Grant Sanderson

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So in that sense basically using it like a very souped-up version of Google on like zero in on the right human written resource.

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And I think a good exposition you care a little bit less about like correctness on the way, but you can like deliberately craft things that are a little bit wrong that you correct along the way that gets like edited out in a crowd source environment.

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So if there's a book you've liked before, read what else that author has written rather than reading another thing on that subject.

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I feel like a relevant insight in learning was um recognizing that like who matters more than what. So, like advice to any college student when they're choosing what courses to take. Uh, care a little bit less about your pre-existing interests because they're kind of arbitrary right now. and care a little bit more about whether like the person teaching it is a good educator and someone you resonate with.

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It becomes insufferable like as a mathematician because you you would basically be like I'm every single time I see one of these I kind of don't know if it's worth my time even if 99 out of 100 of them are right.

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And so I think you are right that lean is maybe overrated on the side of the importance of it being used as a VR environment for any kind of like just progress in math generally. But I I I definitely wouldn't write it out of the story.

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And so having anything that's able to give you that green check mark that says even if this is going to be complicated to understand, even if it's going to be a pain, you at the very least know it is correct. Like every other field would kill for that, right?

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That's a very unique thing that math has that nothing else has where you could press go and then just like just just poor compute at it and like look away for 10 years and then come back and say like what do you have and there's there's going to be something, right?

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Which actually goes to show you that you there's not a correct huristic for science. You actually just need multiple independent research programs with their own huristics.

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You could imagine systematizing that or like having multiple different agents deliberately given different pieces of context and try to like compare and contrast there. Like we we don't have the same level of manipulation on our own context.

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but that's my guess on what most of the useful progress uh from these models will look like like in the next five years is just really filling in that landscape of like connections that you can draw if you're an expert in multiple fields.

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I think we would always still prefer like a human that we had a relationship with because the way that we get motivated to be interesting interested in things is a social phenomenon.

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So my role and arguably that of like other mathematicians might actually just shift subtly into that curation direction of what ideas are are worth displaying.

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I kind of suspect that actually they'll also be like quite good at doing that and probably just like better than most humans are at like doing the explanation half and distilling half and that's actually not what's left for the mathematicians is like digesting and and explaining what was going on.

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One is it seems like there's a really strong correlation between the people who come up with genuinely novel insights and also who are actually quite clear in their communication of it.

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Um even if it's proven just like there is a difference between proof and explanation.

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Uh but I don't think it's easy but I do think it's something you would have to do in order to uh reward the gawwa like instinct rather than just rewarding have you solved a problem.

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what makes the GAWA theory such an interesting example is you have um literally this 100-year segment of like an idea that like flows through many different people's heads before it like settles into something that the math community like agrees is good.

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I think the way that you'd measure conjecture generating ability is going to be more subjective on like that tone shift where um it'll be mathematicians saying they're not just using it to like solve their problems, but as they step back and decide what their research field should even be that a conversation with such and such model like was genuinely helpful for that.

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that like if it's capable of building mountains uh that are, you know, the correct new theory that like crystallizes how we should be thinking about a subject, that's just such a level of intelligence that then it starts to feel like it would be surprising if that didn't permeate into other aspects of the economy besides like just the mountain building for math itself.