How Shannon Entropy Imposes Fundamental Limits on Communication
What’s a message, really? Claude Shannon recognized that the elemental ingredient is surprise.
A Question About a Rotating Line Helps Reveal What Makes Real Numbers Special
The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.
Special Surfaces Remain Distinct in Four Dimensions
For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.
Mathematicians Clear Hurdle in Quest to Decode Primes
Paul Nelson has solved the subconvexity problem, bringing mathematicians one step closer to understanding the Riemann hypothesis and the distribution of prime numbers.
How Tadayuki Watanabe Disproved a Major Conjecture About Spheres
Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.