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What is a Hilbert Space?

To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/AbideByReason/ . You’ll also get 20% off an annual premium subscription. What is a Hilbert Space? David Hilbert and John von Neumann both played played key roles in the development of Hilbert Spaces, with Hilbert laying much of the groundwork and von Neumann finishing it off by giving the first complete definition of them. These spaces then quickly became useful in areas like Quantum Mechanics, the physics of heat transfer, and even modeling sound waves. Here, you will see that they are really just a natural generalization of the spaces we encounter in basic high school geometry. _____ Join my Patreon community:   / abidebyreason   _____ Lebesgue Integral Video:    • The Integral That Changed Math Forever   Music: Epidemic Sound Animations created using Manim: https://www.manim.community/ Illustrations and Thumbnails: Christine Kosakowski _____ References: "Princeton Companion to Mathematics" Edited by Timothy Gowers "Intro to Quantum Mechanics" by David Griffiths This video was sponsored by Brilliant