Mathematicians Dubbed His Work "Evil". It Broke Mathematics

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 - The Math That Powered the Modern World 04:23 - Karl Weierstrass & The "Deplorable Evil" 08:29 - The Two Schools of Thought 12:10 - Self-Similarity and Fractals ----------- Learn how the Weierstrass function shattered mathematics by creating a continuous function that is differentiable nowhere. In this video, we explore how Karl Weierstrass challenged Isaac Newton and Gottfried Wilhelm Leibniz’s foundations of calculus to spark a revolution in mathematical rigor. Whether you're a math student, a physics enthusiast, or a lover of STEM history, this deep dive breaks down the history of calculus, the failure of geometric intuition, and the birth of modern analysis. We examine how key concepts like derivatives, infinite series, and localized slopes transformed our understanding of dynamic systems. Turing is a leading publisher 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 ---------------- Check out 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: MIT OpenCourseWare Khan Academy Massachusetts Institute of Technology (MIT) MIT Media Lab ASML NASA Science Breakthrough NVIDIA NVIDIA Omniverse Institute of Politics at Harvard Kennedy School