# ChatGPT vs. World's Hardest Exam

TLDRThe video discusses the 'IMO Grand Challenge', an ambitious project to create an AI capable of winning a gold medal at the International Mathematics Olympiad (IMO). It highlights the difficulty of the IMO and the limitations of AI like ChatGPT in solving such complex problems, which require creative problem-solving beyond pattern recognition. The script also explores the potential of proof-solving AI models and their combination with user-friendly AI like ChatGPT, suggesting a promising future in tackling the IMO challenge.

### Takeaways

- 🧠 The IMO Grand Challenge was created to develop an AI capable of winning a gold medal at the International Mathematics Olympiad, showcasing the best mathematical minds.
- 🏆 Previous IMO gold medalists include renowned mathematicians like Terence Tao and Maryam Mirzakhani, emphasizing the prestige of the competition.
- ⏱ The challenge rules require AI to produce proofs checkable within 10 minutes, mirroring the time a human judge takes to evaluate a solution.
- 🕒 AI is given the same time as human competitors, 4.5 hours to solve three problems, without internet access, and must be open-source and reproducible.
- 🤖 As of the video's recording, no AI, including ChatGPT, has competed or won in the IMO, though GPT-4 has excelled in other exams like the SAT and Biology Olympiad.
- 📉 ChatGPT's performance in math is limited; it struggles with counting and tracking operations due to its nature as a language model focused on predicting sentence structure.
- 🧩 The IMO tests true understanding and creative problem-solving, which is different from the predictable and formulaic math questions on exams like the SAT.
- 🔍 The presenter attempts to understand the likelihood of AI passing the IMO by first solving an IMO problem, then analyzing how ChatGPT approaches it, and considering other AI competitors.
- 📝 An IMO problem from 2022 is presented, involving 'Nordic Squares' and the calculation of the minimum number of uphill paths, a complex problem requiring creative solutions.
- 📉 ChatGPT fails to provide the correct solution to the Nordic Square problem, suggesting it lacks the critical reasoning and problem-solving skills needed for the IMO.
- 🔍 A Microsoft paper on GPT-4's abilities indicates it shows 'sparks' of artificial general intelligence but lacks the capacity for mathematical research and critical reasoning.
- 🤖 An alternative AI system by OpenAI, not a language model but a proof-solving model using formal math, has shown promise in solving IMO problems, suggesting a potential path to success in the IMO Grand Challenge.

### 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).

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

-The AI must produce proofs that are checkable 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, released publicly, reproducible, and cannot query the internet.

### Why is ChatGPT considered not very good at math?

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

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

-Math questions on the SAT can be predictable and formulaic, while IMO problems are designed to test true understanding and creative problem-solving.

### What is a Nordic square and what is the objective of the problem presented 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. The objective is to find the smallest possible number of uphill paths in a Nordic Square as a function of n.

### What is the key to solving the Nordic square problem presented in the script?

-The key is recognizing that for the minimum number of paths, there should be only one valley and for every pair of adjacent numbers, there should be only one path back to the valley.

### What is the minimum number of uphill paths in a Nordic Square for a 3x3 board?

-The minimum number of uphill paths for a 3x3 Nordic Square is 13.

### How does the script describe the potential solution for any size of Nordic Square?

-The solution involves arranging the numbers in a tree-like structure where there is only one valley and for every adjacent pair of numbers, there is only one path back to it.

### What was the result when the script's author gave the 2022 IMO problem to ChatGPT?

-ChatGPT provided the wrong answer, suggesting that the smallest number of paths is equal to n and failed to correctly count the paths even when prompted.

### What is the difference between the AI system developed by OpenAI and ChatGPT in terms of solving math problems?

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

### What does the Microsoft paper suggest about the potential of combining a formal math AI with ChatGPT?

-The paper suggests that combining an AI that can speak formal math and correctly prove statements with something like ChatGPT to make it more user-friendly could be a promising approach to pass the IMO Grand Challenge.

### Outlines

### 🧠 AI's Pursuit of Mathematical Brilliance

The paragraph introduces the ambitious 'IMO Grand Challenge' set by AI researchers and mathematicians in 2019, aiming to create an AI capable of winning a gold medal at the International Mathematics Olympiad (IMO). The challenge emphasizes the AI's need to produce verifiable proofs within 10 minutes, adhere to human competitor time limits, and be open-source and reproducible without internet access. The script mentions that despite the capabilities of AI like ChatGPT and GPT-4 in other areas, no AI has yet competed or won in the IMO. It highlights the difference between AI's language prediction skills and the creative problem-solving required for IMO, exemplified by a complex Nordic square problem from the 2022 competition.

### 📚 Understanding the Nordic Square Problem

This paragraph delves into the process of solving the Nordic square problem from the IMO. It explains the concept of a valley and uphill path within the square and how to minimize the total number of uphill paths. The solution involves recognizing that there should only be one valley and a single path back to the valley from each pair of adjacent numbers. The paragraph provides a step-by-step approach to arranging numbers in a tree-like structure to achieve the minimum path count, which is calculated as 2n(n-1) + 1 for any n-sized Nordic square. It also discusses the limitations of ChatGPT in solving this problem, as it fails to correctly identify the minimum number of valleys and paths, indicating a lack of critical reasoning and creative problem-solving skills.

### 🤖 The Future of AI in Mathematical Research

The final paragraph discusses the broader implications of AI in mathematical research and problem-solving. It contrasts the capabilities of ChatGPT, which is based on language prediction and struggles with complex mathematical reasoning, with a proof-solving AI model that uses formal math language and iterative search for proofs. The paragraph mentions that this proof-solving AI has successfully solved some IMO problems and could potentially combine with user-friendly AI like ChatGPT to create a more effective tool for mathematicians. It also reflects on the potential need for exams to evolve to better reward creative problem-solving, as traditional exams may not be sufficient to challenge advanced AI systems.

### Mindmap

### Keywords

### 💡AI

### 💡International Mathematics Olympiad (IMO)

### 💡IMO Grand Challenge

### 💡Language Model

### 💡Nordic Square

### 💡Valley

### 💡Uphill Path

### 💡Proof-Solving Model

### 💡Formal Math Language

### 💡Lean Theorem Prover

### 💡Artificial General Intelligence (AGI)

### Highlights

The IMO Grand Challenge was created to develop 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.

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

AI is given the same time as human competitors to solve problems.

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

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

GPT-4 has excelled in exams like the SAT and biology Olympiad but struggles with IMO problems.

Chat GPT is not adept at math due to its nature as a language model focused on predicting the next word.

IMO problems require true understanding and creative problem-solving, unlike SAT math questions.

A detailed walkthrough of an IMO Nordic Square problem is provided to illustrate the complexity.

The minimum number of uphill paths in a Nordic Square can be calculated as a function of n.

Chat GPT's response to the Nordic Square problem was incorrect, showing its limitations in mathematical reasoning.

AI systems like the one using the lean theorem prover are better suited for formal mathematical proofs.

Combining formal math AI with user-friendly interfaces like Chat GPT could be a promising approach.

GPT-4's success in exams may indicate a need for exams to evolve to better reward creative problem-solving.

The unique human trait of creative problem-solving may be challenged by advancing AI capabilities.

A special thanks to Patreon supporters and the Patron Cat of the Day, Cathulhu.