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Learn about the future of Computer Algebra Systems in this 26-minute talk that explores basic primitive groupoid theory, semagrams, and symbolic functions. Discover insights from the Topos Institute's research as Owen Lynch presents innovative approaches to algebraic computation, supported by detailed slides and practical implementations in Gatlab code. Delve into the theoretical foundations and practical applications of algebraic geometry while exploring the intersection of mathematical theory and computational tools. Access accompanying resources including comprehensive slides, GitHub repository with Gatlab.jl implementation, and a detailed blog post covering algebraic geometry concepts to deepen understanding of the presented material.