A journey from Prince Rupert’s late‑17th‑century bet to a 2025 breakthrough that ends the Rupert conjecture. We explore how Jakob Steininger and Sergey Yurkevich designed the Noperthedron—an ornate 152‑faced shape engineered to fail the Rupert test—and how, by partitioning orientation space into about 18 million regions and applying a global and a local theorem, they proved no convex solid has the Rupert property. We also meet the Ruperthedron, a Rupert shape that is not locally Rupert, and d...
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A journey from Prince Rupert’s late‑17th‑century bet to a 2025 breakthrough that ends the Rupert conjecture. We explore how Jakob Steininger and Sergey Yurkevich designed the Noperthedron—an ornate 152‑faced shape engineered to fail the Rupert test—and how, by partitioning orientation space into about 18 million regions and applying a global and a local theorem, they proved no convex solid has the Rupert property. We also meet the Ruperthedron, a Rupert shape that is not locally Rupert, and d...
Jacobi’s exact four-square formula makes r4(n) elegant, but five squares lead to deeper territory with half-integral weight forms and L-functions. In this episode we trace Emil Grosswald’s clever reduction of r5(n) to a sum of r4(n), bypassing the circle method to yield a sharp asymptotic, and we unpack the main term, the role of L-series, the cusp-form error, and what this reveals about the boundary between exact formulas and structured approximations in number theory. Note: This podcast wa...
Intellectually Curious
A journey from Prince Rupert’s late‑17th‑century bet to a 2025 breakthrough that ends the Rupert conjecture. We explore how Jakob Steininger and Sergey Yurkevich designed the Noperthedron—an ornate 152‑faced shape engineered to fail the Rupert test—and how, by partitioning orientation space into about 18 million regions and applying a global and a local theorem, they proved no convex solid has the Rupert property. We also meet the Ruperthedron, a Rupert shape that is not locally Rupert, and d...
