They were right. The previous attempts did in fact use the wrong approach, and people have now successfully turned lead into gold. The only problem is that it’s too expensive to be worth doing.
I don't agree. If you could ask a prime Newton if he'd be satisfied converting lead into gold in a cost prohibitive manner I would bet any amount of money his answer would be a quick "no". The goal of alchemy was to convert lead into gold in a way that made the discoverer rich, it's just not proper to say the second part explicitly, but I believe most people understand it that way.
> The goal of alchemy was to convert lead into gold in a way that made the discoverer rich
That definitely needs a citation. The Wikipedia page mentions no such motivation, and describes Alchemy as a proto-scientific endeavor aimed at understanding the natural world.
However, the analogy is still accurate, because the right approach involved several steps which no one thought were conceivably part of the solution: "understand how forces work at macro scales", "understand electricity", "understand magnetism", "develop a mathematical framework for summing tiny localized effects over large and irregular shapes", "develop a mathematical framework for understanding how continuous distributions evolve based on simple rules", "learn to look accurately at extremely small things", "learn to distinguish between approximate and exact numerical relationships", "develop a mathematical framework for understanding the large-scale interaction of huge numbers of tiny components", and so on.
If you went back in time to an age where people were working hard on changing lead into gold and your mission was to help them succeed as soon as possible, your best bet would probably be something like teaching them the decimal place value system, or how to express algebraic problems as geometric ones. 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.
> 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?
'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.
