Mathematical Breakthrough: 300-Year-Old Problem Solved

A pair of European mathematicians have made a significant breakthrough by solving a 300-year-old geometry problem that originated from a royal wager. The problem dates back to an argument between Prince Rupert of the Rhine and mathematician John Wallis, regarding the ability to slide one cube through another using a hole bored in the first.

Historically, Rupert claimed that by tilting a cube and creating a hole towards its inner diagonal, a second cube could pass through, which Wallis later formalized into what is known as the Rupert property.

Over the years, this property has been tested on various shapes, including tetrahedrons and octahedrons, and has been confirmed for complex shapes like dodecahedrons and icosahedrons as well. Recently, however, Jakob Steininger and Sergey Yurkevich have achieved a groundbreaking discovery by creating a shape they call the Noperthedron, a unique 180-sided object that does not possess the Rupert property.

This means that no matter how it is positioned or how a hole is bored into it, it cannot allow another identical shape to pass through. Their journey began when they viewed a video of a cube passing through another cube, igniting their interest in the mathematical problem.

Utilizing computer simulations, they developed a pair of theorems to isolate points of shadows cast by shapes, aiding in their discovery of the first true Nopert. This innovative shape, composed of 150 triangles and two regular 15-sided polygons, was confirmed after the program ruled out every possible position of the shapes in a rigorous analysis involving eighteen million examination blocks.

The discovery represents a momentous advancement in mathematical inquiry, showcasing the collaborative spirit of researchers. As Steininger noted, they are committed to continuing their exploration of mathematical challenges, emphasizing their humble approach to their work.

Their achievement is a reminder of the enduring nature of mathematical inquiry and the excitement that comes with solving age-old problems. This breakthrough not only resolves a historical debate but also opens new avenues for future research in geometry and mathematics.