AI could soon spew out hundreds of mathematical proofs that look "right" but contain hidden flaws, or proofs so complex we ...

There is a rule in mathematics that feels so obvious it barely seems worth stating. Yet accepting it leads to objects with no size, spheres that duplicate themselves, and sets that cannot be measured ...

Visually, the “Klein bottle” doesn’t seem all that impressive. On first glance it looks like a trendy Japandi-style vase. And yet it has fascinated mathematicians for more than 140 years. To ...

When a delicate object crashes onto the floor, most people expect it to shatter into several pieces. What they might not know, however, is that the sizes of those fragments—whether from a broken plate ...

"When you put it into context, Punctum is astonishingly bright." When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works. Breaking space news, the latest ...

Meet “impossibagel,” a physically impossible bagel that mathematicians use to resolve intricate geometry problems. But impossibagel—and other “impossible objects” in mathematics—is notoriously ...

Experts have confirmed that the mysterious object hurtling towards us, previously dubbed A11pl3Z, is an "interstellar object." The cosmic interloper, officially named 3I/ATLAS, is only the third of ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier-sounding rhombus or trapezoid. But to mathematicians, shapes encompass a vast universe of surprising ...