Problem About Mathematical Curves

Eric Larson and Isabel Vogt have solved the interpolation problem — a centuries-old question about some of the most basic objects in geometry. Some credit goes to the chalkboard in their living room.

The artwork brings Brill-Noether curves to life by depicting key points on the curve as if they are shaped by giant celestial iridescent hands, compressing the surrounding space. These hands serve as a metaphor for the fundamental constraints imposed by Brill-Noether theory, where the existence of special divisors dictates the structure and embeddings of algebraic curves.

The gripping hands symbolize the mathematical forces that shape the geometry of the curve, illustrating how these distinguished points influence its behavior and possible mappings in projective space. The contrast between the fluidity of the curve and the firm grasp of the celestial hands highlights the tension between mathematical freedom and restriction, echoing the balance at the core of Brill-Noether theory.

By merging abstraction with mathematical precision, this visual interpretation captures the profound interplay of combinatorial conditions, geometric constraints, and the almost cosmic inevitability of mathematical order.