# Outsmarting Chat GPT 4 - can it do math?

TLDRIn this video, the host challenges Chat GPT with a series of mathematical problems to test its reasoning and computational abilities. The AI demonstrates proficiency in arithmetic and identifies prime numbers, but struggles with more complex tasks like identifying Friedman numbers and the six sixes challenge. It shows improvement in solving algebraic problems and understanding the four fours challenge, yet occasionally provides incorrect or incomplete solutions, highlighting the unpredictable nature of AI in complex problem-solving.

### Takeaways

- 🧠 The video tests Chat GPT's mathematical reasoning capabilities beyond basic computation.
- 🤖 Chat GPT demonstrates proficiency in arithmetic and understanding of natural language in math-related queries.
- 🔍 The script explores if Chat GPT can identify prime numbers and correctly answers that the sum of two primes can be prime in specific cases.
- 📚 It showcases Chat GPT's ability to reason about mathematical properties, such as the result of raising odd numbers to powers and adding an even number.
- 🔢 The video challenges Chat GPT with complex expressions involving large odd numbers to the power of other large odd numbers, plus an even number, to determine primality.
- 🕵️♂️ Chat GPT almost correctly identifies that such a massive number cannot be prime due to the addition of an even number, showing an understanding of number properties.
- 🔍 The script tests Chat GPT's knowledge of Friedman numbers and its ability to reconstruct numbers from their digits, with mixed results in reasoning.
- 🧩 The 'four fours challenge' and 'six sixes challenge' are mentioned as examples of human superiority in creative number manipulation, where Chat GPT struggles.
- 📉 Chat GPT fails to correctly identify or create expressions for Friedman numbers, showing gaps in its problem-solving approach for specific types of mathematical puzzles.
- 📚 The system of equations involving perfect squares is solved by Chat GPT using algebraic manipulation, demonstrating its ability to handle complex mathematical reasoning.
- 🤷♂️ Despite successes, Chat GPT sometimes provides incorrect or nonsensical answers, highlighting the unpredictability of its performance in certain mathematical contexts.

### Q & A

### What is the main purpose of the video script?

-The main purpose of the video script is to test the capabilities of an AI, specifically its mathematical reasoning and problem-solving skills, by posing various mathematical questions and challenges.

### How does the script demonstrate the AI's proficiency in arithmetic?

-The script demonstrates the AI's proficiency in arithmetic by asking it to calculate the sum of the first three odd numbers and explaining that computers are very good at raw computation.

### What is the significance of the question about the sum of two prime numbers being prime?

-The question about the sum of two prime numbers being prime is significant as it tests the AI's understanding of prime numbers and its ability to reason about mathematical properties and exceptions.

### Why does the script mention the improvement in the AI's response to the prime number question?

-The script mentions the improvement in the AI's response to highlight the AI's ability to learn and adapt over time, showing that it can provide more accurate answers in subsequent interactions.

### What is the challenge presented by raising an odd number to a large power and then adding 17?

-The challenge is to determine if the resulting number is prime. The script explains that since the base is odd and raised to a power, the result is odd, and adding 17 (another odd number) results in an even number, which cannot be prime.

### What is a Friedman number and why is the AI's understanding of it tested in the script?

-A Friedman number is a number that can be reconstructed from its own digits using basic arithmetic operations. The AI's understanding of Friedman numbers is tested to evaluate its ability to recognize patterns and perform complex mathematical reasoning.

### What is the 'four fours challenge' and how does it relate to the AI's capabilities?

-The 'four fours challenge' is a mathematical puzzle where the goal is to create expressions for consecutive integers using exactly four fours and basic arithmetic operations. It relates to the AI's capabilities as it tests its creativity and problem-solving skills with numbers.

### Why does the script discuss the AI's failure in the 'six sixes challenge'?

-The script discusses the AI's failure in the 'six sixes challenge' to illustrate that even though the AI is proficient in raw computation, it may struggle with tasks that require creative manipulation of numbers, which is an area where humans may excel.

### What is the system of equations presented in the script, and how does the AI approach solving it?

-The system of equations presented is 9M + 16 = A and 16M + 9 = B, with A and B being perfect squares. The AI approaches solving it by rearranging the equations algebraically and using reasoning to find the possible integer values of M.

### How does the script conclude about the AI's performance in mathematical reasoning?

-The script concludes that the AI has shown impressive progress in mathematical reasoning, especially in algebraic manipulation and problem-solving. However, it also points out that the AI can fail completely in certain tasks, often being unaware of its mistakes.

