What's up in

# topology

## Latest Articles

### Proof Assistant Makes Jump to Big-League Math

Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

### Nathan Seiberg on How Math Might Complete the Ultimate Physics Theory

Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, talks about the gaps in QFT and how mathematicians could fill them.

### Mathematicians Prove 2D Version of Quantum Gravity Really Works

In three towering papers, a team of mathematicians has worked out the details of Liouville quantum field theory, a two-dimensional model of quantum gravity.

### The Mystery at the Heart of Physics That Only Math Can Solve

The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.

### A Number Theorist Who Connects Math to Other Creative Pursuits

Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.

### How Mathematicians Use Homology to Make Sense of Topology

Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.

### Topology 101: The Hole Truth

The relationships among the properties of flexible shapes have fascinated mathematicians for centuries.

### Mathematicians Resurrect Hilbert’s 13th Problem

Long considered solved, David Hilbert’s question about seventh-degree polynomials is leading researchers to a new web of mathematical connections.

### 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.