The hero of the novel, Martin Padway, gets his start teaching Arabic numerals to a Syrian banker in Rome, and then distilling brandy. By the end of the novel he's running a newspaper and has a semaphore telegraph network set up throughout Italy. Good fun reading.
I also needed the relationship to go both ways, not just Marcus getting ideas from the future. That makes the plot more interesting.
And one thing that really stands out is that there are really not that many shortcuts. To build something like a steam engine, you need to invent advanced steelmaking, casting, advanced tooling (lathes, drills, etc.), and so on.
In general, ancient people were able to exploit the tech available to them with great efficiency.
There are some technologies that were overlooked longer than they should have, but not that many. For example, rubber could have been invented 400 years earlier. Hooke had a microscope capable of resolving micro-organisms in 1665, but the germ theory of diseases took 300 more years to develop.
The Romans were very capable engineers. If you give them a few key ideas and steer them away from dead ends, progress can compress a lot.
Even if you have a blueprint, a bronze engine is still a major research project.
Albeit 2nd-3rd c. AD
Featured in Connections "Faith in Numbers" S1E04 1978
Great article on why the premise doesn't make sense.
One of the big, if easy, mistakes to make about history is to assume that a historical society is just like modern society at a lower tech level. Bret Devereaux is fond of dunking on George R. R. Martin's question "but what was Aragon's tax policy like?" as malformed because Gondor is a polity that doesn't really have the capacity to have a tax policy in the first place (it's pretty clearly modeled off of something like the Byzantine state). Not that Tolkien is immune from this either--the Shire suffers from being a Victorian-era English countryside being transplanted to a ~15th century tech level.