Google AI just solved 56-year-old math problems on its own
What's the story
Google's DeepMind has announced that its AI system, AlphaProof Nexus, has autonomously solved nine open Erdos problems. The mathematical puzzles were first posed by the legendary mathematician Paul Erdos in 1946 and some had remained unsolved for as long as 56 years. The groundbreaking achievement was accomplished with just a few hundred dollars worth of computing resources.
Additional accomplishments
AlphaProof Nexus also proved 44 open OEIS conjectures
Along with solving the Erdos problems, AlphaProof Nexus also proved 44 open OEIS conjectures and solved a 15-year-old problem in algebraic geometry. The AI system even discovered a new algorithmic parameter in optimization theory that had never been found by humans before. This is particularly significant as it highlights the autonomous capabilities of the system, which generated and verified proofs using computer-level verification tools without any human intervention.
Verification challenges
The announcement reignites debate over AI-generated mathematical proofs
The announcement from Google DeepMind has reignited the debate over how to verify the correctness of an AI-generated mathematical proof. Unlike other AI proof systems, Google has taken a different approach by using Lean, a formal verification system. This way, every logical step in the proof is checked automatically using strict mathematical rules, eliminating unsupported claims and missing logic instantly without human intervention.
Hallucination concerns
Google raises concerns about 'hallucinations'
Google has also raised concerns about "hallucinations" in AI-generated mathematics. These are instances where an AI system generates proofs that sound convincing but contain serious logical mistakes. The company explained that sometimes, the AI invents mathematical statements called lemmas and falsely presents them as already established results. Other times, it may avoid solving the hardest part of a problem by simply renaming it as a "helper lemma," making the overall proof appear complete even though the core difficulty remains unsolved.
Future implications
Proof attempts by agents enhanced human understanding of a problem
The researchers at Google DeepMind believe that their combination of AI reasoning and formal verification could change the way mathematicians work in the future. They found that proof attempts by their agents enhanced human understanding of a problem, even when an agent couldn't prove the claim at hand. This suggests that formally verified proof sketches could allow human experts to focus directly on unresolved parts instead of spending time re-checking entire arguments.
AGI debate
AI still 'nowhere near' true AGI, Demis Hassabis clarifies
The announcement from Google DeepMind has also sparked a debate over whether these advancements mean AI is getting closer to artificial general intelligence (AGI). However, Demis Hassabis, the CEO of DeepMind, has clarified that today's AI systems are still "nowhere near" true AGI. He said that current systems are far from the kind of deep originality shown by legendary thinkers such as Srinivasa Ramanujan.