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topology

Animation showing two sets of tangrams cycling between identical squares and different shapes.
geometry

Mathematicians Cut Apart Shapes to Find Pieces of Equations

October 31, 2019

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

foundations of mathematics

With Category Theory, Mathematics Escapes From Equality

October 10, 2019

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

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.