  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.
