Math.
[Unless you follow some variant of Platonic theory which defines it as a discoverable system.]
Added:
I wanted to say “fiction” at first, but inventing stuff in our heads is so much us that it’s part of our nature.
I don’t know who you are. I don’t know what you want. If you are looking for chuckles, I can tell you I don’t have any. But what I do have are a very particular set of skills, skills I have acquired over a very long career. Skills that make me a nightmare for people like you. If you quit punning right now, that’ll be the end of it. I will not look for you, I will not pursue you. But if you don’t, I will look for you, I will find you, and I will hurt you.
Writing. The answer is writing.
Chocolate.
Well, I’ll stand by my first answer, math, looking into the future; but for the past, I might go with religion, if “most important” equals most influential.
Sewers.
Bloody hell. Ignoring the lame Dad joke, there is nothing lower on the list of important inventions than bloody venetian effing blinds.
The printing press and resultant mass-produced books propelled the Scientific and Industrial Revolutions, but written language and paper were also prerequisites for books. So, if threesomes are not frowned on, I’ll go with {written language, paper, movable-type printing press}.
Poop management, for both humans and the animals they keep.
We didn’t have to keep moving along once we began to manage our poop better, we could set down roots!
Discovering we ought not live among the dung of our animals would be of equal importance, I should think.
I feel these two things might be instrumental in all the developments that followed.
If spoken language qualifies, it was surely the most important invention, IMO.
[Moderating]
Invention might be creativity, but it’s not art. IMHO would be a better fit. Moving.
[Not moderating]
Language is by far the most important, followed by writing. Language transformed the capacity for human thought from a single brain to a whole tribe’s worth of brains. Writing transformed it from a tribe’s worth of brains to the collective brains of all humans, past and present. Further, both enabled other inventions, not only to be developed, but to last: Without language and writing, an invention could be developed, but then lost, with the death of the inventor or es tribe. With them, inventions persist indefinitely.
I think the Gutenberg Printing Press deserves strong consideration. However, human history is (hopefully) ongoing, so the most important invention/discovery may yet await us. Ultimately, it may be a Quantum Theory of Gravity that will allow us to manipulate and direct gravity so as to produce a form of propulsion that will allow us to truly expand into space on a major scale.
I’d say agriculture. Up until some time in either the late 19th or early 20th century, the winners of conflicts were usually the ones with the most population under a cohesive society, and even up until the present it still works that way a lot of the time. You need food to feed your population. The exceptions are horse archer armies who could only operate well in places where they had a lot of naturally growing grass so they could feed their horses while on the go.
The Native Americans didn’t get pushed off their land due to inferior technology, they got pushed off due to sheer numbers. The guns and cannons of Europe didn’t mean anything since the northern native americans were much better warriors per capita even with just their arrows and whatever firearms they could buy. (The central and southern native empires were taken over because they were not united.)
You know I just am not going to be able to avoid a Heinlein quote, right?
He makes a good case.
One that hasn’t been mentioned yet is the clock. Suddenly, we had a mechanical way to gauge time, and lives are run by it.
But nothing took lives over faster and more completely than our modern computers.
Yup, politics is important, all right, but it’s impossible without language.
Those all pre-date modern humans, though, don’t they? I’m inclined to disqualify them on that basis.
I’m going to vote for string, which doesn’t get nearly enough credit, in my opinion.
The horse collar – the increase in agricultural output freed many people from subsistence farming which brought about the beginnings of modern society.
The Fish Weir
You can talk about your modern inventions and how world-changing they were, but the Fish Weir is an extremely simple bit of invention* that works flawlessly and fed uncountable numbers of people for thousands of years with minimal effort. In Back Bay Boston a fish weir dates back up to 5,700 years ago, and was still used in colonial days.
Nowadays, rivers are too polluted, and there are too many people. But for a huge chunk of human history these passive fish-catching devices fed huge numbers of people. And with no moving parts.
I’m going with this - with agriculture, nomadic cultures stayed put, food production created surpluses, which allowed for individuals to diversify their labor (from hunting and gathering), populations expanded which precipitated the formation of organized leadership, etc. etc…which all eventually led to Porn on your iPhone!
Regarding writing - even nomadic cultures had some form of memory recording through marks on a stone or beads on a string, supplemented with oral references. So that to me is a form of “writing”. But we would all still be nomadic hunter gatherers without agriculture.