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Art for "Möbius Strips Defy a Link With Infinity"

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.

Art for "With Ruler and Compass, Amateur Mathematician Tames Fiendish Problem"

Amateur Mathematician Finds Smallest Universal Cover

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.

Art for "A Proof About Where Symmetries Can’t Exist"

A Proof About Where Symmetries Can’t Exist

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

Art for "Why Mathematicians Can’t Find the Hay in a Haystack"
Abstractions blog

Why Mathematicians Can’t Find the Hay in a Haystack

In math, sometimes the most common things are the hardest to find.

Illustration of a complex shape casting a shadow

Tinkertoy Models Produce New Geometric Insights

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

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

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.”

Art for "Three Decades Later, Mystery Numbers Explained"
Abstractions blog

Three Decades Later, Mystery Numbers Explained

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.

Illustration for "Mathematicians Explore Mirror Link Between Two Geometric Worlds"

Mathematicians Explore Mirror Link Between Two Geometric Worlds

Decades after physicists happened upon a stunning mathematical coincidence, researchers are getting close to understanding the link between two seemingly unrelated geometric universes.

Illustration of pentagon tiling
Quantized Academy

The (Math) Problem With Pentagons

Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?