Virtual knot theory extends the classical study of knots by allowing for virtual crossings, which abstractly represent embeddings of closed loops in thickened surfaces of arbitrary genus. This ...

Sometimes, a simple, even childish question turns out to be connected to the deepest secrets of the universe. Here’s one: How many different ways can you tie your shoelaces? Mathematicians have been ...

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 ...

Q: When is a knot not a knot? A: When it's a quantum computer. Steve Simon explains how a remarkable link between knot theory and certain quantum systems may be useful for quantum information ...

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 ...