Dating back to ancient Greece, the idea that any mathematical statement can ultimately be proven true or false, and any apparent contradiction ultimately erased, was as enticing as it was intuitive for many logicians and mathematicians. However, this long-dominant belief was upended in the early 20th century when the logician Kurt Gödel converted a written paradox – ‘This statement cannot be proved’ – into an equation, shattering the notion that mathematics could be built on structures of total certainty. This animation from TED-Ed traces how Gödel was able to use words to transform mathematics forever, and how his ‘incompleteness theorem’ has led to breakthroughs in both his field and the digital world.