[ExI] The Automathician

[Rafal Smigrodzki]

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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