The Complexity of Math Problems - Linguistic, or Computational?

We present a simple, logic-based architecture for solving math problems written in natural language. A problem is firstly translated to a logical form. It is then rewritten into the input language of a solver algorithm and finally the solver finds an answer. Such a clean decomposition of the task however does not come for free. First, despite its formality, math text still exploits the flexibility of natural language to convey its complex logical content succinctly. We propose a mechanism to fill the gap between the simple form and the complex meaning while adhering to the principle of compositionality. Second, since the input to the solver is derived by strictly following the text, it may require far more computation than those derived by a human, and may go beyond the capability of the current solvers. Empirical study on Japanese university entrance examination problems showed positive results indicating the viability of the approach, which opens up a way towards a true end-to-end problem solving system through the synthesis of the advances in linguistics, NLP, and computer math.