> In either case I believe people who can put AI to the most value are the mathematicians themselves
The net output of math will increase, and mathematicians have more work now to unravel all this, and make it useful. AI plays the role of a monkey in the infinite monkey theorem [1]. We now need an LLM corollary - Something like: A finite number of LLM agents will almost surely find all theorems given an infinite token budget.
It's impossible for finite number of LLMs to solve all theorems. This would imply that the busy beaver sequence is computable which implies the halting problem is decidable.
For any finite program (eg some LLMs), there is a true math theorem which they cannot prove or disprove (given fixed input of the statement with no other information sources). If that weren’t true, BB would be computable.
Math is beyond computation. Since AI is just bits in bits out, it has this fundamental limitation.
Any magic of AI systems comes from the transformed meaning of its input data. With fixed weights any LLM is just an artifact. For example a human prompting an LLM constitutes an extra information source, which removes the above limitations. In theory any input from the natural world would remove the limitations too. The natural world is a black box and we don't know what kind of meaning or intelligence could underly it.
> It's impossible for finite number of LLMs to solve all theorems. This would imply that the busy beaver sequence is computable which implies the halting problem is decidable
LLMs use RNG for sampling, so they are not pure computers.
bwfan123 · · focus · HN ↗
The net output of math will increase, and mathematicians have more work now to unravel all this, and make it useful. AI plays the role of a monkey in the infinite monkey theorem [1]. We now need an LLM corollary - Something like: A finite number of LLM agents will almost surely find all theorems given an infinite token budget.
[1] <a href="https://en.wikipedia.org/wiki/Infinite_monkey_theorem" rel="nofollow">https://en.wikipedia.org/wiki/Infinite_monkey_theorem
srcreigh · · focus · HN ↗
For any finite program (eg some LLMs), there is a true math theorem which they cannot prove or disprove (given fixed input of the statement with no other information sources). If that weren’t true, BB would be computable.
Math is beyond computation. Since AI is just bits in bits out, it has this fundamental limitation.
Any magic of AI systems comes from the transformed meaning of its input data. With fixed weights any LLM is just an artifact. For example a human prompting an LLM constitutes an extra information source, which removes the above limitations. In theory any input from the natural world would remove the limitations too. The natural world is a black box and we don't know what kind of meaning or intelligence could underly it.
BoredomIsFun · · focus · HN ↗
LLMs use RNG for sampling, so they are not pure computers.
fsmv · · focus · HN ↗
BoredomIsFun · · focus · HN ↗