What's up in

# topology

## Latest Articles

### Quantum Field Theory Pries Open Mathematical Puzzle

Mathematicians have struggled to understand the moduli space of graphs. A new paper uses tools from physics to peek inside.

### 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.

### The Year in Math

Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

### After a Quantum Clobbering, One Approach Survives Unscathed

A quantum approach to data analysis that relies on the study of shapes will likely remain an example of a quantum advantage — albeit for increasingly unlikely scenarios.

### Why Mathematicians Study Knots

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

### The New Math of Wrinkling

A comprehensive mathematical framework treats wrinkling patterns as elegant solutions to geometric problems.

### Special Surfaces Remain Distinct in Four Dimensions

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.

### Unimaginable Surfaces Discovered After Decades-Long Search

Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

### 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.