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# topology

## Latest Articles

### Color-Changing Material Unites the Math and Physics of Knots

Mathematicians have studied knots for centuries, but a new material is showing why some knots are better than others.

### Mathematicians Cut Apart Shapes to Find Pieces of Equations

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

### With Category Theory, Mathematics Escapes From Equality

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

### Möbius Strips Defy a Link With Infinity

A new proof shows why an uncountably infinite number of Möbius strips will never fit into a three-dimensional space.

### Scientists Learn the Ropes on Tying Molecular Knots

As chemists tie the most complicated molecular knot yet, biophysicists create a “periodic table” that describes what kinds of knots are possible.

### A Master of Numbers and Shapes Who Is Rewriting Arithmetic

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”

### Physicists Aim to Classify All Possible Phases of Matter

A complete classification could lead to a wealth of new materials and technologies. But some exotic phases continue to resist understanding.

### The Atomic Theory of Origami

By reimagining the kinks and folds of origami as atoms in a lattice, researchers are uncovering strange behavior hiding in simple structures.

### Visionary Mathematician Vladimir Voevodsky Dies at 51

Voevodsky’s friends remember him as constitutionally unable to compromise on the truth — a quality that led him to produce some of the most important mathematics of the 20th century.