[zepto]

> However, the analogy is still accurate, because the right approach involved several steps which no one thought were conceivably part of the solution

I don’t see how that follows. It’s just a truism that nobody figured out how to do it until someone finally did. The fact that the path wasn’t obvious at various points in the past seems irrelevant.

> But if you also told people that this knowledge was the key to solving the two problems they were working on, "how to make very pure versions of a substance", and "how to understand what makes specific types of matter different" you would reasonably have been regarded as deluded.

If they were listening to you at all, it’s not at all obvious why this part would sound deluded.

How is it any more exotic than any of the failed alchemies?

As far as I can see they were all quite abstract.

This one that happens to be correct, no less so.

[zinok]

'It' (most of 17th, 18th and 19th and some early 20th century mathematics, chemistry and physics) is clearly a lot more abstract than the failed alchemies.

The point is that 'just keep trying' would not have been a good strategy.

[zepto]

'just keep trying' is a straw man that nobody has mentioned until just now.

Yes, it’s possible that there are some concepts we have yet to think of.

See: https://numinous.productions/ttft/

The explanation of how hard it would be to come up with Arabic numerals if you didn’t already have them covers this.

However the point here is that we can learn from this, and we now know a lot more about how to do hard things.

‘It’s too hard and we should give up’ (the countervailing straw man) is even less supported by history than ‘keep trying’.