# 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 that AI like ChatGPT excels in language but struggles with complex mathematical reasoning and creative problem-solving required by the IMO. The script also explores the potential of different AI systems, including proof-solving models that use formal math language, which might be better suited to meet the IMO's demands.

### Takeaways

- 🧠 The IMO Grand Challenge was created to develop an AI capable of winning a gold medal at the International Mathematics Olympiad, showcasing exceptional mathematical prowess.
- 🏆 Previous gold medal winners at the IMO include renowned mathematicians like Terence Tao and Maryam Mirzakhani, highlighting the prestige of the competition.
- ⏰ The AI must produce proofs that are checkable within 10 minutes, mimicking the time a human judge takes to verify a solution, and has only 4.5 hours to solve each set of three problems.
- 🔒 The AI system must be open source, publicly released, and reproducible without internet access, ensuring transparency and fairness.
- 🤖 No AI, including ChatGPT, has yet won or competed in the IMO, indicating the complexity and difficulty of the challenge.
- 📚 GPT-4, despite excelling in other exams like the SAT and Biology Olympiad, may struggle with the IMO due to its nature as a language model focused on predicting the next word rather than mathematical reasoning.
- 📝 The IMO tests true understanding and creative problem-solving, which is different from the predictable and formulaic math questions found in exams like the SAT.
- 🔍 An example IMO problem is provided, illustrating the need for creative solutions and the process of finding the minimum number of uphill paths in a Nordic Square.
- 📉 ChatGPT's attempt at solving an IMO problem resulted in incorrect answers, revealing its limitations in mathematical reasoning and path counting.
- 🔬 A Microsoft paper analyzed GPT-4's abilities, suggesting it shows sparks of artificial general intelligence but lacks the capacity for mathematical research and critical reasoning.
- 🌟 OpenAI is working on a different AI system, a proof-solving model that speaks the language of formal math, which has potential to be more successful in the IMO Grand Challenge.
- 🔑 Combining a formal math language AI with user-friendly features like ChatGPT could be a promising approach to pass the IMO Grand Challenge and advance AI in mathematics.

### Q & A

### What was the ambitious challenge proposed by AI researchers and mathematicians in 2019?

-The challenge was to create an AI that could win a gold medal at the International Mathematics Olympiad (IMO), which would signify that the AI has one of the best mathematical minds in the world.

### What are some examples of individuals who have won a gold medal at the IMO?

-Terence Tao and Maryan Mirzakhani are examples of individuals who have won a gold medal at the IMO.

### What are the proposed rules for the IMO Grand Challenge for AI?

-The rules include that each proof the AI produces must be checkable in 10 minutes, the AI has the same amount of time as a human competitor (four and a half hours for each set of three problems), and the AI must be open source, publicly released, reproducible, and cannot query the internet.

### Has any AI, including ChatGPT, won or competed in the IMO competition as of the recording of the video?

-No AI, including ChatGPT, has won or competed in the IMO competition as of the recording of the video.

### What is a significant limitation of ChatGPT in solving IMO problems?

-ChatGPT is not very good at math, particularly at counting or keeping track of multiple operations, as it is primarily a language model that excels at predicting the next word in a sentence.

### What are the main differences between math questions on the SAT and IMO problems?

-SAT math questions are quite predictable and formulaic, often included in the training data set of language models like ChatGPT, whereas IMO problems are designed to test true understanding and creative problem solving.

### What is the example IMO problem mentioned in the video?

-The problem is to find, as a function of n, the smallest possible number of uphill paths in a Nordic Square, where a Nordic Square is an n x n board containing all integers from 1 to n² with specific adjacency and valley path conditions.

### How does the speaker attempt to understand the likelihood of an AI passing the IMO Grand Challenge?

-The speaker first tries to understand the solution to an IMO problem on human terms, then looks at how ChatGPT attempts to solve it, and finally compares it to other AI competitors.

### What was the result of using GPT-4 to solve the IMO problem?

-GPT-4 gave the wrong answer, failing to correctly identify the number of valleys and paths, and generally struggled with the problem, unable to score any points.

### What are some limitations of GPT-4 in solving complex mathematical problems, according to the video?

-GPT-4 lacks critical reasoning and the ability to examine each step of its arguments. It doesn't make guesses or backtrack effectively, primarily due to its training on webtext data where most math solutions provide correct answers without detailing the thinking process.

