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In this 58-minute talk from the Simons Foundation, mathematician Sergei Gukov explores the fascinating intersection of artificial intelligence and mathematics in "AI and AC" (alternatively titled "Learning Hardness"). Discover how solving challenging, research-level mathematical problems not only advances mathematics itself but also plays a crucial role in developing next-generation AI systems. Explore specific examples from knot theory and combinatorial group theory that illustrate how mathematics and AI can mutually benefit each other. The concept of "hardness" - particularly in contexts like hard ribbon knots and hard AC presentations - serves as a central theme throughout the presentation. The talk draws on collaborative research with A. Shehper, A. Medina-Mardones, L. Fagan, B. Lewandowski, A. Gruen, Y. Qiu, P. Kucharski, and Z. Wang, offering insights into this exciting frontier where mathematical challenges drive AI innovation.
