When Does Water Find the Shortest Path Downhill? The Geometry of Steepest Descent Curves. - Daniel Drucker; Stephen A. Williams (Am. Math. Mon., 2003)

A Comprehensive Pythagorean Theorem for all Dimensions. - Daniel Drucker (Am. Math. Mon., 2015)

The Counterexample Game: Iterated Conceptual Analysis and Repair in Language Models. - Daniel Drucker; Kyle Mahowald (CoRR, 2026)