An AI system named 'Theo Conjecture' has solved a 35-year-old mathematical conjecture related to common-divisor graphs. This conjecture, originally posed in the 1980s and refined by mathematicians like Paul Erdős, involved finding the largest independent set in a graph where vertices represent integers and edges connect numbers sharing a factor greater than one. The primes, when colored gold, formed the largest independent set, leading to the identity α(Gₙ) = π(n).

While finding the largest independent set is computationally difficult, a simpler measure called the residue (R(G)) can be calculated quickly. Mathematicians hypothesized that the residue might approximate the size of the largest independent set. Siemion Fajtlowicz's program Graffiti explored these ideas, and the conjecture that the residue could be used to approximate prime counting was recorded as 'Written on the Wall.'

Randy Davila, developing a successor to Graffiti called Tx Graffiti, fed the problem to 'Theo Conjecture.' The AI not only proved the long-standing conjecture but also identified an unexpected extra term. This achievement highlights the potential for AI agents and human mathematicians to collaborate on complex problems, offering a glimpse into the future of mathematical discovery.