Explore the fascinating world of mathematical paradoxes, impossibilities, and mind-bending concepts in this comprehensive TED-Ed video series. Delve into topics ranging from perpetual motion machines and Newton's three-body problem to the Infinite Hotel Paradox and exponential growth. Discover the history of banned numbers, unravel the mathematics behind sidewalk illusions, and ponder Zeno's Dichotomy Paradox. Examine the unexpected math in Van Gogh's "Starry Night," contemplate the concept of infinity, and venture into other dimensions. Learn about airline overbooking strategies, the physics of "impossible" free kicks in football, and the mystery of missing fractals. Conclude with an exploration of Gödel's Incompleteness Theorem, a paradox at the heart of mathematics.