Some knowledge, if no one points it out, you could struggle forever and still not get a clue. But once it's revealed, it's hardly extraordinary: take the gunpowder formula for example.
"The simplest mnemonic goes 'one nitrate, two sulfur, three charcoal, add a bit of sugar, voila!'" Saltpetre, sulfur, and charcoal, using the copper scales of this era that weigh sixteen taels to a jin, results in a ratio of 16:2:3.
Adding sugar is to increase the volume of gas produced during combustion. This gunpowder mixture, when exploded in a confined space, is comparable to a miniature nuclear bomb indoors; even an Executive Officer like Yun Yang or Si Cao wouldn't be able to withstand it.
Sulfur can be found at the Medical Hall.
Charcoal is easy to produce.
As for the so-called saltpetre, scientifically known as Potassium Nitrate, it's actually the efflorescence on soil walls; when ancient people made fireworks, they obtained saltpetre by "digging at the base of the wall."