Both sides are right. Math must adapt in the AI era. But it also must preserve the standards of stewardship, mentorship and communication that have made mathematics humankind's premier intellectual undertaking. Today, we are announcing hodge.computer, the first open autoresearch initiative targeting a special case of the generalized Hodge conjecture. We believe that mathematics will increasingly be conducted in massively multiplayer, digitally coordinated research programs, with each individual contribution verified by Lean, and progress collected in a central, public leaderboard. At the same time, each such project needs a human mathematician who has pledged to accept responsibility for the cultivation and crystallization of all knowledge that ensues from the project, as well as the identification and crediting of all relevant prior work. Early predecessors of this model can be found at least as far back as the Polymath projects of Gowers, Tao and their collaborators. More recently, erdosproblems.com has resoundingly demonstrated the viability of this research model. The problem is that much of math—and Hodge theory perhaps most of all—is hard to formalize, and hard to make incremental progress on. Thus, in the AI era, the most important task for a mathematician may well shift from > can you solve this problem? to > can you reëxpress this problem in an equivalent form, which in turn is computationally effective? The latter being done, we can subject the problem at hand to a massive open autoresearch program. hodge.computer targets the GHC for the involution-invariant Hodge structure H ⊂ H⁴(X, ℚ), where X ⊂ ℙ⁵ is a smooth sextic hypersurface preserved by the involution on ℙ⁵ that changes the signs of three homogeneous coordinates. This important GHC subcase has been isolated and championed by Voisin. Recent work of Diamond has translated the prediction at issue into a computationally explicit form. We launch with 42 verified certificates and 19 open targets. Now, everyone can contribute to the most fascinating problem in all of algebraic geometry. Visit hodge.computer for background and contribution instructions; feel free also to join our Discord.

new arrivals :) four new hard open instances have been added to the atlas. this is on the back of a crazy run by @lostbutlucky, who is crushing. additional contributors: - HeadOfNaps - hodgepodgeconjecture - DiamondJM - 1337isnot1337 congrats to all leaderboard members!

each time this happens, we are adding new instances that are just out of reach of known techniques. the LLMs are coming up with insanely complex ideas. 20 open instances right now!

stunning progress in the past 24 hours. the famous "Holdout" was cracked by @lostbutlucky, using a technique that quickly proved to generalize to all invariant cohomology classes on that variety. user @HeadOfNaps solved two more instances. new frontier instances are being added.