Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades.
Machine learning and deep neural networks can capture and analyze the “language” of animal behavior in ways that go beyond what’s humanly possible.
We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”
A surprisingly youthful estimate of the age of the rings has stirred a backlash.
Neural networks can be as unpredictable as they are powerful. Now mathematicians are beginning to reveal how a neural network’s form will influence its function.
Quanta Magazine is committed to in-depth, accurate journalism that serves the public interest. Each article braids the complexities of science with the malleable art of storytelling and is meticulously reported, edited and fact-checked. Launched and funded by the Simons Foundation, Quanta is editorially independent — our articles do not reflect or represent the views of the foundation.