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

SackVideo
8 May 202304:29

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

00:00

🀖 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

Multiplication is a mathematical operation where one number is added to itself a certain number of times, indicated by the other number. In the video, it is mentioned that ChatGPT struggles with multiplication, suggesting that despite AI's capabilities, it still faces challenges in performing basic arithmetic operations accurately, as it relies on statistical patterns rather than true understanding.

💡Language Models

Language models are AI systems designed to understand and generate human language. The script discusses how ChatGPT, a type of language model, makes predictions based on patterns it has seen in text, rather than truly understanding the concepts it discusses, which is why it fails in tasks like multiplication.

💡Statistical Observations

Statistical observations refer to the analysis and interpretation of data to identify patterns or trends. The video explains that ChatGPT uses statistical observations to make predictions, such as the likely end digits of a multiplication result, but struggles with more complex calculations that require understanding beyond patterns.

💡SAT Solver

A SAT solver is a tool used in mathematical research to solve Boolean satisfiability problems. The script mentions that SAT solvers can determine if a set of logical statements can be true simultaneously, which is useful for certain types of mathematical problems, like the Boolean Pythagorean triples problem.

💡Boolean Satisfiability

Boolean satisfiability is a concept in logic where the goal is to find an assignment of truth values to a set of variables that makes a given logical formula true. The script uses the Boolean Pythagorean triples problem as an example of how SAT solvers can tackle complex mathematical questions by converting them into Boolean sentences.

💡Heuristics

Heuristics are problem-solving strategies that use a practical approach to find a solution when classic methods are too slow or impossible. The video script explains that modern SAT solvers use heuristics and optimizations to efficiently solve problems that would normally require checking an exponential number of possibilities.

💡Neural Networks

Neural networks are a set of algorithms designed to recognize patterns and learn from data. The script discusses how neural networks can be used in pure math research, such as finding counterexamples to mathematical conjectures using the cross entropy method.

💡Cross Entropy Method

The cross entropy method is an optimization technique used to generate solutions that are likely to be optimal for a given problem. In the context of the video, Adam Wagner used this method with neural networks to generate counterexamples for combinatorics problems, demonstrating a novel application of AI in mathematical research.

💡Combinatorics

Combinatorics is a branch of mathematics concerned with counting, combination, and permutation of sets. The script mentions a paper by Adam Wagner where neural networks were used to find counterexamples to problems in combinatorics, showing AI's potential to contribute to this field.

💡Conjectures

A conjecture is an proposition or hypothesis that is proposed as a possible truth on the basis of being plausible or likely, but requires proof or disproof. The video script refers to how neural networks can be used to test conjectures in mathematics, such as generating counterexamples to disprove them.

💡AI in Math Research

AI in math research refers to the application of artificial intelligence techniques to assist in mathematical investigations and problem-solving. The script explores various ways AI, including SAT solvers and neural networks, is currently being used to aid mathematicians in their research, emphasizing the potential of AI as a tool rather than a replacement.

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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