The book presents much creative, original and stimulating ideas on the various approaches which could be taken to tackle five important open problems in mathematics, viz., the twin primes, Goldbach and Polignac’s conjectures, and, the Navier-Stokes equations and turbulence, and the Riemann hypothesis which are both Millennium Prize problems. Technical areas such as calculus, differential equations, group theory/symmetry and complex analysis are covered, as well as logic and mathematical reasoning in general, and they are presented as clearly as possible for easier assimilation. For those who are interested in mathematical reasoning and logic, and researchers working on the open problems in mathematics, the book will offer much food for thought and inspire further advancement of the ideas presented in the book.