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# Knot theory

## Latest Articles

### Mathematicians Eliminate Long-Standing Threat to Knot Conjecture

A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t.

### Why Mathematicians Study Knots

Far from being an abstract mathematical curiosity, knot theory has driven many findings in math and beyond.

### Surfaces So Different Even a Fourth Dimension Can’t Make Them the Same

For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.

### How Complex Is a Knot? New Proof Reveals Ranking System That Works.

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

### Untangling Why Knots Are Important

Steven Strogatz explores the mysteries of knots with the mathematicians Colin Adams and Lisa Piccirillo.

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Deep Curiosity Inspires *The Joy of Why* Podcast

The noted mathematician and author Steven Strogatz explains how the conversations with experts in his new *Quanta Magazine* podcast address his lifelong fascination with timeless mysteries.

### Machine Learning Becomes a Mathematical Collaborator

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

### The Year in Math and Computer Science

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

### In a Single Measure, Invariants Capture the Essence of Math Objects

To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.