On the Role of AI in Scientific Discovery - From Signal Signatures to Collaborative Mathematical Discovery

Description

This talk traces the interdisciplinary journey of a mathematical concept from its creation to its modern-day AI-inspired evolution. We begin by exploring how the Wavelet Transform was developed to overcome the limitations of the Fourier Transform, providing a multi-resolution analysis framework that became fundamental to signal and image processing. Its discrete variant, the DWT, is a cornerstone of the JPEG 2000 image compression standard and enabled powerful digital watermarking algorithms, where information can be embedded imperceptibly into the coefficients of a transformed image for copyright protection and authentication.

The talk then draws a direct conceptual line from the mathematical operation of convolution at the heart of the wavelet transform to the convolutional layers that define modern convolutional neural networks (CNNs). This connection highlights how signal processing principles have profoundly influenced the architecture of deep learning. Finally, we examine how AI, now a mature field, is giving back to the scientific disciplines that fostered its growth. We provide a short overview of AI's expanding role in scientific discovery, with a particular focus on mathematics. This includes advances in automated theorem proving, where AI suggests new proof strategies, and the development of AI-based solvers for complex linear systems, demonstrating a powerful new synergy between computational mathematics and artificial intelligence. This narrative underscores a continuous cycle of innovation where tools created for one domain become foundational to another, which in turn revolutionizes the original.

Period	22 Aug 2025
Held at	School of Mathematics and Physics
Degree of Recognition	Local