Financial mathematics and its unexpected connections to accounting and corporate finance

Abstract Investment analysis requires frameworks that combine theoretical rigor with real-world complexity. While financial mathematics offers powerful tools, its reliance on simplifying assumptions may limit practical applicability. Conversely, accounting and corporate finance provide transaction-level detail and managerial insight, but their integration with financial mathematics remains underexplored. This paper introduces a unifying framework, presenting foundational insights and architectural principles that integrate these disciplines through two universal concepts: the law of motion (governing capital dynamics) and the law of conservation (ensuring equilibrium). These principles, foundational in economics, converge in the Split Screen Matrix, a novel architecture that reveals connections across financial mathematics, accounting, and corporate finance. The Split Screen Matrix uncovers the mathematical linkage between financial statements, integrating balance sheets, income statements, and cash flow statements (traditionally treated in isolation) and shows how these connections mirror market-traded portfolios to capture economic profitability. It also acts as a diagnostic device, allowing validation of models and detection of internal inconsistencies. This interdisciplinary approach demonstrates that cash flows, incomes, and capital amounts are interdependent variables governed by these laws and must be modeled jointly. This integration unifies financial planning, valuation, and decision making, resolving theoretical gaps. Researchers can align their models with accounting and corporate finance principles, clarifying interdisciplinary relationships and exploring new research avenues. Pedagogically, the framework supports student understanding by reducing cognitive load and integrating traditionally fragmented areas of financial analysis into a unified paradigm that mirrors real-world transactions. This approach advances theory and practice, offering practitioners advanced tools, researchers new exploration avenues, and educators innovative teaching strategies, thereby reflecting AMASES’s enduring mission to bridge theory and practice, dissolve disciplinary boundaries, and illuminate economic realities through mathematics.