Are the spells in the magical world of Harry Potter invented or discovered?
Maybe someone just said “Avada Kedavra” and the rest is history.
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While thinking over this question, I think spells must have been discovered. As we know, wizards and witches can perform magic unknowingly. Harry makes Aunt blow up like balloon, makes glass disappear in zoo.
So maybe in ancient time, certain people observed this unusual happening in their times and created a way to channel these powers out. This channel can be spells and wands their medium.
By considering this theory, we can say once the wizards and witches mastered this skill, they started combining raw spells to form more complex spells with more impact. Thus, some magical spells might have also been invented.
To Justify my case, lets assume 'Person A' getting unusual experiences like making flowers float. He shares this information with 'Person B' who claims that 'Person C' can make stones disappear for some time. 'Person A' and 'Person C' start experimenting and find way to control it, use it desired manner. Thus, Discovering spells. This knowledge spreads all over a certain region and people with unusual experiences form a group. They combine these spells in various formats to invent new spells.
From 1st movie, it is seen that even a mild flick of wand, Harry could spawn some random spells (Scene from Oliwanders Shop).
In Harry Potter and the Half Blood Prince, Harry finds scrawlings in his borrowed copy of the required book for Potions that indicate that the previous owner of the book was not only improving on potions recipes, but also creating new spells, such as the dangerous "Sectumsempra" spell.
Whether or not the spell was "invented" or "discovered" by the owner of the book is up for debate - but being as wand movement and (usually) a word is needed to cast a spell, it would indicate that the magic required to use the spell existed beforehand and is "called" by the combination of a magical user, a certain wand movement and a specific word, rather than invented and then assigned a wand movement and a word in order to recall it.
I think most of the spells in the magical world were invented. We know from the books that Severus Snape invented spells.
The Killing Curse was invented during the early Middle Ages, by Dark witches or wizards. The curse was created primarily as a means of quickly and efficiently slaying one's opponent in a duel
This is referred from http://harrypotter.wikia.com/wiki/Killing_Curse