# AI won silver at the Olympics of Math

TLDRAn AI based on Google's Gemini recently won a silver medal at the International Math Olympiad (IMO), narrowly missing a gold by one point. This AI, named Alpha Proof, combines Gemini's capabilities with Lean software to ensure all mathematical steps are valid. The achievement raises questions about whether AI has reached artificial general intelligence (AGI). While impressive, some believe true AGI would require a pure LLM without assistance from systems like Lean. Google's experiments suggest that future AIs might achieve this, indicating promising advancements in AI's problem-solving abilities.

### Takeaways

- ๐ AI named Alpha Proof, based on Google's Gemini, won a silver medal at the International Mathematical Olympiad (IMO), showing it was just one point away from a gold medal.
- ๐ง The achievement is considered significant because it suggests AI is approaching the level of Artificial General Intelligence (AGI), which requires creativity and complex reasoning.
- ๐ Alpha Proof is not just Gemini; it's Gemini assisted by a software called Lean, which ensures the mathematical steps taken are legal and logical.
- ๐ค Lean acts as a checker for Gemini, preventing it from making illegal moves in the mathematical proof process, similar to how certain moves are restricted in chess.
- ๐ Alpha Proof's success involved training Gemini to translate informal math proofs into the formal Lean system, which is more structured and precise.
- ๐ Despite the impressive result, the transcript's author expresses a desire for a pure language model (LM) AI to achieve such a feat without the need for Lean's assistance.
- ๐ค The collaboration between Gemini and Lean demonstrates how AI can be fine-tuned to produce high-quality results while adhering to strict logical frameworks.
- ๐ Only five out of over a thousand professional participants correctly solved one of the IMO problems, which Alpha Proof also managed to solve, highlighting the difficulty level of the competition.
- ๐จโ๐ซ Fields Medal winner and mathematician Tim Gowers, who judged the AI's work, found the AI's non-obvious construction to be very impressive and beyond the current state of AI.
- ๐ฎ The transcript hints at future experiments with a natural language reasoning system based on Gemini for advanced problem-solving without the need for formal language translation.
- ๐ The author speculates that in the near future, a pure LM AI might win a gold medal at the IMO, indicating ongoing advancements in AI's reasoning and problem-solving capabilities.

### Q & A

### What is the International Mathematical Olympiad (IMO) and why is it considered prestigious?

-The International Mathematical Olympiad (IMO) is a prestigious competition for high school students that tests their mathematical problem-solving skills. It is considered prestigious because it attracts the brightest young minds from around the world and challenges them with complex and creative math problems.

### What does it mean for an AI to achieve AGI (Artificial General Intelligence)?

-Achieving AGI means that an AI has demonstrated the ability to perform any intellectual task that a human being can do. It implies that the AI has general intelligence and can apply its problem-solving skills to a wide range of disciplines, not just a specific, narrow task.

### How close did the AI, based on Google's Gemini, come to winning a gold medal at the IMO?

-The AI, based on Google's Gemini, won a silver medal at the IMO and was just one point shy of winning a gold medal, out of a total of 42 points.

### What is the difference between the AI's approach to solving a math problem and solving an equation?

-The AI's approach to solving a math problem at the IMO level is not about solving equations but about proving properties and relationships. For example, it might involve proving that if certain functions obey a given relationship, they also possess another specific property.

### Why is it significant that only five out of over a thousand professional mathletes got a particular question right?

-This signifies the high level of difficulty of the question and the exceptional performance of the AI, Alpha Proof, which managed to solve the question correctly, showcasing its advanced problem-solving capabilities.

### What is the role of the software 'Lean' in the AI's problem-solving process?

-Lean is used to rigorously check that every step the AI takes in its problem-solving process is mathematically legal and valid, ensuring the correctness of the proof.

### How does the AI's problem-solving process relate to playing chess?

-Both involve starting from an initial state and making a series of legal moves to reach a desired end state. In chess, it's checkmate, while in math, it's proving a theorem. The AI, like a chess player, must foresee and creatively navigate a path to the solution.

### What did Tim Gowers, a Fields Medalist and judge at the IMO, say about the AI's performance?

-Tim Gowers found the AI's ability to come up with a non-obvious construction very impressive, stating it was beyond the state of the art in automatic theorem proving.

