According to a quick google search, Greek myths existed 2700 years ago. Far from advanced medical knowledge. However, according to the myth of Prometheus, his liver regenerated every night so that an eagle can torture him by ripping it from him and eating it.
Is there evidence that humans at least 2500 years ago knew that a resected liver could regenerate itself?
No probably we didn’t.
Most likely the liver was chosen as the focus of torture because the liver in that time was seen as the site of our soul/passion/intelligence - so for someone who stole from the gods it was the most fitting punishment. Being a Titan, Prometheus wasn’t able to die so for the torture to be eternal it had to regenerate.
Another reason the Greeks chose the liver as the site of injury might be because of hepatoscopy: the practice of predicting the future by looking at a sacrificed animals’ liver. The name Prometheus means something like ‘foresight’, so it would make sense to pick the liver because of its role in divination.
The Greeks had little knowledge of the anatomy and the physiology of the human body because they didn’t usually perform dissections. They knew of the liver by studying animals, or by looking at war wounds, but they probably had no way of knowing the liver would regenerate.
It’s a cool story tho.
Edit: if you want to read more. Power & Rasco. Whither Prometheus' Liver? Greek Myth and the Science of Regeneration Article in Annals of internal medicine 149(6):421-6 · October 2008
The Prometheus myth has an enduring role in medical education: reportedly it's usually accompanied by viewings of Rubens' painting Prometheus bound (Tiniakos et al. 2010: 359).
But that doesn't tell us what the ancient Greeks thought about it. The short answer is: a minority of hepatologists think the myth was informed by knowledge of liver regeneration; not a single classicist is on record as thinking that. For my money, the dominant theme is mutilation of an enemy's body, not the specific organ that's being mutilated.
[Edited: my initial answer neglected an excellent 2016 post to AskHistorians by u/mythoplokos. My references are now in a second post.]
Here's a review. First, the hepatological side.
Chen and Chen 1994 devote half their space to a review of art history in the modern era, then assert without substantive argumentation ('we believe') that hepatic regeneration was known in early Greece. This piece may be safely ignored.
Power and Rasko 2008 is not available to me, and their abstract does not give away their answer to the question, but their programmatic statements indicate a more responsible approach: they say they will pose the more fundamental questions (1) What opportunities did ancient Greeks have for observing the liver's function? (2) How did ancient Greeks understand Prometheus' immortal liver? They also imply that they have actually read some relevant work by Hesiod scholars, which is a rarity in this kind of study. Two posts to AskHistorians, one in 2014 and one in 2016, cite the article and report that the authors conclude that it's unlikely that ancient Greeks knew about hepatic regeneration. The 2016 post points out their finding that although we have plenty of discussion of liver ailments in ancient sources, liver regeneration appears only in myth.
Tiniakos, Kandilis, and Geller 2010 argue two things: (1) Hepatological teaching ought to cite the Tityos myth as well as Prometheus. (2) '[T]here is no convincing evidence that ancient Greeks had any specific knowledge about liver regeneration, a concept introduced in the early 19th century.' Their paper is primarily a review of the more popular primary sources, then (like Chen and Chen) turns bewilderingly to a review of pictorial representations in the modern era. In the only place where they engage with actual scholarship on the subject, they err: the Greek word for 'liver', hēpar (ἧπαρ), isn't related to hēdonē 'pleasure', but is cognate with Sanskrit yakr̥t 'liver', Latin iecur 'liver' (the long ē is unique to Greek).
This paper is of interest for someone who wants to know more about what sources are available, but mustn't be mistaken for substantive research. There is little here that you wouldn't find in an encyclopaedia. They cite only three pieces of scholarship written by a classicist, and of these only one is less than a century old, and is rather fringe-y (Kerényi). They do not cite any scholarship on Hesiod.
Van Gulik, Van Gulik, and Koning 2018 is not available to me (there's a 5-year moving wall), and is reportedly in Dutch. The online abstract merely parses the question and gives no hint as to the answer supplied. However, Koning is a well-known and reputable Hesiod scholar. So if you're looking for a study that is specifically published in a medical journal, this will be the one to choose.
On to classicists. Classicists give no air time to the business of liver regeneration. Their discussion normally focuses on the origin of the story, and its role in depicting Zeus' autocracy, rather than talking about what it has to tell us about biological knowledge in that era.
The most important thing to know is that Prometheus' punishment isn't unique. There are four major archaic-era sources that are related to one another:
West 1966: 313-315 has a decent review of classicists have written about the Hesiod passage -- and, rather depressingly, it's still up to date (with the exception of Koning's involvement in the 2018 piece mentioned above). West cites Bapp (1896) for the view that Tityos is the original version of the story, since his crime was one of lust, and in Aeschylus the liver is cast as the seat of passions (esp. Libation bearers 271-272; 458 BCE). West rejects this interpretation. He cites Kretschmer (1918) for the view that the eagle's role is based on something that could actually happen to someone who was crucified or bound to a pillar as Prometheus is. He cites Olrik (1922) for the view that the story is based on a myth of earthquakes being caused by a giant who is being punished in a cavern or bound to a pillar (the most famous example is Loki). The last is the view that West prefers, mainly because of the geographic placement of Prometheus' punishment in the Caucasus mountains. Personally I don't support any of these -- though I'm very willing to accept that Tityos represents a more original form of the story, not for Bapp's reasoning, but because vultures are more natural as scavengers than Zeus' eagle.
Some earlier answers on AskHistorians cover various aspects of the topic:
I'm going to add that, of the four archaic references listed above, numbers 3 and 4 are the key to understanding the story, and I'll point to Segal 1971. Segal's monograph isn't a discussion of Hesiod or Prometheus, but of mutilation of bodies. In the case of Hekabe devouring Achilleus' liver, and Achilleus devouring Hektor's flesh, the point isn't punishment: these events are imagined as happening after the victim's death. Instead, the point is to desecrate the corpse of a particularly hated enemy.
This fits pretty well for Prometheus and Tityos, too, in different ways. Tityos is post mortem, like Achilleus and Hektor, but is different because it's imagined that the devouring takes place in the afterlife, with the implication that he's suffering excruciating pain (the text refers to him being unable to drive off the vultures with his hands). Prometheus doesn't have a post mortem, since he's divine, so he too suffers conscious agony.
But they're all actions taken by someone against an especially hated enemy: Zeus hates Prometheus 'because he rivalled (Zeus) in schemes' (Theogony 534), Zeus hates Tityos because he tried to rape Leto, Hekabe hates Achilleus because he killed her son, and Achilleus hates Hektor because he killed Patroklos.
Other accounts of the Prometheus myth tend to support the idea that the story is about pain, rather than the liver itself. Prometheus bound 1021-1025 focuses on his suffering, with no mention of his liver; pictorial representations focus on the eagle's mutilating him, without strong sign that the liver is its particular target. A fragment of Aeschylus' lost play Prometheus unbound (fr. 193 Nauck/Radt = Cicero Tusc. disp. 2.23-25) focuses mainly on his pain, though admittedly with a certain amount of attention to the liver regenerating (lines 13 and 16). See further Podlecki 2005, 2-5 on Prometheus in archaic Greece, and 37-41 on depictions of his punishment in ancient art.