Witch Burning in the Fourteenth Century Was Completely Pointless — discuss was the name of a summer essay Professor Cuthbert Binns assigned his upcoming third year students in 1993. As suggested by the topic title, the essay was supposed to cover witch burnings during the 14th century by Muggles, and why these burnings were ineffective in actually decreasing the wizarding population.
Harry Potter wrote part of this essay on the night of 30 July, continuing on into his birthday the following morning. He consulted Bathilda Bagshot's A History of Magic for information on the subject, and incorporated Bagshot's account of wizards resisting burning using the Flame-Freezing Charm and the stories of Wendelin the Weird. After approximately an hour of writing, at which point it was one o'clock in the morning, Harry decided he was too tired to finish the essay and put it and his other supplies away under the loose floorboard in his room. Later that summer, Florean Fortescue, who was knowledable on the subject of medieval witch burning, helped Harry Potter finish this essay when he was lodged in the Leaky Cauldron for a few weeks in August 1993.
Hermione Granger, on the other hand, used her summer vacation to France with her parents to research the local history of witch burnings. She rewrote her entire essay based on information she discovered, and ended up writing enough to cover two more rolls of parchment than Professor Binns's requirement.