advanced background in these subjects. The more understanding of math and science a reader has, the more likely they are to fully enjoy this book.
Because of the background knowledge required, I would never recommend Symmetry: De Rerum Structura to anyone who doesn't enjoy mathematical problem solving or who hasn't completed some calculus coursework at the bare minimum, except perhaps as a practical joke. For people who are passionate about advanced mathematics or are doing research into higher-degree polynomials, this book is a very interesting read, as well as a potentially invaluable resource.
I'll leave determining if Faustini has truly made a breakthrough in his field to professional mathematicians. For its communication and style, though, I rate Symmetry: De Rerum Structura 4 out of 4 stars. It's an academic book through and through, and the clean, thorough way it organizes ideas is nothing short of impeccable. While I can't say I completely understood some of the more advanced topics it covered, this book has piqued my interest in the development of formulas for this extremely thorny problem. I'm looking forward to discussing some of the elements it covered with my acquaintances who have more formal training in mathematics.
Symmetry: De Rerum Structura
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