MathDSL: A Domain-Specific Language for Concise Mathematical Solutions Via Program Synthesis

MathDSL is a domain-specific language that lets the DreamCoder program-synthesis system write short, readable equation-solving programs. It is a 2024 arXiv paper led by Sagnik Anupam.

Posted to arXiv on September 26, 2024, by Sagnik Anupam, Maddy Bowers, Omar Costilla-Reyes, and Armando Solar-Lezama, MathDSL gives the DreamCoder program-synthesis system a domain-specific vocabulary for mathematical problem solving. The research was led by Anupam while an undergraduate at MIT; he had worked with Dr. Costilla Reyes as a SuperUROP student and presented an earlier version of the project, “Neurosymbolic Reasoning for Mathematical Domains,” at MIT in December 2022.

Program synthesis is the practice of having a computer write programs that meet a goal, and DreamCoder is a system that does this while learning reusable functions from the programs it finds. A domain-specific language (DSL) is a small, purpose-built set of operations. In MathDSL, a solution to an equation is a short program made of algebra operations, so each answer can be read and checked one step at a time.

In experiments on linear equations, the authors report that DreamCoder using MathDSL improves accuracy and conciseness over the reinforcement-learning methods evaluated in the paper, including when earlier reinforcement-learning action spaces are used as DSLs. They also introduce a quantitative measure of how concise a solution is, and show that the strategies DreamCoder learns can be converted into human-readable solution strategies, which the authors note could be useful in mathematics education. Together these results show that a domain-specific language lets program synthesis produce shorter, readable solutions to linear equations.

In August 2025 Dr. Costilla Reyes shared an explanatory video about the research, describing the result as state-of-the-art test accuracy and solutions more concise than popular AI baselines, with far less training data. He framed the work as a response to the observation that today’s AI still fails at basic mathematics: teaching a system to solve equations by writing small, human-readable programs gives each solution a form that can be verified step by step. MathDSL is related to LEMMA, which learns higher-level symbolic actions for equation solving, and to the broader Neurosymbolic Programming for Science agenda he coordinated at MIT CSAIL.