# Outsmarting Chat GPT 4 - can it do math?

TLDRIn this video, the host tests the mathematical capabilities of the latest iteration of Chat GPT, focusing on reasoning rather than raw computation. They explore prime numbers, Friedman numbers, and complex number properties, noting Chat GPT's improvements and occasional failures. The host also challenges Chat GPT with creative math puzzles, revealing both its strengths in algebra and its struggles with number manipulation, ultimately highlighting the AI's evolving abilities and unpredictable shortcomings.

### Takeaways

- 🧠 Chat GPT is being tested for its mathematical reasoning capabilities beyond simple computation.
- 🔢 It can perform arithmetic in natural language, such as calculating the sum of the first three odd numbers.
- 🤔 The AI struggles with some reasoning problems, such as determining if the sum of two prime numbers can ever be prime.
- 📈 There is an improvement in Chat GPT's performance over time, as it has updated its responses to some questions correctly.
- 🎲 When presented with extremely large numbers resulting from odd numbers raised to powers and then added to an odd number, Chat GPT correctly identifies that the result cannot be prime.
- 🔍 The AI has difficulty with identifying Friedman numbers, which are numbers that can be reconstructed from their own digits.
- 🕵️♂️ In the 'four fours challenge', Chat GPT demonstrates an understanding of the task but fails to create expressions for consecutive integers using only the number four.
- 🔢 Similarly, it fails to create expressions for the first 50 positive integers using only the number six, indicating a limitation in its ability to manipulate numbers creatively.
- 📚 Chat GPT shows an ability to solve algebraic problems, such as finding values of M in a system of equations where the results are perfect squares.
- 🤷♂️ The AI sometimes provides incorrect or nonsensical answers, especially when dealing with abstract or novel mathematical problems.
- 🚫 It may confidently provide wrong answers without recognizing its mistakes, which can be concerning for users relying on its responses.

### Q & A

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

-The main purpose of the video script is to test the capabilities of Chat GPT, particularly its ability to handle mathematical questions and reasoning problems.

### What does the script imply about Chat GPT's performance on arithmetic problems?

-The script implies that Chat GPT is very good at arithmetic and can handle natural language arithmetic questions effectively.

### What is the first mathematical concept tested in the script?

-The first mathematical concept tested in the script is the identification of prime numbers and the question of whether the sum of two prime numbers can ever be prime.

### What is a Friedman number and why does the script mention it?

-A Friedman number is a number that can be reconstructed from its own digits using basic arithmetic operations. The script mentions it as part of testing Chat GPT's ability to recognize and work with unique mathematical properties.

### What is the 'four fours challenge' mentioned in the script?

-The 'four fours challenge' is a mathematical puzzle where the goal is to create expressions for as many consecutive integers as possible using exactly four fours and basic arithmetic operations.

### How does the script describe Chat GPT's performance on the 'six sixes challenge'?

-The script describes Chat GPT's performance on the 'six sixes challenge' as a failure, as it struggles to create expressions for the first 50 positive integers using only six sixes.

### What is the significance of the Pythagorean triple in the final problem presented in the script?

-The Pythagorean triple is significant in the final problem as it provides a hint for finding integer values of M where both A and B are perfect squares in the given equations.

### How does the script evaluate Chat GPT's ability to solve the abstract problem involving the sum of an integer's square and its cube?

-The script evaluates Chat GPT's ability by presenting an abstract problem and observing its approach to finding the largest number that cannot be written as the sum of an integer's square and its cube, noting that it laid out a mathematical research program but made a mistake in identifying the largest number.

### What does the script suggest about Chat GPT's awareness of its own mistakes?

-The script suggests that when Chat GPT makes mistakes, it seems to be completely unaware of them and fails in unpredictable ways.

### What is the overall conclusion of the script regarding Chat GPT's mathematical capabilities?

-The overall conclusion of the script is that Chat GPT has shown impressive capabilities in handling mathematical problems, but it also has moments of complete failure, indicating that its performance can be inconsistent.

