Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly ...

Researchers uncover the mathematical structure behind mesmerizing tiling patterns, linking their visual appeal to the ...

As artificial intelligence (AI) takes on increasingly critical roles—from managing power grids to piloting autonomous vehicles—making sure these systems are safe has never been more important. But how ...

Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion ...

Artificial intelligence (AI) systems, particularly artificial neural networks, have proved to be highly promising tools for uncovering patterns in large amounts of data that would otherwise be ...

Equations are ordered, elegant mathematical constructs used to describe specific patterns. Can you imagine some formulas depict the very opposite: chaos and randomness? What's more intriguing, they ...

Maxwell’s equations of electromagnetism and the Euler equation top a poll to find the greatest equations of all time. Robert P Crease discusses the results of his reader survey First among equals – ...

Why is it that particular equations, formulas and expressions become icons, asks Robert P Crease For some people this expression, named after the 18th-century Swiss mathematician Leonhard Euler, even ...

In the Fall I'll be starting teaching again, after a semester away on sabbatical and then enjoying teaching relief during my first semester at Penn. I'll be teaching a course that I truly love, and ...

Work with experts to tackle some of the biggest ideas in science and expand your understanding of advanced mathematical tools. Apply now for 2026 entry or register your interest to find out about ...