Young couple solving old algebraic geometry problem

If you distribute two points in a plane, then there is always a straight line that connects them both. This fact has been known to scholars for thousands of years. However, if more dots are scattered, you’re out of luck. A single straight is unlikely to hit them all. However, you can always draw a circle through any three points and a conic section (an ellipse, parabola or hyperbola) through five points.

These considerations have to do with one of the most important questions in geometry, the interpolation problem: when can a curve be defined that meets any number of points in n dimensions? “Actually, it’s about understanding what curves are,” explains mathematician Ravi Vakil from Stanford University.

Although curves in high-dimensional space have been studied by sophisticated means for hundreds of years, they are extremely elusive…