DeepMind's journey toward mathematical AI dominance took a major leap last year when AlphaProof and AlphaGeometry nearly clinched gold at the International Math Olympiad (IMO). Now, with the latest upgrade, AlphaGeometry2 (AG2) has officially surpassed top human competitors in geometry, marking a milestone in AI-driven mathematical reasoning. The general consensus among IMO competitors is that geometry problems are among the toughest in each day of the Olympiad. AG2 represents a significant advancement in AI-driven mathematical reasoning, particularly in solving Olympiad geometry problems. Building on its predecessor, AlphaGeometry, AG2 surpasses the performance of an average gold medalist in the International Mathematical Olympiad (IMO). This essay provides a technical overview of AG2's architecture, key improvements, and broader contributions to AI....

Our series about RAG continues with an expxloration of Self-RAG. The engineering section dives into Txtai, a new framework for LLM workflows. In research we are going to dive into DeepSeek-R1( finally). And in the opinion section we will discuss another controversial topics in AI. DeepMind's journey toward mathematical AI dominance took a major leap last year when AlphaProof and AlphaGeometry nearly clinched gold at the International Math Olympiad (IMO). Now, with the latest upgrade, AlphaGeometry2 (AG2) has officially surpassed top human competitors in geometry, marking a milestone in AI-driven mathematical reasoning. The general consensus among IMO competitors is that geometry problems are among the toughest in each day of the Olympiad. AlphaGeometry2 (AG2), an improved version of AlphaGeometry, was released in early 2025 and has demonstrated gold-medalist level performance in solving Olympiad geometry problems. The system builds upon its predecessor by expanding its domain-specific language to handle more complex problems, including those with object movements and linear equations involving angles, ratios, and distances. The coverage rate of the AG2 language on International Math Olympiad (IMO) geometry problems from 2000-2024 increased from 66% to 88%. Furthermore, AG2 utilizes a Gemini architecture for better language modeling and incorporates a knowledge-sharing mechanism that combines multiple search trees, improving its overall solving rate to 84% on IMO geometry problems from the past 25 years, compared to 54% previously. This enhanced performance has allowed AG2 to surpass an average IMO gold medalist. The system also achieved a silver-medal standard at IMO 2024....

MIT physicists and colleagues have for the first time measured the geometry, or shape, of electrons in solids at the quantum level. Scientists have long known how to measure the energies and velocities of electrons in crystalline materials, but until now, those systems' quantum geometry could only be inferred theoretically, or sometimes not at all. The work, reported in the Nov. 25 issue of Nature Physics, 'opens new avenues for understanding and manipulating the quantum properties of materials,' says Riccardo Comin, MIT's Class of 1947 Career Development Associate Professor of Physics and leader of the work. 'We've essentially developed a blueprint for obtaining some completely new information that couldn't be obtained before,' says Comin, who is also affiliated with MIT's Materials Research Laboratory and the Research Laboratory of Electronics. The work could be applied to 'any kind of quantum material, not just the one we worked with,' says Mingu Kang PhD '23, first author of the Nature Physics paper who conducted the work as an MIT graduate student and who is now a Kavli Postdoctoral Fellow at Cornell University's Laboratory of Atomic and Solid State Physics....

In a recent issue of this newsletter, we discussed NuminaMath, an AI model that achieved the top score in the AI Math Olympiad(AIMO). But what about the real International Math Olympiad(IMO)' IMOs are elite high school competitions where the top six students from each participating country must answer six different questions over two days, with a four-hour time limit each day. Some of the most renowned mathematicians of the past few decades have been medalists in IMO competitions Today, I would like to dive into the work that Google DeepMind has been doing in that area with the combination of two models: AlphaProof and AlphaGeometry 2 that recently achieved silver medalist level in the IMOs. More specifically, AlphaProof and AlphaGeometry 2, have successfully solved four out of six problems from this year's IMO, which came just short of reaching the gold medal level....