On Thursday, Google DeepMind introduced that AI methods referred to as AlphaProof and AlphaGeometry 2 reportedly solved 4 out of six issues from this yr’s Worldwide Mathematical Olympiad (IMO), reaching a rating equal to a silver medal. The tech big claims this marks the primary time an AI has reached this stage of efficiency within the prestigious math competitors—however as common in AI, the claims aren’t as clear-cut as they appear.
Google says AlphaProof makes use of reinforcement studying to show mathematical statements within the formal language referred to as Lean. The system trains itself by producing and verifying tens of millions of proofs, progressively tackling tougher issues. In the meantime, AlphaGeometry 2 is described as an upgraded model of Google’s earlier geometry-solving AI modeI, now powered by a Gemini-based language mannequin skilled on considerably extra information.
In line with Google, outstanding mathematicians Sir Timothy Gowers and Dr. Joseph Myers scored the AI mannequin’s options utilizing official IMO guidelines. The corporate reviews its mixed system earned 28 out of 42 attainable factors, simply shy of the 29-point gold medal threshold. This included an ideal rating on the competitors’s hardest downside, which Google claims solely 5 human contestants solved this yr.
A math contest not like another
The IMO, held yearly since 1959, pits elite pre-college mathematicians in opposition to exceptionally tough issues in algebra, combinatorics, geometry, and quantity principle. Efficiency on IMO issues has grow to be a acknowledged benchmark for assessing an AI system’s mathematical reasoning capabilities.
Google states that AlphaProof solved two algebra issues and one quantity principle downside, whereas AlphaGeometry 2 tackled the geometry query. The AI mannequin reportedly failed to resolve the 2 combinatorics issues. The corporate claims its methods solved one downside inside minutes, whereas others took as much as three days.
Google says it first translated the IMO issues into formal mathematical language for its AI mannequin to course of. This step differs from the official competitors, the place human contestants work instantly with the issue statements throughout two 4.5-hour periods.
Google reviews that earlier than this yr’s competitors, AlphaGeometry 2 might remedy 83 p.c of historic IMO geometry issues from the previous 25 years, up from its predecessor’s 53 p.c success charge. The corporate claims the brand new system solved this yr’s geometry downside in 19 seconds after receiving the formalized model.
Limitations
Regardless of Google’s claims, Sir Timothy Gowers provided a extra nuanced perspective on the Google DeepMind fashions in a thread posted on X. Whereas acknowledging the achievement as “nicely past what automated theorem provers might do earlier than,” Gowers identified a number of key {qualifications}.
“The primary qualification is that this system wanted so much longer than the human rivals—for among the issues over 60 hours—and naturally a lot sooner processing pace than the poor outdated human mind,” Gowers wrote. “If the human rivals had been allowed that kind of time per downside they might undoubtedly have scored greater.”
Gowers additionally famous that people manually translated the issues into the formal language Lean earlier than the AI mannequin started its work. He emphasised that whereas the AI carried out the core mathematical reasoning, this “autoformalization” step was executed by people.
Concerning the broader implications for mathematical analysis, Gowers expressed uncertainty. “Are we near the purpose the place mathematicians are redundant? It is exhausting to say. I’d guess that we’re nonetheless a breakthrough or two in need of that,” he wrote. He advised that the system’s lengthy processing occasions point out it hasn’t “solved arithmetic” however acknowledged that “there’s clearly one thing attention-grabbing occurring when it operates.”
Even with these limitations, Gowers speculated that such AI methods might grow to be invaluable analysis instruments. “So we may be near having a program that may allow mathematicians to get solutions to a variety of questions, offered these questions weren’t too tough—the type of factor one can do in a few hours. That may be massively helpful as a analysis software, even when it wasn’t itself able to fixing open issues.”
