David Chalmers’ essay on the hard problem of consciousness has sparked many analyses, arguments, and counterclaims. Here I explain why we should think about the hard problem as two different problems, ...

This blog was co-authored by Gregg Henriques, Ph.D., and John Vervaeke, Ph.D. Since the dawn of human consciousness, people have grappled with the problem of what it is and how it works. In academic ...

If Ms. Smith’s 8th grade algebra class works through 10 word problems in an hour, and Ms. Jones’ class works through 10 equation problems during the same time, which class is likely to learn more math ...

Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.

Physics-informed neural networks (PINNs) represent a burgeoning paradigm in computational science, whereby deep learning frameworks are augmented with explicit physical laws to solve both forward and ...