Using the Proof-Checking Word Processor Lurch to Teach Proof-Writing

Lurch is a free word processor that can check the mathematical reasoning in a document.1 Although it would be easy to make a word processor that could check simple arithmetic, or even algebra, Lurch aims to do much more than that. It can check the steps of a mathematical proof, even a proof not written in a formal style. The current version works best for introduction-to-proof courses, covering topics such as logic, introductory set theory, algebra, and number theory. As we add features it becomes more able to handle a wider variety of mathematics courses. Lurch has been tested at the authors’ two institutions. Bentley University (where the first author teaches) is a selective business university of about 4,000 undergraduates and 1,500 graduate students in the greater Boston area, with a liberal arts focus. The University of Scranton (where the second author teaches) is a Jesuit university in Scranton, PA, of similar size to Bentley and also with a liberal arts focus. While Bentley has very few theoretical mathematics courses (focusing instead on the mathematics of finance and actuarial sciences), Scranton has majors in mathematics and various types of mathematics education (secondary, middle-school) and thus has several upper-division, proof-based mathematics courses.