Our February Insights puzzle sent readers on a treasure hunt based on complex numbers. First we provided a bit of a primer, demonstrating that complex numbers (expressions of the form a + bi, where ...

Real and imaginary: The time-dependent Schrödinger equation formulated using complex numbers. (Courtesy: iStock/piranka) Complex numbers are essential to achieve the most accurate quantum-mechanical ...

William Ross does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...

Harry Zandberg Wiggins does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations ...

AlphaProof and AlphaGeometry 2 are steps toward building systems that can reason, which could unlock exciting new capabilities. AI models can easily generate essays and other types of text. However, ...