What's up in

topology

Art for "Möbius Strips Defy a Link With Infinity"
topology

Möbius Strips Defy a Link With Infinity

February 20, 2019

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

Art for "Scientists Learn the Ropes on Tying Molecular Knots"
chemistry

Scientists Learn the Ropes on Tying Molecular Knots

October 29, 2018

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

Photo of Dr. Peter Scholze
2018 Fields Medal and Nevanlinna Prize

A Master of Numbers and Shapes Who Is Rewriting Arithmetic

August 1, 2018

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.”

520px illustration of classification of phases
condensed matter physics

Physicists Aim to Classify All Possible Phases of Matter

January 3, 2018

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

Michael Assis folding a large, beige sheet or Miura-ori
statistical physics

The Atomic Theory of Origami

October 31, 2017

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

Vladimir Voevodsky
Abstractions blog

Visionary Mathematician Vladimir Voevodsky Dies at 51

October 11, 2017

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.

Classes of geometric structures
Abstractions blog

Why Mathematicians Like to Classify Things

August 15, 2017

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.

Heavenly billiards
geometry

New Shapes Solve Infinite Pool-Table Problem

August 8, 2017

Two “rare jewels” have illuminated a mysterious multidimensional object that connects a huge variety of mathematical work.

Maryam Mirzakhani
Quantized Columns

The Beautiful Mathematical Explorations of Maryam Mirzakhani

July 24, 2017

After her untimely death, Maryam Mirzakhani’s life is best remembered through her work.