### Outlines

### 🧠 Testing Chat GPT's Mathematical Abilities

The script begins with an introduction to testing Chat GPT's capabilities, focusing on its mathematical reasoning rather than raw computation. The host demonstrates Chat GPT's proficiency in arithmetic and natural language by asking it to calculate the sum of the first three odd numbers and using the formula for the sum of an arithmetic series. The video then transitions into more complex reasoning problems, including testing for prime numbers and understanding the concept of twin primes. The host notes improvements in Chat GPT's responses over time and its ability to catch errors in reasoning.

### 🔢 Complex Mathematical Challenges for Chat GPT

This paragraph delves into more intricate mathematical challenges for Chat GPT, such as determining the primality of large numbers resulting from odd numbers raised to high powers and then further powered or added to other numbers. The host explains the reasoning behind why certain numbers cannot be prime, based on their properties as odd numbers and the effects of exponentiation and addition. Chat GPT shows an improved ability to handle these problems, although it makes a minor mistake in reasoning about the addition of odd numbers to even numbers.

### 🔍 Exploring 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 on identifying whether a given large number is a Friedman number, but it fails to provide the correct reasoning and solution. The script then moves on to the 'four fours challenge,' a classic puzzle involving creating expressions for consecutive integers using only the number four and basic arithmetic operations. Chat GPT struggles with a similar 'six sixes' challenge, demonstrating difficulty in creative number manipulation.

### 🏆 Solving Advanced Mathematical Problems Like Olympiad Questions

The script presents an Olympiad-style problem involving a system of equations where the variables represent perfect squares. Chat GPT successfully identifies the possible integer values for the variable M, showcasing its algebraic manipulation skills. The host encourages viewers to solve the problem independently and notes the presence of an additional, non-obvious solution that Chat GPT manages to find, indicating its ability to handle complex reasoning tasks.

### 🤔 Chat GPT's Limitations and Abstract Mathematical Reasoning

In the final paragraph, the host highlights Chat GPT's limitations by presenting it with an abstract mathematical problem involving the sum of an integer's square and cube, and its odd differences. Chat GPT attempts to outline a research program to find the largest number that cannot be expressed in this way but makes a mistake in its reasoning, incorrectly identifying the largest number. The host reflects on Chat GPT's performance, noting its impressive capabilities in arithmetic but also its unpredictable failures in more abstract reasoning tasks.

### Mindmap

### Keywords

### 💡Chat GPT

### 💡Arithmetic Series

### 💡Prime Numbers

### 💡Friedman Numbers

### 💡Four Fours Challenge

### 💡Exponentiation

### 💡Perfect Squares

### 💡Pythagorean Triple

### 💡Algebraic Rearrangement

### 💡Cube and Square

### Highlights

Chat GPT's latest iteration is tested with mathematical questions to evaluate its reasoning capabilities beyond raw computation.

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

Use of an arithmetic series formula to calculate the sum of odd numbers, showcasing Chat GPT's mathematical reasoning.

Testing Chat GPT's ability to determine if the sum of two prime numbers can ever be prime, and its improvement over previous responses.

Introduction of a complex mathematical problem involving large odd numbers raised to powers and the addition of 17, to test prime number identification.

Chat GPT's reasoning that an odd number to a power plus an even number cannot be prime, indicating an understanding of number properties.

The presenter's surprise at Chat GPT's improved performance in mathematical reasoning compared to previous tests.

Exploration of 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, highlighting its limitations in certain mathematical puzzles.

The four fours challenge is introduced, a mathematical puzzle using four fours to create different numbers.

Chat GPT's struggle with the six sixes challenge, indicating a difficulty in creating number patterns beyond basic arithmetic.

A system of equations involving perfect squares is presented, and Chat GPT begins to solve it using algebraic manipulation.

Chat GPT successfully finds solutions to the system of equations, demonstrating its algebraic reasoning capabilities.

The presenter's observation that Chat GPT's failures are often complete and unaware, posing unpredictability in its performance.

Chat GPT's attempt to solve an abstract problem involving the sum of an integer's square and cube, with mixed results.

The presenter concludes the session by reflecting on Chat GPT's performance, noting its impressive capabilities but also its unpredictable failures.