If accounting promises to provide high quality financial information, why have global financial crisis and failures occurred repeatedly? Hence, we might call it the accounting paradox. Today there is a tendency for the practice of accounting to be governed more and more by regulations.This paper uses a mathematical perspective to review the existing theory of double entry bookkeeping (DEB). Contrary to the existing works, which treat rules of debit and credit (RDC) as merely customary, arbitrary, or practical, this paper proposes the rationality of these rules based on mathematics. Further, this paper proposes another theory of DEB, called the "law of funds." Next, this paper demonstrates the power of the proposed DEB theory in identifying and resolving questionable beliefs in accounting education, standard-setting, and research. This book contributes to the literature on intellectual accounting foundations, or specifically, the theory of DEB. The present book contributes to the current literature by proposing the development of DEB theory from a mathematical perspective, as DEB was originally written in mathematical text and documented by a mathematics professors.