> simply referencing established knowledge would ever get the correct answer to novel problems, absent any understanding of that knowledge.
What is a concrete example of this?
What is a concrete example of this?
If I prove a new math theorem, it's novel - even though it's unlikely that thousands of humans have worked on that specific theorem for decades.
LLMs have proven novel math theorems and solved novel math problems. There are more than three examples already.
Show me these novel problems, that were solved by LLMs, name more than 3 then.
An example problem includes the "Erdos set" problems (see problem 124).
But also, LLMs have solved Olympia problems, see the results of IMO 2025. You can say that these are not interesting or challenging problems, but in the context of the original discussion, I don't think you can discount them as "novel". This is what the original comment said:
> Not so much amazing as bewildering that certain results are possible in spite of a lack of thinking etc. I find it highly counterintuitive that simply referencing established knowledge would ever get the correct answer to novel problems, absent any understanding of that knowledge.
I think in this context, it's clear that IMO problems are "novel" - they are applying knowledge in some way to solve something that isn't in-distribution. It is surprising that this is possible without "true understanding"; or, alternatively, LLMs do have understanding, whatever that means, which is also surprising.
If you want to define "novel problems" as those requiring novel algorithms and data structures etc, well, how often do humans solve those in their day-to-day coding?
I'm probably just rephrasing what you mean, but LLMs are very good at applying standard techniques ("common solutions"?) to new use-cases. My take is, in many cases, these new use-cases are unique enough to be a "novel problem."
Otherwise, this pushes the definition of "novel problems" to something requiring entirely new techniques altogether. If so, I doubt if LLMs can solve these, but I am also pretty sure that 99.99999% of engineers cannot either.