[ExI] The Automathician

[Jason Resch]

I think you're right, this could be a very powerful tool. In the same way
AlphaZero used intuition to narrow its game search tree, automated theorem
provers could use a mathematical intuition to find interesting and useful
proofs and avoid slogging through the full exponentially growing search
tree.

There's already a strong mathematician within GPT-4, see for example, page
40:

https://arxiv.org/pdf/2303.12712.pdf

Jason



On Sun, Mar 26, 2023, 8:35 PM Rafal Smigrodzki via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> It occurred to me that LLMs mated to a mathematical inference engine (like
> the Wolfram Alpha plug-in for GPT) and enhanced with visual data
> processing capabilities might make excellent automatic mathematicians.
>
> Mathematical inference in the sense of symbol manipulation and theorem
> proving can be automated relatively easily but up till now such systems
> lacked the intuition and imagination as well as the sense of beauty that
> mathematicians use to select among the infinite numbers of mathematical
> objects and properties the ones that are worth thinking about. A theorem
> prover without this intuition would just aimlessly churn out proofs and
> never create anything useful. But add an intuition trained on the patterns
> imprinted in the mathematical literature by the minds of the mathematicians
> who create math, and the Automathician could write math like a human. Since
> its breadth of mathematical knowledge and raw symbol manipulation ability
> would be vastly superior to any human, its high-level mathematical insights
> could become superhumanly mathemagical.
>
> A modest LLM training project using a corpus of mathematical papers with
> RLHF provided by mathematicians could be a very interesting endeavor. Who
> knows what kind of very non-obvious and ground-breaking truths could be
> discovered? The algorithms based on such non-human insights could be of
> immense practical value, too.
>
> Rafal
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