De Hilbert a los algoritmos cuánticos: el rol del álgebra en el desarrollo de la computación

Abstract

This presentation examines the fundamental and transformative role algebra has played in the evolution of computing, from the formulation of Hilbert's problems to the development of modern quantum algorithms. By starting with a historical analysis, it highlights how the evolution of algebra is intrinsically intertwined with advances in solving the problems posed by Hilbert. As we move along the timeline, the influence of solid algebraic foundations on the emergence of computation theory and early algorithms is clear, paving the way for an unprecedented era of technological development. In the contemporary era, quantum computing emerges as an emerging Industry 5.0 technology, which relies on advanced algebraic concepts for its operation. It concludes with a discussion of the continuing relevance of algebra in past and future technological developments and the importance of a solid mathematical foundation to address the challenges of Industry 5.0. Through this exploration, the importance of algebra as a central pillar in the development of computer science is highlighted, and ultimately its impact in shaping our technological future.