Ai has a interior world model thus it can do math if a chain of proof is walking without uncertainty from room to room. the problem is its inability to reflect on its own uncertainty and to then overrife that uncertainty ,should a new room entrance method be selfsimilar to a previous entrance
Can AI do maths yet? Thoughts from a mathematician
61–70 of 364 posts
Re: Can AI do maths yet? Thoughts from a mathematician
#62Earlier quoted context omitted.
>in the quantum research to demonstrate any valuable forward progress you must compute something that is impossible to do with a traditional computer This is factually wrong. The most interesting problems motivating the quantum computing research are hard to solve, but easy to verify on classical computers. The factorization problem is the most classical example. The problem is that existing quantum computers are not…
> This is factually wrong. The most interesting problems motivating the quantum computing research are hard to solve, but easy to verify on classical computers. You parent did not talk about quantum computers . I guess he rather had predictions of novel quantum-field theories or theories of quantum gravity in the back of his mind.
Then his comment makes even less sense.
Re: Can AI do maths yet? Thoughts from a mathematician
#63Eventually we may produce a collection of problems exhaustive enough that these tools can solve almost any problem that isn't novel in practice, but I doubt that they will ever become general problem solvers capable of what we consider to be reasoning in humans.
Historically, the claim that neural nets were actual models of the human brain and human thinking was always epistemically dubious. It still is. Even as the practical problems of producing better and better algorithms, architectures, and output have been solved, there is no reason to believe a connection between the mechanical model and what happens in organisms has been established. The most important point, in my view, is that all of the representation and interpretation still has to happen outside the computational units. Without human interpreters, none of the AI outputs have any meaning. Unless you believe in determinism and an overseeing god, the story for human beings is much different. AI will not be capable of reason until, like humans, it can develop socio-rational collectivities of meaning that are independent of the human being.
Researchers seemed to have a decent grasp on this in the 90s, but today, everyone seems all too ready to make the same ridiculous leaps as the original creators of neural nets. They did not show, as they claimed, that thinking is reducible to computation. All they showed was that a neural net can realize a boolean function—which is not even logic, since, again, the entire semantic interpretive side of the logic is ignored.
Re: Can AI do maths yet? Thoughts from a mathematician
#64As far as ChatGPT goes, you may as well be asking: Can AI use a calculator?
The answer is yes, it can utilize a stateful python environment and solve complex mathematical equations with ease.
Re: Can AI do maths yet? Thoughts from a mathematician
#65I didn't see anyone else ask this but.. isn't the FrontierMath dataset compromised now? At the very least OpenAI now knows the questions if not the answers. I would expect that the next iteration will "magically" get over 80% on the FrontierMath test. I imagine that experiment was pretty closely monitored.
Re: Can AI do maths yet? Thoughts from a mathematician
#66Earlier quoted context omitted.
Wolfram Alpha is better at actually doing math, but far worse at explaining what it’s doing, and why.
What’s worse about it? It never tells you the wrong thing, at the very least.
Its understanding of problems was very bad last time I used it. Meaning it was difficult to communicate what you wanted it to do. Usually I try to write in the Mathematica language, but even that is not foolproof.
Hopefully they have incorporated more modern LLM since then, but it hasn’t been that long.
Re: Can AI do maths yet? Thoughts from a mathematician
#67Earlier quoted context omitted.
Wolfram Alpha is better at actually doing math, but far worse at explaining what it’s doing, and why.
What’s worse about it? It never tells you the wrong thing, at the very least.
When you give it a large math problem and the answer is "seven point one three five ... ", and it shows a plot of the result v some randomly selected domain, well there could be more I'd like to know.
You can unlock a full derivation of the solution, for cases where you say "Solve" or "Simplify", but what I (and I suspect GP) might want, is to know why a few of the key steps might work.
It's a fantastic tool that helped get me through my (engineering) grad work, but ultimately the breakthrough inequalities that helped me write some of my best stuff were out of a book I bought in desperation that basically cataloged linear algebra known inequalities and simplifications.
When I try that kind of thing with the best LLM I can use (as of a few months ago, albeit), the results can get incorrect pretty quickly.
Re: Can AI do maths yet? Thoughts from a mathematician
#68Eventually we may produce a collection of problems exhaustive enough that these tools can solve almost any problem that isn't novel in practice, but I doubt that they will ever become general problem solvers capable of what we consider to be reasoning in humans. Historically, the claim that neural nets were actual models of the human brain and human thinking was always epistemically dubious. It still is. Even as the…
Can you define what you mean by novel here?
Re: Can AI do maths yet? Thoughts from a mathematician
#69I didn't see anyone else ask this but.. isn't the FrontierMath dataset compromised now? At the very least OpenAI now knows the questions if not the answers. I would expect that the next iteration will "magically" get over 80% on the FrontierMath test. I imagine that experiment was pretty closely monitored.
I figured their model was independently evaluated against the questions/answers. That's not to say it's not compromised by "Here's a bag of money" type methods, but I don't even think it'd be a reasonable test if they just handed over the dataset.
Re: Can AI do maths yet? Thoughts from a mathematician
#70So here's what I'm perplexed about. There are statements in Presburger arithmetic that take time doubly exponential (or worse) in the size of the statement to reach via any path of the formal system whatsoever. These are arithmetic truths about the natural numbers. Can these statements be reached faster in ZFC? Possibly—it's well-known that there exist shorter proofs of true statements in more powerful consistent sys…
> There are statements in Presburger arithmetic that take time doubly exponential (or worse) in the size of the statement to reach via any path of the formal system whatsoever. This is a correct statement about the worst case runtime. What is interesting for practical applications is whether such statements are among those that you are practically interested in.
I would certainly think so. The statements mathematicians seem to be interested in tend to be at a "higher level" than simple but true statements like 2+3=5. And they necessarily have a short description in the formal language of ZFC, otherwise we couldn't write them down (e.g., Fermat's last theorem).
If the truth of these higher level statements instantly unlocks many other truths, then it makes sense to think of them in the same way that knowing BB(5) allows one to instantly classify any Turing machine configuration on the computation graph of all n ≤ 5 state Turing machines (on empty tape input) as halting/non-halting.