Go is too complex for computers to master

What actually happened

The complexity argument was real. Go's branching factor is around 250 against chess's 35, and there is no simple way to score a position, which is why the search-and-evaluate approach that cracked chess got stuck around strong-amateur level for years. In 2014 and 2015 serious people were still saying a decade or more.

AlphaGo combined deep neural networks for policy and value with Monte Carlo tree search, trained first on human games and then on itself. The turning point in the public imagination was move 37 of game two: a shoulder hit on the fifth line that commentators initially thought was a mistake, and which Lee Sedol left the room to process. It was not a mistake. In game four Lee found move 78, the "divine move," and won one game, which is now the last game any human has won against a top engine under normal conditions.

AlphaGo Zero landed the harder blow in 2017. Given nothing but the rules, it rediscovered centuries of human joseki, discarded some as inferior, and beat the version that beat Lee Sedol 100 games to nil. The lesson that stuck was not about Go. It was that "machines can never do X because X requires intuition" has a poor track record, and that expert timelines for it are usually too long.