Proof Atlas1 part 19 min

Proof Atlas: The Geometry of a Formal Proof

Can an entire Lean proof be read as a geometric object? An interactive first experiment, a carefully separated syntax graph and mathematical argument, and a research program for navigating formal proofs at different scales.

Proof Atlas: The Geometry of a Formal Proof
Hidden protostars2 parts 27 min

Hidden protostars: a research program

A dark dust clump can already contain a young star. What can survey data actually tell us—and what would it take to observe a stellar birth?

Hidden protostars: a research program
Mathematics 54 min

The Shortest Path When You Cannot Move Sideways

An interactive guide to the geometry of motion in the plane: from a simple constraint to the pendulum, competing routes, and the complete shortest-path solution.

The Shortest Path When You Cannot Move Sideways
Geodesics on SE(2)1 part 28 min

Beyond the Shortest Path: Geodesics on SE(2)

One research program, three questions: when a path loses local optimality, where nearby paths focus, and how many paths reach the same position and heading. Follow the pendulum, explore the conjugate locus, and count the inverse images.

Beyond the Shortest Path: Geodesics on SE(2)