An AI just started inventing its own math proofs, solving geometry riddles that have left humans stumped for decades.
March 20, 2026
Original Paper
$R$-equivalence on Cubic Surfaces I: Existing Cases with Non-Trivial Universal Equivalence
arXiv · 2603.19215
The Takeaway
Researchers used a next-generation AI model to discover and prove original 'lemmas' in algebraic geometry that have been intractable since the 1970s. This marks a major shift where AI is no longer just a processing tool, but a genuine scientific partner capable of independent abstract discovery.
From the abstract
Let $V$ be a smooth cubic surface over a $p$-adic field $k$ with good reduction. Swinnerton-Dyer (1981) proved that $R$-equivalence is trivial on $V(k)$ except perhaps if $V$ is one of three special types--those whose $R$-equivalence he could not bound by proving the universal (admissible) equivalence is trivial. We consider all surfaces $V$ currently known to have non-trivial universal equivalence. Beyond being intractable to Swinnerton-Dyer's approach, we observe that if these surfaces also ha