What we’re witnessing right now in AI for math is a dramatic improvement in objective-driven problem-solving, but it does not speak to non-objective discovery. I have always maintained that objectives are achievable when they are one stepping stone away, which means that they are within reach if their necessary prerequisite stepping stones are already laid. We say as much in Why Greatness Cannot Be Planned. Furthermore, I have identified “the stepping stepping already laid” as every invention and idea ever hatched over the course of human history. That is the frontier of civilization. But a massive challenge for every creative field is to make all the relevant stepping stones actually accessible to its practitioners. How can anyone be aware of all of human knowledge in their field? To the extent they cannot, some dots cannot be connected even if they’re already uncovered. AI advances today have suddenly made the existing stepping stones vastly more accessible. It can see something close to “all” of them, which means it has the possibility of leaping to many more next stepping stones in the chain. Combined with a brute force-ish “try every known stepping stone under the sun”, that’s what we’re seeing in the pursuit of popular objectives. But discovery and innovation are not only about finding the right existing stepping stones to solve your objective because for many problems the stepping stones are not already laid and also do not follow directly from existing stepping stones. If those problems are ever to be solved, they will require open-ended, non-objective search through spaces of ideas that are motivated not by solving a problem as an objective, but by being interesting in their own right. The advances we’re seeing today speak only faintly to that purpose, which is why open-endedness remains firmly at the frontier of AI.