Several papers have investigated sequences which have no k-term arithmetic progressions, finding bounds on their density and looking at sequences generated by greedy algorithms. Rankin in 1960 ...

Ancient pottery reveals early farmers were using math thousands of years before numbers, embedding geometry and patterns into ...

In mathematics, a geometric progression is a sequence of numbers in which each term after the first is found by multiplying the previous one by a fixed non-zero number. In mathematics, a geometric ...

Sam Raskin has wrapped his head around a math problem so complex it took five academic studies — and more than 900 pages — to solve. The results are a sweeping, game-changing math proof that was ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

Google DeepMind has developed an artificial intelligence system that can solve complex geometry problems better than top human minds. Named AlphaGeometry2 (AG2), the AI has outshined International ...