Google DeepMind's AlphaProof Nexus solved nine open Erdős problems autonomously, some untouc...
Google DeepMind's AlphaProof Nexus autonomously solved nine open Erdős problems this week, some of which had resisted mathematicians for 56 years, at a cost of just a few hundred dollars of compute per problem. For anyone tracking how AI is starting to produce verifiable scientific output rather than plausible looking text, this is one of the cleanest signals yet.
The architecture is the part worth understanding. AlphaProof Nexus pairs a large language model with Lean, a formal proof assistant. The LLM generates candidate proofs and Lean checks every logical step with machine level rigor. When a step does not hold, it fails completely. There is no room for hallucination, no fuzzy partial credit, no confident sounding nonsense. The model is forced to operate inside a system that will reject anything that is not actually true.
The nine problems sat in combinatorics and graph theory, fields where progress often depends on a flash of human intuition that may or may not arrive across an entire research career. For scale, a single postdoc costs six figures a year, and these problems had resisted generations of mathematicians. A few hundred dollars of compute closed them out. Erdős himself famously offered cash bounties for many of his open problems precisely because he expected them to remain hard for a long time.
The timing matters too. One day after OpenAI made headlines for solving a single 80 year old conjecture, DeepMind solved nine. The two labs are clearly converging on the same approach, which is using formal verification as the ground truth layer underneath a generative model. That convergence usually signals a real capability rather than a stunt.
The deeper shift is structural. A Lean verified proof is not a confident sounding output, it is a certificate. Anyone can rerun the checker and confirm the result independently. That property matters far beyond pure mathematics. In cryptography, drug discovery, and materials science, almost correct is functionally the same as wrong, and the bottleneck has often been trust in machine generated results. A verifiable output changes the economics of who can do research and how quickly results can be accepted.
What I will be watching is whether this architecture generalizes outside mathematics, where Lean and similar systems give you a clean formal target. Physics, biology, and computer science have plenty of unsolved problems, but most do not come pre formalized. The next interesting question is whether we see formal verification layers built for those domains, or whether researchers find ways to translate fuzzier problems into shapes these systems can attack. Either way, the queue is forming.
Originally posted on LinkedIn.