The Erdős Gap

Hey, it’s Marek.This episode starts with socks. Specifically, the drawer where I keep the lonely ones, waiting for their missing pairs that I refuse to believe are gone forever.That philosophical stubbornness turns out to be surprisingly relevant to a wave of mathematical “breakthroughs” in October 2025, where AI helped close 23 of Paul Erdős’ famously stubborn problems. Except, and here’s the twist, many weren’t actually solved. They were found. The solutions had existed for years, sometimes decades, buried in obscure journals that nobody had connected to Erdős’ challenges.I call this the Erdős Gap: when your answer already exists, but finding it costs more than re-solving it.In the episode, I explore where this gap hides in organisations: scattered archives, vocabulary silos, and knowledge systems so impenetrable that (as we used to joke at one company I worked for) Saddam Hussein should have stored his weapons of mass destruction there, had he had any.Your responses to the newsletter were fantastic. Gaurish Dessai shared a case of 40 R&D labs running duplicate experiments across the globe because data sat on siloed servers. Marshall Kirkpatrick asked about that moment when “the relative cost of retrieval vs. re-creation flips” - a simple framing I wish I’d thought of. And Michael Rosemann offered this gem: the secret to AI engagement might be comfort with being found rather than expansive (and expensive) search.The question I leave you with: Where in your organisation do you suspect the answer already exists?Stay curious! This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit marekkowal.substack.com