Where do ideas come from? A mathematician ponders eureka moments and solving complex problems

Mathematician Geordie Williamson had a dramatic "aha moment" in a hotel shower — and it got him thinking about where brilliant ideas come from. This idea began in 2009 when a well-known mathematician, Tim Gowers, asked 'Is massively collaborative mathematics possible?' One can ask an apparently easier question: are there infinitely many prime numbers that differ by at most 1,000, or 1 million, or 1 billion? In 2013, Yitang Zhang, working alone, had a crucial breakthrough, showing that there are infinitely many prime numbers separated by at most 70 million.