Richard G. Baraniuk, Randall Balestriero, and  Ahmed Imtiaz Humayun explore the mathematical underpinnings of deep learning in their latest article published in the Notices of the American Mathematical Society (April 2025). The paper highlights a decade of progress connecting deep networks to function approximation via affine splines, shedding light on how these models tessellate input space and revealing geometric insights into their behavior. This perspective offers a promising framework for analyzing and enhancing deep network performance through a more principled mathematical lens.