In the Spring term of 2025 I worked with Sam Thiel on a project they proposed based on an Abbot and Costello bit in which Costello "proves" that 7 times 13 is 28. Sam was inspired to ask how this erroneous division could be made into a rigorous algorithm and what properties it might have. They were able to prove that remainders under normal division and remainders under this Costello division coincide exactly! A paper on the subject is forthcoming.
