{"podcast":{"title":"Beyond Proof: Stories in Mathematics","slug":"beyond-proof-stories-in-mathematics-7730628","podcast_index_feed_id":7730628,"rss_url":"https://anchor.fm/s/10fa0520c/podcast/rss","website_url":"https://podcasters.spotify.com/pod/show/val99","image_url":"https://d3t3ozftmdmh3i.cloudfront.net/staging/podcast_uploaded_nologo/45471323/45471323-1772314744207-f7c3a3b18f708.jpg","author":"The Turing App","episode_count":14,"summary":"Stories in Math is the podcast I wanted when I was younger and math felt like this sealed-off world I couldn’t get into. Math has always been a very human thing. It’s people arguing, guessing, getting stuck, getting lucky, and sometimes accidentally stepping into an idea so big it changes everything. This show is a collection of those stories, that bring out the journey and stories behind mathematical discoveries Stories in Math is for anyone who’s curious. If you love math, you’ll get the backstory you didn’t get in class. If you’ve always felt shut out by math, this is a way in.","last_synced_at":"2026-06-26T14:18:23.809377+00:00","page_url":"https://stenobird.com/podcast/beyond-proof-stories-in-mathematics-7730628"},"episode":{"title":"Evil Function That Broke Mathematics","slug":"evil-function-that-broke-mathematics","published_at":"2026-04-10T02:12:00+00:00","page_url":"https://stenobird.com/podcast/beyond-proof-stories-in-mathematics-7730628/evil-function-that-broke-mathematics","show_page_url":"https://stenobird.com/podcast/beyond-proof-stories-in-mathematics-7730628","url":"https://podcasters.spotify.com/pod/show/val99/episodes/Evil-Function-That-Broke-Mathematics-e3g0s8m","audio_url":"https://anchor.fm/s/10fa0520c/podcast/play/116469462/https%3A%2F%2Fd3ctxlq1ktw2nl.cloudfront.net%2Fstaging%2F2026-2-6%2Fe0f6b53f-a131-7dd9-08f8-863b8cf1b406.mp3","summary":"Calculus, the mathematics of change developed by Newton and Leibniz, has been the bedrock of modern science for centuries, powering everything from the Industrial Revolution to the development of semiconductors and AI. However, for two hundred years, it relied on the intuitive \"smoothness\" of functions—the belief that any continuous, unbroken curve would eventually resemble a straight line if you zoomed in far enough. While mathematicians like André-Marie Ampère attempted to formally prove that continuity implied differentiability almost everywhere, they viewed \"problem points\" like sharp corners as mere isolated exceptions. This comfortable dogma was shattered in 1872 by Karl Weierstrass, a German mathematician whose unconventional career began in fencing and secondary school teaching before he revolutionized mathematical rigor at nearly age 40. Weierstrass unveiled a mathematical object that contemporaries decried as a \"deplorable evil\" and an \"outrage against common sense\": a function that is continuous everywhere but differentiable nowhere. By adding an infinite series of cosine waves with rapidly increasing frequencies, he constructed an infinitely jagged line that possesses no smooth parts and no tangent lines at any point. This creation horizontally defied geometric intuition and forced a radical choice upon the mathematical community: either abandon the field’s status as a steadfast discipline or rebuild its foundations from the ground up. This \"jagged function\" ultimately transitioned mathematics away from purely visual, physical intuition toward a new era of absolute logical rigor, forever remaking the architecture of the infinite.","meta_description":"Calculus, the mathematics of change developed by Newton and Leibniz, has been the bedrock of modern science for centuries, powering everything from the In…","key_points":[],"chapters":[],"topics":[],"duration_seconds":1162,"processing_state":"not_requested","actions":[{"name":"request_transcript","method":"POST","url":"https://stenobird.com/v1/public/podcasts/beyond-proof-stories-in-mathematics-7730628/episodes/evil-function-that-broke-mathematics/transcription-requests","description":"Idempotently request low-priority transcript generation for this episode."},{"name":"read_markdown","method":"GET","url":"https://stenobird.com/podcast/beyond-proof-stories-in-mathematics-7730628/evil-function-that-broke-mathematics.md","description":"Read the agent-friendly Markdown representation of this episode resource."}]}}