Were alchemists right? When I was in school, I learned about alchemists, a group of scientists who sought a way to convert other materials into gold. They were never successful, so whenever I studied or read about them, they were portrayed as failures or foolish people, and that’s the impression I had about them.
However, more recently, I was preparing for something else, and I read a question which said:

Copper can be converted into gold by artificial radioactivity

I’m not a science guy, but when I looked into this, it seemed to be true. Is it? And if it's true, were the alchemists right all along, not foolish people as history portrays them?
 A: The Alchemist of the time thought the conversion could be done through chemistry. By that I mean dealing with electrons. That is not true, not even close (pardon the pun). In fact, all the naturally occuring elements were formed from Hydrogen.
A: Fundamentally, no, alchemists weren’t right.
Well, to be even more fundamental, “alchemists” aren’t a coherent group or a consistent philosophy. It’s a term that’s been broadly used by a lot of different people over the course of several hundred years, and it covers a lot of very-different things. “Lead into gold” isn’t even necessarily a goal of all alchemists—and for some, it’s not literal in the first place, but rather a symbolic spiritual transformation.
Anyway, for the most part, Western alchemy is based on the ideas of some ancient Greek philosophers, most notably Plato and Aristotle. A lot of work along those lines was performed in Hellenistic Egypt, and then after the fall of the Roman Empire, moved to the Arabic world. With Europe’s Rennaisance, they discovered the work in Arabic and moved on from there.
Alchemical theory comes from that lineage. Plato’s four elements, air, earth, fire, and water, play a large role, as do the underlying “qualities” of dryness/wetness, coldness/hotness that they were supposed to be made up of. The chemical processes of calcination, dissolution, separation, conjunction, fermentation, distillation, and coagulation were espoused by the possibly-mythical Jābir ibn Ḥayyān, known in Europe as Geberus or Geber, as the fundamental processes by which alchemy is wrought. Those seven processes are paired with seven forms of matter, seven days of Creation in Genesis, seven planets, and so on. Numerology, as the repetition of “seven” suggests, became a big part of things. So did a number of other mystical and esoteric practices—astrology, for instance, was always closely linked with alchemy, and that only got tighter. Many alchemists believed the summoning of spirits—angels, demons, djinn, etc—was crucial to transmutation. By the seventeenth century, Kabbalah, a Jewish mystic practice, was heavily entwined with the practice of what was then called alchemy. And so on.
And all of that was basically wrong. Plato was wrong, Aristotle was wrong, numerology is meaningless, the pseudo-religious mysticism I won’t call right or wrong but it certainly doesn’t notably contribute to physical knowledge, and so on. Jābir ibn Ḥayyān produced some really genuinely useful data on various chemical processes and what they resulted in for various ingredients—and so did many other alchemists before and after that—but all of it was ensconced in a theoretical framework that was simply inaccurate, and this led to many beliefs about those processes that were incorrect.
And ultimately, even if we ignore all the mysticism and everything, those seven chemical processes will never contribute in any significant way towards the transmutation of any element into another. Alchemy isn’t just “turning lead into gold,” it’s “turning lead into gold via the application of these processes in the right sequence with the right combination of ingredients,” and that approach is simply not ever going to work.
It is really telling that the trend with alchemy was towards the mystical and esoteric. Early alchemists produced better and more useful results than later alchemists, because the early alchemists had more “low-hanging fruit” to reach regarding basic empirical facts (not to call the work performed easy—many doubt the historicity of Jābir ibn Ḥayyān precisely because the amount of work required to produce everything attributed to him is more than any one man could hope to have performed). But once the empirical facts were determined as well as they could be with the tools they had, alchemy kind of devolved. It was initially assumed that once you had all the facts you’d be able to analyze them to figure out how to solve the various primary aims of alchemy, but that didn’t happen. And rather than throw out what wasn’t working, alchemists just got more and more mystical, until eventually it wasn’t even about physical substances at all.
On the other hand, chemistry was founded on more scientific principles—which, to be fair, didn’t exist when alchemy got its start—and while it could be said that eventually chemistry also settled on a theory by ancient Greek philosophers—Leucippus and Democritus rather than Plato and Aristotle—it happily threw out almost everything from that philosophy beyond the word atomos itself. Chemistry was founded largely in opposition to alchemy, rather than as a development of alchemy. Maybe if scientific ideas had debuted earlier, alchemy could have pruned itself of its philosophy and mysticism in favor of the scientific method, and we’d be using the word “alchemy” to refer to modern science, but that’s not how things happened.
Also, it’s worth pointing out that ultimately, it isn’t chemistry that transmuted one element to another, either. Obviously, atomic theory and the work that chemists had done to isolate the elements and build up the periodic table were absolutely crucial to the development of nuclear physics, but it’s still nuclear physics for a reason. Which means that, really, alchemy is yet another step removed here.
A: Even a broken clock marks the correct time twice a day
They were wrong.
Yes, the goal they aimed at was achievable.
But all of the theory behind their attempts was complete and utterly wrong. They did not know that gold was an "element" in the modern sense of the word, or what was the factor that differentiated the different elements or even the modern definition of element.
And of course, they failed at every attempt.
What the alchemists had was a desire, not a working method nor even an approximate theory of how to achieve the result.
To put an analogy, a medieval physician could try to apply leeches to you to cure the plague. Now we have antibiotics that are very effective against it. Of course, that does not mean that medieval physicians were right when using leeches on their patients.
A: They were wrong in the same way the people who made human-sized wings to fly were wrong. The goal of flight/metal transmutation is not impossible, but the methodology is naive and hopeless.
A: There are ways that gold can be produced by radioactivity:

