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.

[1] https://en.wikipedia.org/wiki/Lest_Darkness_Fall

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.

Albeit 2nd-3rd c. AD

Featured in Connections "Faith in Numbers" S1E04 1978

https://youtu.be/z6yL0_sDnX0

Great article on why the premise doesn't make sense.