Zeno's paradoxes were unsolved for 2,000 years — and led to calculus

Around 450 BC, the Greek philosopher Zeno of Elea proposed paradoxes that seemed to prove motion was impossible. Most famous: Achilles and the tortoise. If the tortoise has a head start, Achilles must first reach where the tortoise was — but by then it has moved. He must again reach that point — but again it has moved. Achilles must complete infinitely many steps, which seems impossible. The paradox was only resolved by Newton and Leibniz's invention of calculus in the 17th century, which showed that infinite series can have finite sums. An impossibility proof that lasted 2,000 years accidentally generated one of history's most powerful mathematical tools.

Source: Huggett, N., 'Zeno's Paradoxes', Stanford Encyclopedia of Philosophy (2019)