Chrysopoeia, the artificial production of gold, is the symbolic goal of alchemy. Such transmutation is possible in particle accelerators or nuclear reactors, although the production cost is currently many times the market price of gold. Since there is only one stable gold isotope, 197Au, nuclear reactions must create this isotope in order to produce usable gold.

Italics mine.
In a sense the goal of alchemists is reached,but they were aiming at getting gold for its value, not for the fun of it.

Most readers probably are aware of several common claims about alchemy—for example, ... that it is akin to magic, or that its practice then or now is essentially deceptive. These ideas about alchemy emerged during the eighteenth century or after. While each of them might have limited validity within a narrow context, none of them is an accurate depiction of alchemy in general

They were the "chemists " of their time , in their various pursuits.
A: There are two aspects to this. First, what kind of physical process can transform one chemical element into another. Second, the contribution of alchemy to the development of science.
On the first aspect, the methods employed by the alchemists were, we now know, not going to succeed. But the idea that it might be possible to transform one chemical element into another is not at all a stupid idea. It is a perfectly sound idea. However it turns out that it requires processes that change the atomic nucleus, and this requires either the use of radioactivity or else high-energy collisions. It cannot be done by chemical reactions. So no amount of heating stuff up in ordinary fires or pouring one liquid into another or adding ingredients of this or that is going to work.
On the second aspect, the alchemists made a mixed contribution to the development of science. On the one hand some of their ideas were way off-base. On the other hand some of them, sometimes, took an empirical approach and tried things out, which is good. This provided a counter-balance to other approaches which tried to get at knowledge of the physical world merely by abstract mathematical and philosophical debate. What was needed was a combination which was both empirical and willing to experiment, but also careful about the reasoning and willing to learn and apply mathematical methods. In the medieval period there was a lot of painstaking debate about all kinds of abstruse questions, and sometimes one feels that what they needed to do was just try mixing up a few chemicals and see what happens. So although the alchemists usually were not thinking very clearly, their humble contribution should not be completely dismissed.
To find out more about this you might try the history of science stack exchange.
Thanks to all commenters; I made an adjustment suggested by KRyan.
A: I don't know about copper, but some gold was indeed made experimentally of bismuth (https://www.scientificamerican.com/article/fact-or-fiction-lead-can-be-turned-into-gold/). So it can be done, but the cost is much higher than the cost of the resulting gold. Alchemists' attempts to turn lead into gold by chemical methods were doomed though. One needs to use methods of nuclear physics for that (for example, accelerators).
A: They are known for trying to find a solution for a practical problem: obtaining gold, (or silver, failing for gold), in a process that is more efficient than mining these metals.
They weren't right or wrong. They did research. They based their research on what was known at the time. They tried a methods similar to the solutions of known problems that were considered similar (transforming one substance into another). They failed in this particular task and failed for a reasons that became known much later.
Then again,

they were portrayed as failures or foolish people

... is plain wrong.
They created and maintained a lot of the knowledge body that later became chemistry. They discovered a lot of previously-unknown substances (some of them being new chemical elements, even if the understanding of "chemical element" shaped later). They even invented some less-impressive than creating gold, but pretty much useful things.
A: At the risk of getting flamed, I think that Rutherford's reported comment deserves consideration:
Soddy: "Rutherford, this is transmutation!"
Rutherford: "For Christ's sake, Soddy, don't call it transmutation. They'll have our heads off as alchemists."
He did not say "this is not transmutation", he said "don't call it that".
Now when I was at school, we were taught that there were chemical processes and physical processes, that they were distinct, and that chemical processes could not transmute one element to another. But these days that distinction is being eroded, one obvious example being the singlet delta oxygen phenomenon where a chemical reaction produces an intermediate which then decays with a defined half-life.
So it is undeniable that alchemists lacked the intellectual framework which would have allowed them to understand what they were attempting. It's also undeniable that they lacked effective physical and chemical processes which would have achieved transmutation. But were they actually wrong?
I'd settle for 99% wrong. But I'd argue that the Western tradition of alchemy was the precursor of the painstaking, methodical and repetitive laboratory procedures without which we'd never have been able to refine and exploit the scientific method that superseded it.
