Informally, a dynamic system is any physical system that evolves with time (e.g., a pendulum, a planet orbiting the sun, the weather, etc). From a more mathematically precise perspective, one can ...

Knot theory investigates the embeddings of closed curves in three-dimensional space and employs algebraic structures to capture their essential features. At its core, the knot group, together with ...

When Lisa Piccirillo solved a decades-old mystery about the “Conway knot,” she had to overcome the knot’s uncanny ability to hoodwink some of the most powerful tools mathematicians have devised. Known ...

The artificial intelligence (AI) program DeepMind has gotten closer to proving a math conjecture that's bedeviled mathematicians for decades and revealed another new conjecture that may unravel how ...

Two recent collaborations between mathematicians and DeepMind demonstrate the potential of machine learning to help researchers generate new mathematical conjectures. Mathematicians often work ...

A mathematician’s intuition plays an enormously important role in mathematical discovery—“It is only with a combination of both rigorous formalism and good intuition that one can tackle complex ...

AI software has collaborated with mathematicians to successfully develop a theorem about the structure of knots, but the suggestions given by the code were so unintuitive that they were initially ...