Finding a combinatorial characterization for rigid bar-and-joint frameworks in dimensions higher than 3 is an easy-to-state yet elusive, long standing open problem in rigidity theory, originating in two geometry papers from the 19th century of the renowned physicist James Clerk Maxwell. I will summarize our current state of knowledge on Maxwell’s problem, and present recent developments leading to a surprising range of applications, from folding robot arms and origami to anayzing the flexibility of molecules and designing materials with unusual mechanical properties.

No advanced prerequisites are necessary. To help build the geometric and kinematic intuitions, the relevant mathematical concepts and techniques will be introduced primarily through physical models and animated graphics.