# ChatGPT vs. World's Hardest Exam

TLDRThe video discusses the 'IMO Grand Challenge', an initiative to create an AI capable of winning a gold medal at the International Mathematics Olympiad. It highlights the difficulty of this task, given the creative problem-solving required, which is beyond the capabilities of current AI like ChatGPT. The script explores the limitations of language models in mathematics, introduces an example IMO problem, and discusses the potential of a different AI system that uses formal math language for proof-solving, suggesting a combination of such systems could be the key to passing the IMO challenge.

### Takeaways

- 🌟 The IMO Grand Challenge aims to create an AI capable of winning a gold medal at the International Mathematics Olympiad (IMO).
- 🏅 Previous gold medal winners at the IMO include renowned mathematicians like Terence Tao and Maryam Mirzakhani.
- ⏱ The AI must produce proofs checkable within 10 minutes, mirroring the time taken by a human judge to evaluate a solution.
- 🕒 AI has the same time constraints as human competitors, with four and a half hours to solve three problems.
- 📜 The AI system must be open source, publicly released, and reproducible without internet access.
- 🤖 As of the video's recording, no AI, including ChatGPT, has won or even competed in the IMO.
- 🧠 GPT-4, despite its achievements in other exams, may struggle with the IMO due to its nature as a language model focused on predicting the next word, not deep mathematical reasoning.
- 📚 The IMO tests true understanding and creative problem-solving, which is different from the formulaic and predictable nature of some other exams.
- 🔍 The provided IMO problem from 2022 illustrates the complexity and creativity required to find the minimum number of uphill paths in a Nordic square.
- 📉 ChatGPT's attempt at solving the IMO problem resulted in incorrect answers, demonstrating its current limitations in mathematical reasoning and path counting.
- 🔧 A different AI system by OpenAI, which uses a proof-solving model and the lean theorem prover, has shown promise in solving IMO problems by breaking down complex ideas into simpler statements.
- 🔑 Combining formal math language capabilities with user-friendly interfaces could be key to creating an AI that can pass the IMO Grand Challenge.

### Q & A

### What is the 'IMO Grand Challenge' mentioned in the script?

-The 'IMO Grand Challenge' is an initiative by AI researchers and mathematicians to create an AI system capable of winning a gold medal at the International Mathematics Olympiad (IMO), which is considered a prestigious event showcasing top mathematical minds.

### What are the rules proposed for an AI system to pass the IMO Grand Challenge?

-The AI system must produce proofs that can be checked in 10 minutes, have the same time as a human competitor (four and a half hours for each set of three problems), be open source and publicly released, and not have access to the internet.

### Why is ChatGPT not considered very good at math according to the script?

-ChatGPT is not very good at math because it is a language model that excels at predicting the next word in a sentence, rather than counting or keeping track of multiple operations, which are essential for solving complex mathematical problems.

### What is the difference between the math questions on the SAT and the IMO problems?

-Math questions on the SAT can be predictable and formulaic, often similar to problems found in the training data set, while IMO problems are designed to test true understanding and creative problem-solving, making them more challenging and less formulaic.

### Can you explain the concept of a 'Nordic square' as described in the script?

-A 'Nordic square' is an n by n board containing all integers from 1 to n squared, with each cell containing exactly one number. Adjacent cells are those that share a common side. A 'valley' is a cell adjacent only to cells with larger numbers, and an 'uphill path' is a sequence of cells starting from a valley with increasing numbers.

### What is the task given to the AI in the 2022 IMO problem presented in the script?

-The task is to find the smallest possible number of uphill paths in a Nordic Square as a function of n, the size of the square.

### How does the script describe the minimum number of paths in a Nordic Square?

-The minimum number of paths in a Nordic Square is achieved when there is only one valley and for every pair of adjacent numbers, there is only one path back to the valley. The total minimum paths are the number of adjacent pairs plus one for the valley itself.

### Why does the script suggest that ChatGPT might not be able to score points on the IMO problem presented?

-ChatGPT might not be able to score points on the IMO problem because it fails to recognize the need for only one valley and incorrectly counts the number of paths, even when prompted with the correct structure.

### What is the Microsoft paper's analysis of GPT-4's abilities in relation to mathematical research?

-The Microsoft paper suggests that GPT-4 shows sparks of artificial general intelligence but lacks the capacity required for mathematical research due to its inability to conduct critical reasoning and examine each step of its arguments.

