In the book(and movie) Tyler goes on an extended monologue about the origin of soap in Indian burial pyres.
I can't find the passage from the book, but here's the scene from the movie courtesy of IMDB:
Tyler Durden: Now, ancient people found their clothes got cleaner if they washed them at a certain spot in the river. You know why?
Narrator: No.
Tyler Durden: Human sacrifices were once made on the hills above this river. Bodies burnt, water speeded through the wood ashes to create lye. [holds up a bottle]
Tyler Durden: This is lye - the crucial ingredient. The lye combined with the melted fat of the bodies, till a thick white soapy discharge crept into the river. May I see your hand, please?
[Tyler licks his lips until they're gleaming wet - he takes the Narrator's hand and kisses the back of it]
Narrator: What is this? Tyler Durden: This... [pours the lye on the Narrator's hand]
Tyler Durden: ... is chemical burn.
Hi, this question sounds like a job for /r/AskAnthropology - consider x-posting there. While there are some anthropologists here, there are more over there, and with greater emphasis on pre-history.
Just for the sake of consistency, I answered this in /r/AskAnthropology in the following fashiong:
I don't think there's anything that would corroborate that view. After a quick investigation it appears it was the Babylonians who were the first to use soap, that we know of. And they used animal fat, wood ashes, and water to make it. I read on a website that there is a non-substantiated Roman wives' tale that is along these lines.
Though there is no proof of it, an old Roman wives’ tale holds that women who lived near Mount Sapo discovered soap when rain washed a combination of wood ashes and animal fat into the clay soil by the Tiber River where they were doing laundry. The famous Roman natural historian, Pliny, disputed this claim and credited soap’s invention to the Gallic and Germanic tribes the Romans encountered during their conquests. In any event, what is more definitively known is that Romans were using soap in their baths by 200 A.D.
So to clarify, Mount Sapo does not exist. At least not as far as anyone knows. You'll find this tale on multiple websites and other such sources. But there is simply nothing outside of this story that corroborates even the existence of Mount Sapo. The idea was that Mount Sapo was a place where animal sacrifice took place, hence the story. Supposedly the word soap is to be derived from Sapo (which I believe is a Latin translation from Germanic saipo), but this is not the case. As mentioned, Pliny the Elder is the first to mention the invention of soap among the Romans, and he credits it to the Gauls. The etymology of the word does not derive from Latin but either from Gaulish or Germanic.
In addition, I don't believe it is possible for soap to almost spontaneously appear as a river flows through some ash and fat.
The issue can be discussed in more detail, but in short, the story exists but it would have been derived from the Roman myth that follows the same general storyline. However, there exists no proof of the myth beyond word-of-mouth. Either way, since we're talking Romans and we know of soap before this, even if the Romans had discovered soap in this way it would not have been the origin of soap.