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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.
How to Build a Big Prime Number
A new algorithm brings together the advantages of randomness and deterministic processes to reliably construct large prime numbers.
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.
How Math Achieved Transcendence
Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.
Computer Scientists Inch Closer to Major Algorithmic Goal
A new paper finds a faster method for determining when two mathematical groups are the same.
Mathematicians Discover Novel Way to Predict Structure in Graphs
Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.
The Simple Geometry That Predicts Molecular Mosaics
By treating molecules as geometric tessellations, scientists devised a new way to forecast how 2D materials might self-assemble.