A Mathematician with early access to XAI Grok 4.20, found a new Bellman function for one of the problems he had been working on with my student N. Alpay. Not an Erdős problem, but original research.

Abstract: JSON is moving from being an underground secret, known and used by very few, to becoming the clear choice for mainstream data applications. The first Web extra is a video interview with ...

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 ...

SPONSORED – Mathnasium is offering a unique approach to learning math as students head back to school this fall. The math learning center provides a different approach to learning math compared to ...

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, ...

What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as an answer to this question. Mathematics started with numbers — clear, ...