"I invent Greek Fire!" and other PC shenanigans


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This matters why? Honest question.
In a D&D context (3.x and earlier)...
If the PC's are high level, there are lots of "plausibilities" to account for.

Skill points (Alchemy), divination magic (Contact Outer Plane, etc.), Infernal "gifts", Wish spells, plane-hopping to an Alternate Prime Plane with a technological culture...

3rd level PC...nope. 🙂
 

If the PC has been shown to put in the downtime effort to actually study the underlying principles and science of the invention and can actively roleplay the stages they use to acquire the ingredients, equipment and process of development then I see no reason why they shouldnt be able to make the attempt*

Greek Fire was invented around 670 AD and exist in DnD as alchemist fire anyway.

(Note: My oldest surviving character is a gnome alchemist, who has two laboratories, teaches Applied Alchemy at the Royal Research Academy and specializes in pyrotechnics and growing mushroom-based leather, so adventuring to collect weird ingredients and inventing stuff has been a major focus of play over the years - it can be done without being too disruptive )
 
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I like what @VashVet said and maybe allow it, but it only deals what a longsword does for damage. It could be like a healing potion, but deals fire damage and costs 50gp.

I could also allow it and then have the bad guy improve upon it and come back at the PC with the bigger gun.

I could also just say that it will take 2d6 years of invention and have the player make a new PC while retiring the first.
 

There are plenty of reasonable solutions:
  • ""Your character doesn't magically know how to do things no one around them do. I see you have zero levels in 'world-changing inventor' class."
I’m partial to this one, cause the solution involves campaign activity I find fun, if players are up for it: traveling the lands to find people who can bring something relevant to the effort, keeping them supplied and not fighting each other, and figuring out what to do with the stuff that gets cobbled together. The project becomes a significant social force, maybe even if it doesn’t really work out, so factions of powerful and wannabes have their own thoughts about this, and the whole thing snowballs entertainingly.
 


In a D&D context (3.x and earlier)...
If the PC's are high level, there are lots of "plausibilities" to account for.

Skill points (Alchemy), divination magic (Contact Outer Plane, etc.), Infernal "gifts", Wish spells, plane-hopping to an Alternate Prime Plane with a technological culture...

3rd level PC...nope. 🙂
Quite true, but one of those needs to already have the necessary knowledge. I think that's also somewhat besides the point. I suspect that the vast majority of the times this comes up its mostly about the player wanting to be a clever clogs. I'm sure occasionally the notion of greek fire (or gunpowder) comes up in an organic in-game kind of way, which is fine and cool, but I think that's a slim subset.
 

AFAIK, literally nobody has known how to make Greek Fire for hundreds and hundreds of years. There are only some theories.
This. We don’t know the recipe, how it was stored, how it was delivered or how (and if) it was pressurised. Knowledge was highly compartmentalised and secretive.
There are (at least) two levels of lost technology--things we don't know how to do, and things we do not know how they (the subjects of study) did it. For Greek Fire, we don't know how they (the Byzantines) did it, but there are several potential options that it could have been, or more germane to the situation, a PC could 'invent' in a medieval context and use. Even if it isn't 'historically accurate' Greek Fire, it would still be a high-efficacy incendiary that could (depending on how the DM rules it) mildly-to-wildly upend the campaign. That said,
I’m partial to this one, cause the solution involves campaign activity I find fun, if players are up for it: traveling the lands to find people who can bring something relevant to the effort, keeping them supplied and not fighting each other, and figuring out what to do with the stuff that gets cobbled together. The project becomes a significant social force, maybe even if it doesn’t really work out, so factions of powerful and wannabes have their own thoughts about this, and the whole thing snowballs entertainingly.
I alluded to that later (perhaps I should add it to my first post). The question becomes -- does everyone else enjoy turning the campaign into 'The Quest for the Holy Hand Grenade (Construction Supply Chain)' -- If so, absolutely, dive right in. If, as I thought the OP was implying, this is instead something they wanted to shut down, the best response IMO is something along the lines of 'Yes, you can play the guy who invented Greek Fire (but that's going to be almost exclusively what he does for the foreseeable future). Could you also play a guy who will fit into this party of adventurers?'
 

Even if the player wants a character to invent something, the character first has to get the idea for that invention. (Inspiration check.)

I will disagree here. We don't generally roll dice for PCs to have an idea.

However, we should also note that many inventions were, historically, more like discoveries. Gunpowder didn't come about by someone getting the idea to fling metal balls out of cubes, and for that they'd need a powder to pack in before the ball. It was folks futzing around with materials, and stumbling upon a mixture that bruened prodigiously...

Which was all the more a matter of chance given how inaccurate their models of what the materials they were working with were.
 

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