# ChatGPT can't multiply, but can AI do math?

TLDRThe transcript discusses the limitations of AI in mathematical tasks, such as multiplication, due to its reliance on statistical predictions rather than understanding. It highlights the use of AI in mathematical research, particularly SAT solvers, which efficiently solve complex Boolean satisfiability problems, as demonstrated in the Boolean Pythagorean triples problem. Additionally, it mentions the application of neural networks by Adam Wagner to find counterexamples in combinatorics, suggesting AI as a valuable tool for mathematicians, though not a replacement.

### Takeaways

- 🤖 ChatGPT struggles with multiplication because it relies on statistical predictions rather than actual computation.
- 🧮 The first and last digits of ChatGPT's multiplication results are often correct, but it gets confused in the middle.
- 🔢 ChatGPT's method involves predicting outcomes based on patterns in text it has seen before, not actual mathematical understanding.
- 💻 Computers have been performing accurate multiplications since their inception, unlike ChatGPT.
- 🧠 Large language models like ChatGPT are not designed to perform precise mathematical operations.
- 🧩 AI is still useful in mathematical research through tools like SAT solvers, which solve the Boolean satisfiability problem.
- 📏 SAT solvers can handle sentences with thousands of variables efficiently, despite the exponential complexity.
- 🔍 A notable application of SAT solvers was solving the Boolean Pythagorean triples problem in 2016.
- 📚 SAT solvers require converting problems into Boolean sentences, a task that needs human ingenuity.
- 📊 Neural networks and AI techniques are also being used in math research to find counterexamples to conjectures.
- 🧩 The cross entropy method trains neural networks to generate potential counterexamples for mathematical conjectures.
- 🧑🔬 AI is unlikely to replace mathematicians but will continue to be a valuable tool in mathematical research.

### Q & A

### Why does ChatGPT fail at multiplication despite being a computer program?

-ChatGPT fails at multiplication because it makes predictions based on patterns it has seen in text, rather than understanding the mathematical process. It can predict the first and last digits of a product using statistical observations but struggles with the middle digits, which depend on all input digits and require more complex understanding.

### What is the role of AI in mathematical research today?

-AI is currently used by mathematicians as a tool for research, particularly in areas such as SAT solvers for Boolean satisfiability problems and neural networks for finding counterexamples in combinatorics. However, it is not expected to replace mathematicians as it requires human insight to apply these tools effectively.

### What is a SAT solver and how is it used in mathematical research?

-A SAT solver is a software used to solve Boolean satisfiability problems, determining if it's possible to substitute 'true' and 'false' for variables in a sentence to make it true. It is used in mathematical research to solve problems that can be converted into Boolean sentences, with the solver applying reduction rules to find a solution efficiently.

### What was the Boolean Pythagorean triples problem and how was it resolved using a SAT solver?

-The Boolean Pythagorean triples problem asked if it's possible to color positive integers red and blue such that no Pythagorean triple is all the same color. A SAT solver was used in 2016 to prove that it's impossible, generating a 68-gigabyte proof after two days of computation.

### How do neural networks contribute to pure math research?

-Neural networks can be used in pure math research to find counterexamples to conjectures, as demonstrated by Adam Wagner's work in combinatorics. They use techniques like the cross entropy method to generate graphs that are likely to disprove a conjecture, potentially saving mathematicians time in testing false hypotheses.

### What is the cross entropy method used for in the context of neural networks and math research?

-The cross entropy method is a technique used to train a neural network to generate examples that are likely to disprove a mathematical conjecture. It involves predicting how to build graphs for a problem, creating many such graphs, and then retraining the network based on which ones were closest to disproving the conjecture.

### How does the transcript suggest AI techniques like neural networks could be used in the future of mathematical research?

-The transcript suggests that AI techniques like neural networks could be used to find examples that no human would have the time to, serving as a tool to assist mathematicians in their research and potentially saving them time from trying to prove false conjectures.

### What is the current limitation of AI in the field of mathematics as discussed in the transcript?

-The current limitation of AI in mathematics is that it lacks the understanding to replace mathematicians. While it can be used as a tool for specific types of problems, it requires human insight to convert problems into a form that AI can solve, and many mathematical problems cannot be converted into a format suitable for AI.

### How does the transcript describe the process of AI making predictions based on text?

-The transcript describes AI making predictions by observing patterns in the text it has seen before. It does not understand the content but uses statistical observations to make predictions about outcomes, such as the digits of a multiplication result.

### What is the transcript's stance on the future of AI in mathematics?

-The transcript suggests that AI is unlikely to replace mathematicians during the author's lifetime but will become another tool in their toolkit, assisting in research and potentially uncovering insights that would be time-consuming for humans to find.

### How does the transcript explain the difference between AI's statistical predictions and true mathematical understanding?

-The transcript explains that AI's predictions are based on statistical observations from patterns in text, which is different from true mathematical understanding. AI can predict certain outcomes based on what it has seen before but lacks the ability to comprehend and calculate the complexities involved in middle digits of multiplication, for example.

### Outlines

### 🤖 AI's Limitations in Multiplication and Mathematical Research

The paragraph discusses the limitations of AI, specifically ChatGPT, in performing multiplication accurately. It explains that AI operates on predictions based on statistical observations from previously seen text, rather than understanding the content. The middle digits of a multiplication result, which depend on all input digits, are particularly challenging for AI. The script also contrasts this with the use of AI in mathematical research, such as SAT solvers, which are used to handle Boolean satisfiability problems efficiently. The SAT solver's ability to solve complex problems with thousands of variables is highlighted, along with its role in solving the Boolean Pythagorean triples problem in 2016.

### Mindmap

### Keywords

### 💡Multiplication

### 💡Language Models

### 💡Statistical Observations

### 💡SAT Solver

### 💡Boolean Satisfiability

### 💡Heuristics

### 💡Neural Networks

### 💡Cross Entropy Method

### 💡Combinatorics

### 💡Conjectures

### 💡AI in Math Research

### Highlights

ChatGPT's inability to accurately multiply numbers is due to its reliance on statistical predictions rather than true mathematical understanding.

AI struggles with the middle digits of multiplication because it lacks the capability for detailed statistical observations.

Large language models like ChatGPT are not yet capable of outperforming mathematicians in complex tasks.

AI is currently being utilized by mathematicians for research, particularly with SAT solvers.

SAT solvers are used to solve Boolean satisfiability problems with efficiency, contrary to traditional methods.

Modern SAT solvers can handle sentences with thousands of variables due to advanced heuristics and optimizations.

The Boolean Pythagorean triples problem was resolved using a SAT solver, resulting in a 68-gigabyte proof.

SAT solvers are powerful but require the problem to be effectively converted into a Boolean sentence.

Neural networks are being explored for pure mathematical research, as demonstrated by Adam Wagner's work.

The cross entropy method is a technique used to generate counterexamples for mathematical conjectures.

Neural networks can be trained to predict and generate graphs that may disprove certain mathematical conjectures.

AI techniques like neural networks have the potential to save mathematicians time by disproving false conjectures.

AI is unlikely to replace mathematicians but may become an additional tool in their research process.

The integration of AI in pure math research opens up possibilities for finding examples that would be time-consuming for humans.

AI's role in mathematics is to assist and augment the capabilities of mathematicians rather than replace them.

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