Problem Factories: almost endless problem generation (Mathematics Colloquium)

October 5, 2021, 4:10-5:00pm | Zoom

Speaker: Dan Ashlock (University of Guelph)


Math educators often have a few cool problems that can be used to dispel the idea that math is awful, a view too often inculcated by pre-university math education. Some of these wonderful problems fit into larger frameworks which we call problem factories. The idea for problem factories arose at a math education conference, probably because of the density of these wonderful problems. The title of the talk is also the title of a book that Andrew McEachern and I wrote that consists of a brief discussion of the idea of problem factories and several examples.

A problem factory is a body of mathematical knowledge that defines a collection of similar problems together with effective techniques for generating instances of the problems. The initial book sticks with problems that use classical theorem-and-proof mathematics with a computer serving as a convenience. A second book is in progress which treats problem factories that seem to require artificial intelligence to locate problem instances. The transition from classical to AI based problem factories is gradual, not crisp, and the talk will contain examples.