# Google AI dominates the Math Olympiad. But there's a catch

TLDRGoogle's AI has made a breakthrough by scoring 28 points in the International Math Olympiad (IMO), solving 4 out of 6 problems. This achievement, however, comes with a catch; the AI was given extra time and human-translated questions into the formal language Lean, which is a significant advantage over students who must interpret and solve within time limits. Despite this, the AI's performance is impressive, showcasing its potential to assist in mathematical proofs and problem-solving in the future.

### Takeaways

- đź§ AI has made significant advancements but is generally not proficient at solving math problems.
- đźŚź Google has developed AI models capable of solving complex math problems from the International Math Olympiad (IMO).
- đźŹ† The AI models achieved a score equivalent to a silver medal in the IMO, solving 4 out of 6 questions.
- âŹł The AI was given more time to solve the problems compared to human participants in the IMO.
- đź“š Google's AI models were trained on past Olympiad problems, similar to how students prepare for the contest.
- đź”Ť The AI models use a formal language called Lean, which allows for verification of proofs for correctness.
- đź¤– The translation of questions into Lean was done manually by humans to ensure accuracy for the AI models.
- đź’ˇ The AI's solution to a geometry problem introduced a novel approach that differed from typical human strategies.
- đźš€ Despite the differences in conditions, solving 4 out of 6 IMO problems is an impressive feat for AI.
- đź› ď¸Ź The development of AI tools that can assist with understanding and learning proofs is a promising advancement.
- đź”® The future may see computers assisting with mathematical proofs, similar to how calculators are used today.

### Q & A

### What is the significance of AI's ability to solve International Math Olympiad (IMO) questions?

-AI's ability to solve IMO questions is significant as it demonstrates the advanced capabilities of AI in mathematical problem-solving, which traditionally has been a challenge for AI models. It also indicates the potential for AI to assist in complex mathematical tasks and education.

### What is the International Math Olympiad (IMO) and how has it evolved over time?

-The International Math Olympiad (IMO) is an annual contest for pre-college students that began with 7 countries in 1959. It has expanded to over 100 countries, each sending a team of 6 students, and is considered one of the most challenging math competitions for young mathematicians.

### How many points is each question in the IMO worth, and what is the average mean score?

-Each question in the IMO is worth 7 points. With a possible total of 42 points, the average mean score is about 16, indicating the high difficulty level of the competition.

### How did Google's AI models perform in solving IMO questions?

-Google's AI models scored 28 points by solving 4 out of 6 questions, a performance equivalent to winning a silver medal in the IMO.

### What specific AI models did Google use to tackle the IMO problems?

-Google used AlphaProof for two algebra and one number theory problem, and AlphaGeometry for the geometry question.

### How quickly was the geometry question solved by Google's AlphaGeometry?

-AlphaGeometry solved the geometry question in just 19 seconds, which is remarkably fast compared to the average human time of 1.5 hours per question.

### What are the limitations in comparing AI's performance to human students in the IMO?

-The comparison is not entirely fair because AI models were given extra time and had the questions manually translated into a formal language, whereas human students had to interpret and solve the questions within a strict time limit.

### What is Lean and how does it relate to the AI models' performance in the IMO?

-Lean is a proof assistant language used to formally represent mathematical proofs. Google's AI models were trained to translate questions into Lean, which allows for the verification of the proofs' correctness.

### How did the AI models handle the translation of questions into Lean?

-Humans manually translated the IMO questions into Lean to ensure accuracy, as the AI models were still in the process of learning to do this translation without errors.

### What was unique about the solution proposed by Google's AI for one of the IMO geometry problems?

-The AI proposed a novel solution by constructing an additional point and using it to create similar triangles, which is a different approach from what many humans would typically use.

### What is the potential future impact of AI in assisting with mathematical proofs and education?

-AI has the potential to become a valuable tool in education, assisting students and mathematicians with understanding complex concepts and proofs, much like calculators are used for intricate calculations today.

### Outlines

### đź§ AI's Breakthrough in Solving Olympiad-Level Math Problems

Presh Talwalkar introduces the remarkable progress in AI's ability to tackle complex math problems, exemplified by Google's AI models scoring 28 points on the International Math Olympiad (IMO), a contest known for its difficulty. The AI models, AlphaProof and AlphaGeometry, solved problems in algebra, number theory, and geometry, with AlphaGeometry solving a geometry question in just 19 seconds. However, Talwalkar emphasizes that the AI's performance should be viewed in context, noting the differences in time constraints and preparation methods between the AI and human contestants. The AI was trained on past Olympiad problems and required human assistance to translate the contest questions into a formal language called Lean, which is used for verification of mathematical proofs. Despite these advantages, the AI's novel solution to a geometry problem demonstrates its potential to offer new insights into mathematical problem-solving.

### đź¤– The Future of AI in Assisting Mathematical Proofs

This paragraph delves into the implications of AI's success in solving IMO problems and its potential to revolutionize the way we approach mathematical proofs. The AI's method of proof construction is highlighted, including its unique approach to a geometry problem by introducing an unconventional solution that involved constructing a new point and using circles to form similar triangles. The discussion acknowledges that while the AI was given extra time and had the questions translated for it, solving four out of six problems is still an impressive feat. Talwalkar expresses excitement about the prospect of using AI as a tool to assist with understanding complex mathematical ideas and proofs, comparing it to the use of calculators for intricate calculations. He concludes by congratulating Google DeepMind for their achievement and looks forward to the future where computers may play a significant role in mathematical problem-solving.

### Mindmap

### Keywords

### đź’ˇAI

### đź’ˇInternational Math Olympiad (IMO)

### đź’ˇAlphaProof

### đź’ˇAlphaGeometry

### đź’ˇLean

### đź’ˇProof assistant

### đź’ˇMistranslation

### đź’ˇFormal language

### đź’ˇReverse proof

### đź’ˇSilver medal

### đź’ˇGemini AI

### Highlights

Google AI has made a breakthrough in solving challenging math problems from the International Math Olympiad (IMO).

AI models are typically not very proficient at general math problem-solving despite their reliance on mathematical calculations.

The IMO is an annual contest for pre-college students that has grown from 7 to over 100 participating countries since 1959.

IMO contestants typically score an average of about 16 points out of a possible 42, indicating the difficulty of the competition.

Google's AI models scored 28 points by solving 4 out of 6 questions, a performance equivalent to winning a silver medal.

AlphaProof and AlphaGeometry are the AI models that tackled algebra, number theory, and geometry problems respectively.

Google's AlphaGeometry solved a geometry question in just 19 seconds, showcasing impressive speed.

The comparison between AI and human performance in math problem-solving is not straightforward due to different conditions.

AI models were given more time to solve problems compared to the time constraints faced by human contestants.

Google's AI models were trained on past Olympiad problems, similar to how students can prepare for the contest.

The Gemini AI translates questions into a formal language called Lean, a proof assistant for verifying correctness.

AI models can learn from mistranslated problems, but for the IMO, humans manually translated the questions to avoid errors.

The translation of text into Lean is not a trivial task and carries the risk of introducing incorrect assumptions.

Google's AI proposed a novel solution to a geometry problem by constructing additional points and circles.

The AI's approach to the geometry problem was different from the common human method, offering a new perspective.

While it's not fair to equate Google AI's performance with a human's due to the different conditions, solving 4 out of 6 problems is still an impressive feat.

The development of AI tools that can assist with understanding and learning mathematical proofs is an exciting prospect.

The potential for computers to aid in mathematical problem-solving and proofs could greatly enhance our capabilities in the field.