The Largest Tweetable Number

What is the largest number you can describe in a tweet? With only 280 characters, there must be a finite number of possibilities, which means a largest tweetable number must exist. Joel David Hamkins takes this question on a journey through ever more powerful notations for large numbers, from googolplex to Knuth's up-arrow notation and beyond. But the real puzzle emerges when a clever contestant tries to win a largest number contest by exploiting the concept of definability itself. This leads directly into Berry's paradox, the halting problem, and Kolmogorov complexity, showing why no computer or formal system can determine which descriptions actually define numbers. Hamkins ultimately invokes Tarski's theorem to resolve the paradox: definability itself is not definable. The lecture reveals how a playful question about tweeting numbers opens onto deep results about the limits of language, computation, and mathematical truth.