### What alternative AI system is mentioned in the script that could potentially pass the IMO Grand Challenge?

-The script mentions an AI system developed by OpenAI that is a proof-solving model using the language of formal math and the lean theorem prover, which is capable of producing proofs with multiple non-trivial reasoning steps.

### How does the script suggest exams might change to better reward creative problem-solving?

-The script suggests that exams might need to become more like the IMO, requiring more creative problem-solving and the ability to 'play around' with the problem, as this is currently a uniquely human trait.

### Outlines

### 🤖 AI's Quest for IMO Gold: The Challenge and Rules

In 2019, AI researchers and mathematicians set an ambitious goal to create an AI capable of winning a gold medal at the International Mathematics Olympiad (IMO). The IMO Grand Challenge was designed with strict rules: AI proofs must be verifiable within 10 minutes, mirroring human judging time; the AI has the same time as human competitors, 4.5 hours for three problems; and the AI must be open source, publicly released, reproducible, and cannot access the internet. Despite advances in AI, no AI has yet competed in IMO, and ChatGPT, while excelling in language prediction, struggles with complex mathematical tasks like those found in the IMO.

### 🧩 Solving the Nordic Square Problem: A Human Approach

The video script presents a Nordic Square problem from the 2022 IMO, illustrating the complexity of these mathematical puzzles. The problem involves finding the minimum number of uphill paths in a square grid filled with integers. The solution requires recognizing that for the minimum number of paths, there should be only one valley and each pair of adjacent numbers should have a single path back to the valley. A detailed explanation of how to arrange the numbers to achieve this minimum is provided, demonstrating the creative problem-solving skills required for such challenges.

### 🤖 AI's Struggles with Mathematical Reasoning: ChatGPT's Limitations

The script discusses the limitations of ChatGPT in solving complex mathematical problems, such as the Nordic Square, due to its nature as a language model that excels in predicting the next word rather than mathematical reasoning. Despite passing exams like the SAT, ChatGPT fails to provide the correct solution to the IMO problem, highlighting the need for AI that can understand and apply mathematical concepts creatively. A recent Microsoft paper also points out that GPT-4 lacks the capacity for mathematical research, emphasizing the AI's inability to make guesses or backtrack, which are crucial for solving complex problems.

### 🔍 The Future of AI in Mathematics: Proof-Solving Models and Beyond

The video script explores the potential of different AI systems in mathematics, particularly a proof-solving model developed by OpenAI that uses formal math language and the lean theorem prover. This model is capable of iteratively searching for new proofs and has successfully solved some IMO problems. The combination of such a model with user-friendly AI like ChatGPT could be a promising approach to pass the IMO Grand Challenge. The script also suggests that exams may need to evolve to reward creative problem-solving and adapt to the capabilities of advanced AI systems.

### Mindmap

### Keywords

### 💡IMO Grand Challenge

### 💡International Mathematics Olympiad (IMO)

### 💡AI System

### 💡Open Source

### 💡Language Model

### 💡Nordic Square

### 💡Uphill Path

### 💡Valley

### 💡Proof-Solving Model

### 💡Formal Math Language

### 💡Lean Theorem Prover

### Highlights

The IMO Grand Challenge aims to create an AI capable of winning a gold medal at the International Mathematics Olympiad.

Winning a gold medal at IMO signifies having one of the best mathematical minds globally.

The AI must produce proofs checkable in 10 minutes, similar to human judging time.

AI has the same time as human competitors, 4.5 hours for three problems.

The AI system must be open source, publicly released, and reproducible.

Chat GPT and GPT-4 have not yet competed or won in the IMO.

Chat GPT excels at language prediction but is not very good at math.

IMO problems require true understanding and creative problem-solving.

Chat GPT's training data may include similar SAT math problems but not IMO level.

Exploring the solution to an IMO problem requires understanding and human terms.

Chat GPT's approach to solving problems differs from the IMO's requirements.

An example Nordic Square problem from the 2022 IMO is presented.

The minimum number of uphill paths in a Nordic Square is explored.

Chat GPT fails to provide the correct solution to the Nordic Square problem.

AI's inability to backtrack may hinder its performance in mathematical problem-solving.

OpenAI's proof-solving model, using formal math language, shows promise for IMO challenges.

Combining formal math AI with user-friendly interfaces could be key to passing the IMO Grand Challenge.

Exams may need to evolve to reward creative problem-solving over memorization.

Chat GPT's success in other exams suggests a reliance on memorizing common problem structures.