### Outlines

### 🧠 Testing Chat GPT's Mathematical Reasoning

The script begins with an introduction to Chat GPT and its capabilities in arithmetic and natural language processing. The host plans to test Chat GPT with mathematical reasoning problems, starting with a simple arithmetic series sum to demonstrate its proficiency. The host then moves on to more complex problems, such as determining the primality of numbers and handling large odd numbers raised to high powers. The script highlights Chat GPT's ability to improve over time and its capacity to handle complex reasoning, despite occasional mistakes.

### 🔢 Exploring Prime Numbers and Exponentiation

This paragraph delves into the topic of prime numbers, specifically questioning whether the sum of two prime numbers can ever be prime. The host challenges Chat GPT with an example and notes an improvement in its response compared to a previous test. The script then presents a problem involving very large numbers raised to powers and the addition of a small even number, testing Chat GPT's understanding of primality and odd-even properties. The host observes that while Chat GPT almost reaches the correct conclusion, it makes a minor error in reasoning, yet overall shows improvement in handling such problems.

### 🔍 Investigating Friedman Numbers and Mathematical Puzzles

The host introduces Friedman numbers, which are numbers that can be reconstructed from their own digits through mathematical expressions. Chat GPT is tested with large numbers to determine if they are Friedman numbers. The script reveals that Chat GPT struggles with this task, providing incorrect reasoning and failing to identify the correct expressions. The host also presents the 'four fours challenge' and a similar 'six sixes challenge,' where Chat GPT attempts to create expressions for consecutive integers using only the digits four and six, respectively. The results show that Chat GPT fails to solve these puzzles effectively, indicating a limitation in its ability to manipulate numbers creatively.

### 🏆 Solving System of Equations and Advanced Reasoning

In this section, the host presents a system of equations involving perfect squares and challenges Chat GPT to find possible integer values for a variable 'M.' The script demonstrates Chat GPT's ability to rearrange equations and find solutions, including a higher value that is not immediately obvious. The host is impressed by Chat GPT's progress and its capacity to use both inspection and algebraic methods to solve the problem. This part of the script showcases Chat GPT's advanced reasoning skills and its potential to tackle complex mathematical problems.

### 🤔 Attempting Abstract Mathematical Problems

The final paragraph presents an abstract mathematical problem involving the sum of an integer's square and cube, along with odd differences. Chat GPT attempts to solve the problem but makes a mistake in its reasoning, incorrectly identifying the largest number that cannot be expressed in the given way. The host notes Chat GPT's occasional failure to recognize its own mistakes and the unpredictability of its performance. The script concludes with a reflection on Chat GPT's capabilities and the host's intention to continue testing and explaining solutions in future sessions.

### Mindmap

### Keywords

### 💡Chat GPT

### 💡Arithmetic series

### 💡Prime numbers

### 💡Exponentiation

### 💡Friedman numbers

### 💡Four fours challenge

### 💡Pythagorean triple

### 💡Algebraic rearrangement

### 💡Perfect squares

### 💡Cube and square

### Highlights

Testing the latest iteration of Chat GPT with mathematical questions to evaluate its reasoning capabilities beyond raw computation.

Demonstrating Chat GPT's proficiency in arithmetic and natural language understanding with the sum of the first three odd numbers.

Using the formula for the sum of an arithmetic series to find the sum of the first 30 odd numbers, showcasing Chat GPT's mathematical abilities.

Chat GPT's improvement in identifying whether the sum of two prime numbers can ever be prime, including understanding twin primes.

Presenting a complex mathematical problem involving large odd numbers raised to powers and adding 17, to test Chat GPT's reasoning about prime numbers.

Chat GPT's incorrect reasoning about the sum of an odd number raised to powers and an even number, highlighting a small mistake in its logic.

Testing Chat GPT with another complex exponentiation problem to see if it can correctly identify composite numbers.

Chat GPT's success in identifying that adding two odd numbers results in an even number, which cannot be prime.

Exploring Friedman numbers, a type of number that can be reconstructed from its own digits, and Chat GPT's attempt to identify them.

Chat GPT's failure to correctly identify a large number as a Friedman number, despite claiming to understand the concept.

The four fours challenge is introduced, a mathematical puzzle that requires creating expressions using only the number four.

Chat GPT's struggle with the six sixes challenge, failing to create expressions for the first 50 positive integers using only the number six.

Solving a system of equations involving perfect squares to find possible values of M, showcasing Chat GPT's algebraic skills.

Chat GPT's impressive solution to a complex problem involving Pythagorean triples and finding integer values of M.

Chat GPT's attempt to solve an abstract problem about the largest number that cannot be written as the sum of an integer's square and cube.

Highlighting Chat GPT's occasional failure to perform basic arithmetic correctly, despite its overall good grasp of mathematics.

The unpredictability of Chat GPT's performance in mathematical reasoning, where it can fail completely without realizing its mistakes.