I feel very comfortable saying, as a mathematician, that the ability to solve grade school maths problems would not be at all a predictor of ability to solve real mathematical problems at a research level. The reason LLMs fail at solving mathematical problems is because: 1) they are terrible at arithmetic, 2) they are terrible at algebra, but most importantly, 3) they are terrible at complex reasoning (more specifica…
On backtracking, I thought tree-of-thought enabled that? "considering multiple different reasoning paths and self-evaluating choices to decide the next course of action, as well as looking ahead or backtracking when necessary to make global choices" https://arxiv.org/abs/2305.10601 Generally with you though, this thing is not leading to real smarts and that's accepted by many. Yes, it'll fill in a few gaps with expon…
The problem with solving such problems with LLMs is that if the solution to the problem is unlike problems seen in training, the LLM will almost every time take the wrong path and very likely won't even think of the right path at all.
The AI really does need to understand why the paths it tried failed in order to get insight into what might work. That's how humans work (well, one of many techniques we use). And despite what people think, LLMs really don't understand what they are doing. That's relatively easy to demonstrate if you get an LLM off distribution. They will double down on obviously erroneous illogic, rather than learn from the entirely new situation.