The Shape Fact That Breaks Every Mathematician's Brain

Moving from 2 to 3 to 1,000 dimensions in 3 steps, a ball inscribed inside a cube fills almost 0% of the space. Everything you learned about shapes stops working. Terence Tao is a Fields Medal winner and professor at UCLA, widely considered the greatest living mathematician. We cover: why geometry in high dimensions defies every low-dimensional instinct, why mathematicians deliberately go to higher dimensions to solve problems in lower ones, what Jim Simons' cone discovery revealed about singularities in 8+ dimensions, and why this isn't abstract — it's exactly where AI and LLMs operate. High-dimensional space doesn't behave. And that's now everyone's problem. Watch the full conversation here: https://www.youtube.com/watch?v=ukpCHo5v-Gc ——— 📬 Get the transcript, fascinating bonus content, and my Monday M.A.G.I.C. Message: https://briankeating.com/yt 🌠 Have a .edu email and live in the USA 🇺🇸? You automatically win a meteorite: https://BrianKeating.com/edu 🔔 Subscribe: https://www.youtube.com/DrBrianKeating?sub_confirmation=1 🎯 Support Into the Impossible on Patreon — get my weekly M.A.G.I.C. Message, unfiltered bonus content, and live monthly Office Hours with me: https://www.patreon.com/drbriankeating ⭐ Join this channel for perks, monthly Office Hours, and your name in the Member Roster at the end of every episode: https://www.youtube.com/channel/UCmXH_moPhfkqCk6S3b9RWuw/join 📚 My books: Losing the Nobel Prize (memoir): http://amzn.to/2sa5UpA Think Like a Nobel Prize Winner: https://a.co/d/03ezQFu Focus Like a Nobel Prize Winner: https://a.co/d/hi50U9U Galileo's Dialogue (first-ever audiobook): https://a.co/d/iZPi9Un Also, if you're open to it, I'd greatly appreciate a small credit in the video description, such as: Video editing by the creative team at North Cat Studio. 🌐 More: 🏄‍♂️ Twitter: https://twitter.com/BrianKeating 📚 Substack https://briankeating.substack.com/ss ✍️ Blog: https://briankeating.com/blog 🎙️ Audio-only: https://briankeating.com/podcast #intotheimpossible #briankeating #science #physics #astronomy #cosmology #podcast #universe