First Progress in 50 Years on Most Famous Computing Problem

Listen to 100s of Science Documentaries on Turing for Free. Check out the App at iOS: https://apps.apple.com/in/app/the-turing-app/id6752724106 Android: https://play.google.com/store/apps/details?id=com.theturingapp.turing&hl=en or listen at https://theturingapp.com TIMESTAMPS: 00:00 - Introduction 04:29 - From Rural Alabama to the Apple II Computer 14:17 - How Computers Optimize Resources 20:14 - What the Future Holds Ryan Williams has spent his life probing the limits of computation and breaking through barriers others thought were impossible. From a childhood in rural Alabama, where an Apple II sparked his love of programming, to landmark breakthroughs at MIT, Williams has reshaped theoretical computer science. His first generational breakthrough came in 2011, when he proved that a powerful class of problems called NEXP cannot be solved by polynomial-size ACC circuits. This result broke through decades of barriers and helped create the algorithms-to-lower-bounds paradigm, a new way of using faster algorithms to prove that other algorithms cannot exist. Then, in 2025, Williams stunned the field again. Building on work by James Cook and Ian Mertz, he improved a 50-year-old result about time and memory in computation, challenging a landmark theorem connected to Leslie Valiant. #ComputerScience #ComplexityTheory #MIT #Algorithms #PvsNP #scienceexplained ----------- Turing is a leading publishers of popular science books. Check out our collection on Amazon: https://www.amazon.com/stores/Turing-Editorial-Team/author/B0GVXKMGGJ/allbooks?ccs_id=4637a82d-44e3-49b7-92d6-ed1aec5fe06b Apple Books: https://books.apple.com/us/author/turing-editorial-team/id1895369034?see-all=books ---------------- Checkout our Series of Weekly Podcasts On Wonders of Science Adventures into Chemistry Spotify: https://open.spotify.com/show/0kqIbkcrhuzFPf5rgRDPkQ?si=88693d8c97934fc6 Apple Podcasts: https://podcasts.apple.com/us/podcast/adventures-into-chemistry/id1801975450 Beyond Proof: Stories in Maths Spotify: https://open.spotify.com/show/0EJXj5CF6wqE79WTwpYKGr?si=a429edd3979b4429 Apple Podcasts: https://podcasts.apple.com/us/podcast/beyond-proof-stories-in-mathematics/id1881693625 Mavericks of Science: Meet the most influential and groundbreaking contemporary researchers Spotify: https://open.spotify.com/show/48c6VqsI8vtH9D2W5MYXfG?si=acc3565470d246ef Apple Podcasts: https://podcasts.apple.com/us/podcast/mavericks-of-science/id1875688838 Million Dollar Problems of Mathematics: Legendary, unsolved puzzles that have baffled the world's sharpest minds, using Everyday Language Spotify: https://open.spotify.com/show/1dHIDxANHtjJtVzITrOwYM?si=8e7b302f198548ac Apple Podcasts: https://podcasts.apple.com/us/podcast/million-dollar-problems-of-mathematics/id1796668358 Mysteries of the Universe: Questions that keep astrophysicists awake at night Spotify: https://open.spotify.com/show/53cFFxbShCGjYBKFFUayNq?si=d47ed62f389c4f8b Apple Podcasts: https://podcasts.apple.com/us/podcast/what-would-worlds-largest-telescope-find/id1796678795?i=1000768443430 Planet Earth: Science of Climate and Earth Spotify: https://open.spotify.com/show/4HRLQiQJ6GUgJs6wotO3xn?si=b99ce74037534f28 Apple Podcasts: https://podcasts.apple.com/us/podcast/planet-earth/id1886256155 Quarks to Cosmos: Journey Inside the Atom to the Far End of Cosmos Spotify: https://open.spotify.com/show/0OtvBwq0GA0SGijgF2GZYv?si=4a2d444aadd94121 Apple Podcasts: https://podcasts.apple.com/us/podcast/quarks-to-cosmos/id1809992176 Realm of Quantum Mechanics Spotify: https://open.spotify.com/show/3ESCY4B2HB03ZpZJB5J6Y9?si=462d90847a4a4077 Apple Podcasts: https://podcasts.apple.com/us/podcast/realm-of-quantum-mechanics/id1796673349 The Future of Medicine Spotify: https://open.spotify.com/show/7ioXdgkNuHThPc8p1DRHxk?si=ebcbfe9b417f48bb Apple Podcasts: https://podcasts.apple.com/us/podcast/the-future-of-medicine/id1793412323 The Science of Us: Biology, neuroscience, and psychology to unpack the machinery behind our daily experiences Spotify: https://open.spotify.com/show/28qepKUu83gGzPXtst5MeT?si=2c2a7aec570d4a54 Apple Podcasts: https://podcasts.apple.com/us/podcast/the-science-of-us/id1887044303 What the Tech: Foundational math and engineering underneath The Frontier Tech Spotify: https://open.spotify.com/show/41I3bea5v66iKTZdOglG0R?si=279f4848e6bd46eb Apple Podcasts: https://podcasts.apple.com/us/podcast/what-the-tech/id1887925458 Wild Origins: Nature, Animals and Us Spotify: https://open.spotify.com/show/0sdLh1dp4jT7WgGNSvzyVG?si=aa15e34f827446ab Apple Podcasts: https://podcasts.apple.com/us/podcast/wild-origins/id1881725041 CREDITS: Association for Computing Machinery (ACM) Paul G. Allen School MIT CSAIL Google DeepMind Anthropic Claude Google FedEx India, Middle East and Africa Google Quantum AI @projectsyncere Auburn Tigers on Auburn Undercover Google Design Cornell University Simons Institute for the Theory of Computing Turing Awardee Clips OpenAI Medium