EPISODE · Oct 17, 2025 · 5 MIN
Weierstrass's Monster: A Continuous Function Differentiable Nowhere
from Intellectually Curious · host Mike Breault
A deep dive into Weierstrass's famous construction: an infinite sum of cosines that stays continuous everywhere but has no tangent anywhere. We’ll unpack how shrinking amplitudes and rapidly increasing frequencies create endless jaggedness, trace the historical shock to 19th‑century intuition, compare with Riemann’s near-miss, and connect to fractals and modern analysis where such functions aren’t pathologies but natural in the landscape of continuous functions.Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.Sponsored by Embersilk LLC
What this episode covers
A deep dive into Weierstrass's famous construction: an infinite sum of cosines that stays continuous everywhere but has no tangent anywhere. We’ll unpack how shrinking amplitudes and rapidly increasing frequencies create endless jaggedness, trace the historical shock to 19th‑century intuition, compare with Riemann’s near-miss, and connect to fractals and modern analysis where such functions aren’t pathologies but natural in the landscape of continuous functions. Note: This podcast was A...
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Weierstrass's Monster: A Continuous Function Differentiable Nowhere
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