### How was the AI, Alpha Proof, trained to produce proofs in Lean?

-Alpha Proof was trained by first translating numerous human-written proofs into Lean format and then fine-tuning Gemini on these proofs to produce its own proofs, with Lean checking each step for correctness.

### What does the future hold for mathematical research with the advancement of AI in theorem proving?

-The future of mathematical research could involve more collaboration between mathematicians and AI systems, potentially leading to new insights and faster advancements in the field.

### What does the mention of a 'natural language reasoning system' at the end of the blog post suggest for future AI developments?

-It suggests that future AI systems may be able to solve complex problems without the need for translation into a formal language, indicating a move towards more advanced and autonomous AI capabilities.

### Outlines

### ๐ AI's Silver Medal at IMO: A Step Towards AGI?

This paragraph discusses the recent achievement of an AI, based on Google's Gemini, earning a silver medal at the International Mathematical Olympiad (IMO), a prestigious math competition. It highlights the claim that winning such a medal would signify the achievement of artificial general intelligence (AGI) due to the demonstration of logical thinking and creativity required to solve complex problems. The script explains the nature of the problems on the IMO exam, which are not about solving equations but proving properties of mathematical functions. The AI, named Alpha Proof, was able to solve difficult problems, including question six, which only five out of over a thousand contestants got right. However, the script also points out that the AI's solution, when directly input into Gemini, was incorrect, indicating the complexity of the task.

### ๐ค The Role of Gemini and Lean in AI's Mathematical Proofs

The second paragraph delves into the process by which the AI, Alpha Proof, was able to achieve its success at the IMO. It explains that Alpha Proof is a fine-tuned version of Gemini, an AI model, which is assisted by a software called Lean. Lean's role is to ensure that every step taken by Gemini in the proof process is mathematically legal, akin to the rules in a game of chess. The script compares mathematical proofs to chess, emphasizing the need for foresight and creativity to reach the correct conclusion. It also mentions that Tim Gowers, a Fields Medal-winning mathematician, was impressed by the AI's ability to come up with non-obvious constructions. The AI was trained on numerous proofs translated into Lean's rigorous system, allowing it to produce its own proofs while being checked by Lean at every step. The paragraph concludes with speculation that a pure language model AI might achieve a gold medal in the future, suggesting that the current system is promising but not yet the epitome of AGI.

### Mindmap

### Keywords

### ๐กAI

### ๐กInternational Mathematical Olympiad (IMO)

### ๐กAGI

### ๐กGemini

### ๐กAlpha Proof

### ๐กLean

### ๐กProof

### ๐กFields Medal

### ๐กTheorem Proving

### ๐กNatural Language Reasoning

### Highlights

AI has won a silver medal at the International Mathematical Olympiad (IMO), a prestigious competition.

Achieving a gold medal at IMO is considered a milestone for AGI (Artificial General Intelligence).

AI's performance was close to winning a gold, missing by just one point.

AI's success involved solving complex problems that required true mathematical thinking and creativity.

The AI, named Alpha Proof, was based on Google's Gemini and used an additional software called Lean.

Lean ensures that every step in the AI's mathematical reasoning is legal and valid.

Only five out of over a thousand professional mathletes got a particular question right, which Alpha Proof also solved.

The process of solving the IMO problems didn't involve just copying and pasting questions into Gemini.

Alpha Proof is a fine-tuned version of Gemini that gets checked by Lean at every step.

Lean does not do the majority of the work; it ensures the AI stays on the right path.

The creativity in solving the problems comes from Gemini, while Lean checks for correctness.

Tim Gowers, a Fields medalist and interested in automatic theorem proving, found the AI's non-obvious construction impressive.

The AI was trained on a large number of proofs translated into Lean to learn the rigorous system.

The training involved around 100 million proofs to fine-tune Gemini's capabilities.

The AI's achievement in the IMO is impressive, but some expected a pure LLM without assistance.

There is ongoing research with a natural language reasoning system based on Gemini for advanced problem-solving skills.

The results with the natural language system were promising, indicating potential for future improvements.

The future of mathematical research with AI involvement is intriguing, with expectations of shifting AGI goalposts.