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In sentence
They were rescued by Joseph-Louis Liouville, the son of a captain in Napoleon's army who became a professor in the Collège de France.
who became a professor: Joseph or his father?
Photo of the source:
Why beauty is truth: a history of symmetry / Ian Stewart. ISBN-13: 978-0-465-08236-0
Poor punctuation leads to poor understanding. The sentence, as written, is ambiguous.
In context, the math was rescued by the son of an army captain. It's unlikely (but not impossible) that the army captain of the Napoleonic era, would go on to become a professor of mathematics. Nor would a man's father's credentials likely be of greater significance than his own in this scenario. So, we can likely conclude this to refer to credentials of the son.
I'm reminded of the title joke of the book Eats, Shoots and Leaves, by Lynne Truss.
A panda walks into a café. He orders a sandwich, eats it, then draws a gun and proceeds to fire it at the other patrons.
"Why?" asks the confused, surviving waiter amidst the carnage, as the panda makes towards the exit. The panda produces a badly punctuated wildlife manual and tosses it over his shoulder.
"Well, I'm a panda," he says. "Look it up."
The waiter turns to the relevant entry in the manual and, sure enough, finds an explanation. "Panda. Large black-and-white bear-like mammal, native to China. Eats, shoots and leaves."
Obviously there's a missing comma but there's almost zero ambiguity, given the specific facts presented and narrative:
JLL seems infinitely more likely to be a professor [and presumably a mathematics professor] than his father. [Unless they were both professors, père et fils, and his father was not necessarily a mathematics professor. But that seems a tortured reading, and in the unlikely event, the article would have said "the professor son of a captain who also became a professor..."]. All this (both explicit and implicit) context allows us to guess around the missing comma, in this particular case.
I mean you could argue that it's linguistically also possible that JLL only later in life, became a professor, and in archaeology not anything mathematics-related. But that sounds very unlikely. It's also possible that JLL was a dolphin. Paraphrasing: all human communication has ambiguities if you scrutinize it hard enough, but we each learn to apply the everyday skill of discarding unlikely and silly hypotheses. This one is no different.
As requested by OP in comments to post this comment as an answer -
As it stands, the sentence is completely ambiguous. Without knowing the historical facts, there is absolutely no way to tell who became a professor as the sentence stands. A comma would make it unambiguously the son, but no comma does not make it the father even half-unambiguously. The antecedent of who can just as well be “the son of a captain in Napoleon’s army” as “a captain in Napoleon’s army” – or indeed, going by mere nested proximity, the current sentence might be saying that Napoleon’s army became a professor!
Credit - Janus Bahs Jacquet
