Is there reason to believe ChatGPT is unusually good at AP Computer Science, or would it do as well on other AP subject tests?
It does seem pretty good at producing code though. And it's able to write stories that have a real structure to them, but they're pretty bland.
(ChatGPT output)
> The ball costs $0.10. Let's prove this using an equation. {uses equation}. The ball costs $0.05.
> The ball costs $0.10. Let's prove this using an equation. {uses equation}. The ball costs $0.10.
> The bat costs $1 more than the ball, so the bat costs $1 + x, where x is the cost of the ball. The bat and the ball together cost $1.10, so the cost of the ball is $1.10 - $1 - x = $0.10 - x. Since the bat costs $1 + x, we know that $1.10 = $1 + x + $0.10 - x = $1 + $0.10. Therefore, the cost of the ball is $0.10 - x = $0.10 - ($1.10 - $1) = $1.10 - $1 - $0.10 = $0. The ball costs $0.
"we get 2k^2 = q^2. Since q^2 is even, this means that q must be even as well. But this contradicts the original assumption that q is not equal to 0, so we must conclude that √2 is irrational"
The language of these fake proofs tends to resemble real math well enough that I hope it doesn't fool people.
In areas other than math I've been very impressed however with it overall. While human experts are obviously still better in terms of depth, accuracy and creativity, it's already pretty good. Whereas in terms of breadth, no human could compare. Given the rate of improvements, these things seem destined to launch a new era
"neural theorem prover that has solved 10 International Math Olympiad (IMO) problems — 5x more than any previous AI system"
> Explain in terms a high school student will understand why there are a finite number of primes.
Sure, a prime number is a whole number greater than one that is only divisible by one and itself. For example, the first few prime numbers are 2, 3, 5, 7, 11, and 13. One way to think about why there are a finite number of primes is to imagine a list of all the whole numbers greater than one. Since there are an infinite number of whole numbers, the list of prime numbers would have to be a subset of the list of whole numbers. But since the prime numbers are only divisible by one and themselves, there must be a point where the list of primes stops, because at some point, every number on the list would be divisible by a prime number that came before it. For example, the number 20 can be divided by 2, and the number 15 can be divided by 3, so these numbers would not be considered prime. Does that help? Let me know if you have any other questions.
On a serious note, I wonder how well the training works when a lot of maths is represented symbolically. For example, when they feed it books, do they convert it to LaTeX? MathML? Just leave it out?
It's a robot...