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Math Proof Draws New Boundaries Around Black Hole Formation
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
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
The numbers count a variety of seemingly unrelated mathematical structures.
New Proof Shows That ‘Expander’ Graphs Synchronize
The proof establishes new conditions that cause connected oscillators to sway in sync.
Math That Lets You Think Locally but Act Globally
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
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
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
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
Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.