We demonstrate that a neural network pre-trained on text and fine-tuned on code solves Mathematics problems by program synthesis. We turn questions into programming tasks, automatically generate programs, and then execute them, perfectly solving university-level problems from MIT's large Mathematics courses (Single Variable Calculus 18.01, Multivariable Calculus 18.02, Differential Equations 18.03, Introduction to Probability and Statistics 18.05, Linear Algebra 18.06, and Mathematics for Computer Science 6.042), Columbia University's COMS3251 Computational Linear Algebra course, as well as questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems specifically designed to assess mathematical reasoning. We explore prompt generation methods that enable Transformers to generate question solving programs for these subjects, including solutions with plots. We generate correct answers for a random sample of questions in each topic. We quantify the gap between the original and transformed questions and perform a survey to evaluate the quality and difficulty of generated questions. This is the first work to automatically solve, grade, and generate university-level Mathematics course questions at scale. This represents a milestone for higher education.

We solve MIT's Linear Algebra 18.06 course and Columbia University's Computational Linear Algebra COMS3251 courses with perfect accuracy by interactive program synthesis. This surprisingly strong result is achieved by turning the course questions into programming tasks and then running the programs to produce the correct answers. We use OpenAI Codex with zero-shot learning, without providing any examples in the prompts, to synthesize code from questions. We quantify the difference between the original question text and the transformed question text that yields a correct answer. Since all COMS3251 questions are not available online the model is not overfitting. We go beyond just generating code for questions with numerical answers by interactively generating code that also results visually pleasing plots as output. Finally, we automatically generate new questions given a few sample questions which may be used as new course content. This work is a significant step forward in solving quantitative math problems and opens the door for solving many university level STEM courses by machine.