The Mathematical Trinity

The book discusses the nine popular propositions in mathematics: “the consistency theorem” from logic; “isosceles triangle theorem” and “Pythagorean theorem” from geometry; “ordered pair proposition” and “mathematical induction principle” from Zermelo–Fraenkel set theory; “remainder theorem” from number theory; “the quadratic equation proposition” and “the subgroup theorem” from algebra; and “Dedekind continuum theorem” from analysis, and thereby cover a sufficiently wide cross-section of modern mathematical sub-domains. Using these propositions, the book primarily has three objectives: to offer a deeper appreciation of these propositions and related concepts; to provide a better understanding of their relationship with other topics of mathematics; and, above all, to throw light on the profound nature of the discipline that has developed and advanced over the millennia through a synergistic combination of imagination, inference, and insights. The book meticulously dissects each of these chosen propositions in separate chapters while simultaneously probing their intricate interrelationships. This approach yields a heightened appreciation of their mathematical significance, bridging the divide between educational levels. These propositions often appear poised between school-level mathematics and university-level rigour, and the book adeptly navigates this middle ground. Furthermore, it goes beyond mere logical inference, embracing the realms of imagination and insight. It offers a holistic, historical, and intellectual perspective, unravelling not just the necessity of each proposition but also its unique contributions to the fabric and evolution of mathematics. In doing so, it sheds light on a constellation of interconnected mathematical concepts, enriching the reader's comprehension of this remarkable discipline.