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Explore a thought-provoking lecture on the foundations of mathematics and operator theory delivered by Bruce Blackadar from the University of Nevada, Reno. Delve into the intriguing concept of Hilbert spaces without relying on the Countable Axiom of Choice (AC). Gain insights into this advanced topic as part of the Workshop on Operator Algebras and Applications: Connections with Logic and the broader Thematic Program on Operator Algebras and Applications. Discover how this 56-minute talk challenges conventional mathematical thinking and opens up new perspectives in the field of operator algebras.