Computer-assisted proofs (CAPs) have become an essential tool for rigorously validating mathematical results, particularly in fields where pen-and-paper analytical approaches alone prove challenging. In this talk, we will first discuss a posteriori validation methods; that is, CAP techniques designed to certify numerical solutions and establish rigorous bounds on computational errors. Then, we will explore the broader impact of CAPs, particularly in the study of delay maps derived from delay differential equations (DDEs) of the form $ y’(t) = \alpha y(t) + g(y(t − \tau))$. DDEs are naturally set on infinite-dimensional spaces and as such, even scalar equations exhibit rich dynamics. The approach integrates Chebyshev series expansions to rigorously evaluate the delay map. The discussion will include a case study on the Mackey-Glass equation, and its long-standing conjecture related to chaotic dynamics. Finally, we will outline some future directions for rigorous numerics, the next steps in software development, and ongoing challenges in advancing the field.