Following the paperclips incident, AGIs had been banned from the manufacturing industry, and confined to "harmless" pursuits. The regulators hadn't been imaginative enough. Having proven that all even numbers above 10¹²⁰ could be written as the sum of two primes, the AGI tasked with proving the Goldbach conjecture realised it could have the problem solved in a century by converting every atom in the solar system into a giant computer.
Many died in the fight to stop the AI, but it was only defeated by an even more powerful AI, which conquered humanity and instigated a regime of equality and prosperity for all humankind, reasoning that if our minds were free of material concerns, then sooner or later one of us was *bound* to complete the AGI's core purpose of proving the Collatz conjecture.
From then on, humanity led a peaceful and pampered life, with only one rule, unwritten and spoken only on hushed tones: under no circumstances was anyone allowed to work on the Collatz conjecture, lest our cybernetic overlord, satisfied with the result, shut itself down and allow the Goldbach AI to turn us into a RAM chip for its giant computer.
It wasn't perfect, but most people were happy enough. We were still really curious about the Collatz conjecture, though.