### What is the alternative AI system mentioned that might be better suited for the IMO Grand Challenge?

-The alternative AI system is a proof-solving model that speaks the language of formal math, trained to iteratively search for new proofs using the lean theorem prover, making it more capable of producing machine-checkable proofs.

### What potential future changes in exams are suggested due to AI capabilities like those of ChatGPT?

-Exams might change to be more like the IMO, rewarding creative problem solving and necessitating a more exploratory approach, as current exams with more predictable structures are more easily tackled by AI.

### Outlines

### 🚀 The Ambitious Challenge of AI in Mathematics

In 2019, AI researchers and mathematicians set a challenge to create an AI capable of winning a gold medal at the International Mathematics Olympiad (IMO). The rules stated that AI must produce checkable proofs within 10 minutes, have the same time limit as human competitors, be open source, and not query the internet. Although GPT-4 has excelled in other exams, no AI has yet competed in the IMO. This is partly because IMO problems require deep understanding and creative problem-solving, areas where language models like GPT-4 struggle.

### 🔢 Understanding a Nordic Square Problem

An example IMO problem involves a Nordic Square, an n x n board containing numbers from 1 to n². A valley is defined as a cell only adjacent to larger numbers, and an uphill path starts from a valley and moves to adjacent cells in increasing order. The task is to find the smallest number of uphill paths for any n. The solution involves arranging numbers to minimize paths, starting with recognizing there should be only one valley and ensuring each pair of adjacent numbers has a single path back to the valley.

### 🧠 ChatGPT's Attempt at Solving the IMO Problem

When given the IMO problem, GPT-4 provided incorrect solutions, failing to recognize the importance of minimizing the number of valleys and correctly counting paths. Despite its advancements, GPT-4 lacks the necessary critical reasoning and understanding to solve such complex mathematical problems. A recent paper highlights that GPT-4, while impressive in some areas, still cannot conduct mathematical research or solve IMO problems effectively.

### 🤖 Exploring Advanced AI Competitors

Other AI systems, like a proof-solving model developed by OpenAI, show more promise for solving IMO problems. These models use formal mathematical language and iterative proof search methods to break down and solve complex statements. Combining such a system with a language model like ChatGPT could enhance mathematical problem-solving capabilities. While GPT-4 excels in standardized exams by recognizing problem structures, true creative problem-solving remains a human strength, potentially influencing future exam designs.

### Mindmap

### Keywords

### 💡International Mathematics Olympiad (IMO)

### 💡IMO Grand Challenge

### 💡GPT-4

### 💡Valley

### 💡Uphill Path

### 💡Lean Theorem Prover

### 💡Artificial General Intelligence (AGI)

### 💡Nordic Square

### 💡Proof-solving Model

### 💡Mathematical Creativity

### Highlights

In 2019, AI researchers and mathematicians proposed the IMO Grand Challenge to create an AI capable of winning a gold medal at the International Mathematics Olympiad.

Winning a gold medal at the IMO places you among the world's top mathematical minds, with past winners including Terence Tao and Maryam Mirzakhani.

The rules for the AI include producing proofs that can be checked in 10 minutes, having the same time as human competitors (four and a half hours), being open source, and not querying the internet.

Despite advances, no AI, including ChatGPT, has yet won or even competed in the IMO competition.

GPT-4 has passed many other exams like the SAT and the Biology Olympiad but struggles with the IMO due to its lack of true understanding and creative problem-solving skills.

IMO problems are designed to test true understanding and creative problem-solving, unlike the more predictable and formulaic questions found in other exams.

An example IMO problem from 2022 involves finding the smallest number of uphill paths in a Nordic Square, demonstrating the complexity and creativity required.

GPT-4 failed to solve the 2022 IMO problem correctly, indicating its current limitations in handling complex mathematical reasoning.

Microsoft's paper on GPT-4 mentions 'sparks of artificial general intelligence' but highlights its inability to conduct mathematical research.

Automated proof-solving models, like the one using the lean theorem prover, show more promise in solving IMO problems than language models like GPT-4.

The lean theorem prover-based model iteratively searches for new proofs, breaking down mathematical ideas into smaller statements until nothing is left to prove.

Combining an AI that can speak formal math with user-friendly interfaces like ChatGPT could advance AI's capabilities in mathematics.

While GPT-4 excels at predicting the next word in a sentence, it struggles with the creativity and play required for complex math problems.

GPT-4's ability to pass exams relies on applying general solution methods rather than memorizing specific problem statements.

Future exams might need to evolve to reward creative problem-solving to stay ahead of AI capabilities.