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....

In a recent Sunday edition of this newsletter, we dedicated the editorial to a remarkable model created by Google DeepMind that is able to solve geometry problems from the Mathematical Olympiads at the level of a gold-medalist. Today, we will dive into the architecture powering this model. A few months ago, the International Mathematical Olympiad announced the AIMO Prize, a $10 million award for an AI model that can achieve a gold medal in an 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. Geometry, an important and one of the hardest aspects of IMO tests, combines visual and mathematical challenges. We might intuitively think that this would be the hardest type of problem for AI models to solve. A few weeks ago, Google DeepMind published a paper unveiling AlphaGeometry, a model capable of solving geometry problems at the level of an IMO gold medalist. The key magic behind AlphaGeometry is the combination of two different ML architectures: a neural language model and a symbolic deduction engine. Together, they tackle complex geometry theorems, bringing a unique approach to problem-solving....

Voisin, who is based at the Jussieu Institute of Mathematics in Paris, studies algebraic geometry, a field of research concerning geometric figures ' called varieties ' that are defined by algebraic equations. The prototypical example is the equation x2 + y2 = 1, which defines a circle. She has been described as the world's foremost expert on the still-unsolved Hodge conjecture, an algebraic-geometry problem that concerns the nature of the varieties that are contained inside a larger variety. The conjecture is one of the Millennium Prize Problems ' seven mathematical questions that each carry a US$1-million prize for the first person to solve them. No. Since I do mathematics, I have always been the first woman to do this, or to do that. Sometimes I feel that the media, each time they speak about me, say, 'the first woman who ''. Personally, I think it's not good to put emphasis on that. For me, I am just a mathematician. I am happy if people appreciate the mathematics that I am doing. Bias certainly still exists. I certainly recognize that mathematics, as a world, is not encouraging to girls at school and to young women. Personally ' maybe because of my personality, because I don't care what people think about me ' I didn't suffer from this....

A few months ago, the International Mathematical Olympiad announced the AIMO Prize, a $10 million award for an AI model that can achieve a gold medal in an 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. Geometry, an important and one of the hardest aspects of IMO tests, combines visual and mathematical challenges. We might intuitively think that this would be the hardest type of problem for AI models to solve. The most interesting aspect of AlphaGeometry is its architecture, which combines a Large Language Model (LLM) with a symbolic model. Neuro-symbolic architectures have long attempted to bridge the gap between the two most established machine learning schools: neural networks and rule-based models. While LLMs excel at identifying patterns in data and reasoning through problems, they struggle with the systematic, multi-step reasoning required in complex geometry problems. Symbolic models, which solve problems using rules, can only operate in very constrained settings. How did AlphaGeometry apply neuro-symbolic models to geometry' The model, based on an LLM and a symbolic rules engine, first uses the symbolic model to attempt a solution. If unsuccessful, the LLM suggests new constructs that open new reasoning paths for the symbolic model. This is an oversimplification, but this is a short editorial after all. '...