# AI won silver at the Olympics of Math

TLDRAI has recently won a silver medal at the International Mathematical Olympiad (IMO), showcasing its advanced problem-solving skills. The AI, named Alpha Proof and based on Google's Gemini, was just one point away from a gold medal. It utilized a combination of Gemini and a software called Lean to ensure the legality of each step in its proofs. This achievement is seen as a significant step towards AGI (Artificial General Intelligence), with some experts impressed by the AI's creativity and reasoning. However, the use of Lean as a check raises questions about the purity of the AI's capabilities. There are hints that a pure LLM (Large Language Model) without such assistance is also showing promise, suggesting that future IMO competitions may see AI contenders without the need for such support systems.

### Takeaways

- 🏅 AI has won a silver medal at the International Mathematical Olympiad (IMO), a prestigious competition.
- 🧠 Some claim that winning a gold medal at IMO would signify the achievement of AGI (Artificial General Intelligence).
- 🤖 Google's Gemini AI system was used as the basis for the AI that won the silver medal.
- 🔢 The AI was just one point away from a gold medal, scoring 41 out of 42 points.
- 📝 The problems in the IMO are not about solving equations but proving mathematical properties and relationships.
- 🤖 Alpha Proof, the AI that won the silver, is a fine-tuned version of Gemini, assisted by a software called Lean.
- 🏁 Lean ensures that every step taken by Gemini in the proof process is mathematically legal and valid.
- 🎓 Only five out of over a thousand professional participants got a particularly difficult question right, which Alpha Proof also solved.
- 📚 The AI was trained on around 100 million proofs translated into Lean's rigorous format from human language proofs.
- 👨🏫 Fields Medalist and mathematician Tim Gowers found the AI's non-obvious constructions impressive and beyond the state of the art.
- 🔮 There are hints that a pure LLM (Large Language Model) without the need for Lean may be capable of winning a gold medal in the near future.

### Q & A

### What is the International Mathematical Olympiad (IMO)?

-The International Mathematical Olympiad (IMO) is the most prestigious mathematics competition for high school students worldwide. It involves solving complex and creative math problems that require advanced thinking and problem-solving skills.

### Why is winning a gold medal at the IMO considered a milestone for AI?

-Winning a gold medal at the IMO is considered a milestone for AI because it would demonstrate the AI's ability to perform at a level of human-like intelligence, showcasing true critical thinking, creativity, and problem-solving skills, which are hallmarks of artificial general intelligence (AGI).

### What is the significance of an AI winning a silver medal at the IMO?

-An AI winning a silver medal at the IMO is significant as it shows that AI is very close to achieving AGI. It indicates that AI can perform at a high level of mathematical reasoning and is capable of understanding and applying complex mathematical concepts.

### What is the role of the software 'Lean' in Alpha Proof's success at the IMO?

-Lean is a software that checks every step taken by the AI, Alpha Proof, to ensure that all moves in the mathematical proof are legal and valid. It acts as a rigorous system to prevent any incorrect steps from being included in the proof process.

### How did Alpha Proof manage to solve the problems on the IMO exam?

-Alpha Proof, which is based on Google's Gemini, was fine-tuned and trained on a large number of proofs written in Lean. It then used this training to produce its own proofs, with every step checked by Lean for correctness.

### What is the difference between a pure language model (LLM) and Alpha Proof's approach?

-A pure LLM would attempt to solve problems without any external assistance or checks for correctness. Alpha Proof, on the other hand, is a fine-tuned version of Gemini that is checked by Lean at every step to ensure the correctness of its proofs.

### What is the importance of the fact that only five out of over a thousand professional mathletes got a particular question right on the IMO exam?

-This highlights the difficulty level of the IMO problems. The fact that Alpha Proof was able to solve these challenging questions indicates its advanced capabilities in mathematical reasoning and problem-solving.

### What does Tim Gowers, a Fields Medalist and judge at the IMO, think about Alpha Proof's performance?

-Tim Gowers found Alpha Proof's ability to come up with a non-obvious construction in its proof to be very impressive, stating that it was beyond what he thought was the state of the art in AI.

### How did the creators of Alpha Proof train it to translate human proofs into Lean proofs?

-They trained a version of Gemini to translate numerous human proofs into Lean proofs. Then, they fine-tuned another version of Gemini using these translated proofs, which allowed it to produce its own proofs while being checked by Lean.

### What does the future hold for AI in mathematical research and the concept of AGI?

-The future of AI in mathematical research looks promising, with the potential for AI to achieve even higher levels of performance in competitions like the IMO. The concept of AGI may continue to evolve as AI capabilities advance and new benchmarks for intelligence are established.

### Outlines

### 🏅 AI's Silver Medal at the International Maths Olympiad

The script discusses recent claims about the potential of AI to achieve a gold medal at the International Maths Olympiad (IMO), considered a hallmark of artificial general intelligence (AGI). It highlights the surprising achievement of an AI named Alpha Proof, based on Google's Gemini, which earned a silver medal, just one point shy of gold. The script explains the nature of IMO problems, which require proving properties of mathematical functions rather than solving equations. It also clarifies that Alpha Proof's success was not due to a direct input into Gemini but was facilitated by an additional software called Lean, which ensures the legality of each step in the proof process. The discussion emphasizes the creativity and foresight required in mathematical proofs, comparing the process to chess, where legal moves must be strategically chosen to reach a goal.

### 🤖 The Role of Creativity and Assistance in AI's Mathematical Success

This paragraph delves into the role of creativity in AI's performance at the IMO and the assistance it received. It mentions that only five out of a thousand contestants correctly answered one of the most challenging questions, which Alpha Proof also solved correctly. The script introduces Tim Gowers, a Fields Medalist and automatic theorem prover enthusiast, who was impressed by the AI's non-obvious construction. The training process of Alpha Proof is explained, involving the translation of numerous 'sloppy' human proofs into the rigorous Lean system, and the fine-tuning of Gemini on approximately 100 million proofs. The script concludes with speculation about the potential for a pure language model LLM to achieve a gold medal in future IMOs without the need for Lean's assistance, hinting at promising results from experiments with a natural language reasoning system.

### Mindmap

### Keywords

### 💡AI

### 💡International Mathematical Olympiad (IMO)

### 💡AGI

### 💡Gemini

### 💡AlphaProof

### 💡Lean

### 💡Proof

### 💡Fields Medal

### 💡Theorem Proving

### 💡LLM

### Highlights

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

Achieving a gold medal at IMO is considered a hallmark of Artificial General Intelligence (AGI).

Google's Gemini AI system was used as the base for the AI that won the silver medal.

The AI was just one point shy of winning a gold medal, scoring 41 out of 42.

The problems in IMO are not about solving equations but proving mathematical properties.

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

Alpha Proof is a fine-tuned version of Gemini, checked by a software called Lean to ensure legality of each step in the proof.

Lean ensures that every move in the mathematical proof is legal, similar to the rules in a game of chess.

The creativity in solving the problems comes from Gemini, while Lean ensures the correctness of the steps.

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

The AI was trained on around 100 million proofs translated into Lean to learn how to produce its own.

The AI's performance on IMO is seen as a significant step towards achieving AGI.

There is an ongoing debate on whether the AI's achievement should be attributed to Gemini or the assisting Lean system.

Experiments with a natural language reasoning system built upon Gemini showed promise for future problem-solving skills.

The potential for a pure LLM to achieve a gold medal at IMO in the future is suggested as a possibility.

The future of mathematical research and the definition of AGI are expected to evolve with advancements in AI.