4 out of 4 stars
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Wanting a project to work on in his spare time, Carlo Faustini began the research that would ultimately comprise his book, Symmetry: De Rerum Structura. The mathematical premise details Faustini’s goal to create a formula for solving quartic polynomial equations, as well as a generic means by which to evaluate and solve any high-degree polynomial equation, using symmetry as the focal point to ascertaining a solution. The idea for the project culminated when Faustini recognized there was an established familiarity with formulas for solving second and third-degree polynomials (quadratic and cubic, respectively), but not for fourth-degree polynomials (quartic).
To begin, Faustini needed to take a closer look at existing formulas for quadratic and cubic equations, so he had something to test his findings against. This book reveals Faustini's discoveries when examining these two formulas. Faustini was diligent in his efforts to not seek out the preferential solution-the tidy solution that produces a clean and relatively simple answer, complete with familiar symbols. The existential problem with seeking the preferential solution is the possibility of systematically discounting alternative solutions. Starting from scratch, Faustini set about deconstructing the equations, discovering the key to “exploiting the one characteristic that binds the roots directly to themselves” could be found in symmetry. Although Faustini’s methodology for solving equations shares many similarities to the existing formulas, his version accounts for the symmetrical properties of the roots, which was not a consideration of the antiquated versions.
The book is organized in a concise stepwise manner, meticulously laying out the procedures Faustini implemented throughout his research. I greatly enjoyed the figures and graphs which provided a visual interpretation of the formulas. Although the book was less than 80 pages (PDF) of reading, it is essentially an intimidating and complex mathematical problem, depicted by symbols and matrices, and revealed by peeling away the layers of its composition.
Faustini should be congratulated on the extensiveness of his research, having devoted decades of his life to this project. It is sealed with his own stamp of approval, which I can only surmise is a stamp well-deserved. This book is suited for a reader with a substantial knowledge of high-level mathematics; it is not a book designed to teach any aspects of the discipline. My own fading memories of calculus were of little assistance as I flipped the pages of this challenging piece.
Finding no fault with the structure or editing of this book, I gladly rate it 4 out of 4 stars. I hope Faustini obtains the consideration of the math and physical science experts who possess the necessary knowledge to validate his findings and evaluate their future implications. Again, I commend Faustini on his dedication and skill in pursuing this massive undertaking.
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Symmetry: De Rerum Structura
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Kudos to you for getting through it, and it seems like a great book for those interested. Thank you for the detailed review!!
