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Math Proof Draws New Boundaries Around Black Hole Formation

August 16, 2023

For a half century, mathematicians have tried to define the exact circumstances under which a black hole is destined to exist. A new proof shows how a cube can help answer the question.

Two Students Unravel a Widely Believed Math Conjecture

August 10, 2023

Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall.

Ninth Dedekind Number Found by Two Independent Groups

August 1, 2023

The numbers count a variety of seemingly unrelated mathematical structures.

New Proof Shows That ‘Expander’ Graphs Synchronize

July 24, 2023

The proof establishes new conditions that cause connected oscillators to sway in sync.

Math That Lets You Think Locally but Act Globally

July 21, 2023

Knowing a little about the local connections on flight maps and other networks can reveal a lot about a system’s global structure.

Mathematicians Solve Long-Standing Coloring Problem

July 19, 2023

A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

New Proof Threads the Needle on a Sticky Geometry Problem

July 11, 2023

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.

The Lawlessness of Large Numbers

July 7, 2023

Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?

Elliptic Curves Yield Their Secrets in a New Number System

July 6, 2023

Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.

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