The town of Empty Interior, NY was a place of spell-bound mathematics. Fantastical concepts like infinities acting the same as other numbers, or horrifying ones like a curse to fail every math exam for eternity, held a high degree of intrigue among the townspeople. Jacobi Crane, a well-known Connecticut mathematician, was keen on studying the area.
Upon arrival, he quickly learned of the spookiest of all tales in Empty Interior — that of the headless Hessian matrix, a specter that roams the town, sending anyone it encounters into the heights of the atmosphere, or the depths of the Earth, based on its negative or positive mood. In awe of the story, Crane felt no sense of fear despite the quavering voices of the old wives who told him.
Also a man of romance, Crane became enamored of the town’s young belle Katrina Vandermonde, the daughter of a wealthy farmer. Abraham Wronskian, a bachelor who grew up in the town, grew quite jealous of the new visitor, who seemed to have all the time he wanted with Vandermonde.
At a party hosted by the Vandermonde, Crane, after imbibing a fair amount of the house punch, decided to propose to his new crush. Vandermonde, while flattered, declined his offer, on account of not knowing Crane for that long, and because he was a mathematician. Crane, defeated, left the party, but on his way home, noticed something strange.
The ground began to shake, and then warp, as he felt himself losing balance. He eventually fell on his back, and when he looked up, there he saw it. A block-like structure floated above him, its top rows seemingly missing. It bellowed, “I’m the headless Hessian, and I need you, Jacobian, to regain my top rows!”
The next morning, the townsfolk went looking for Crane, but all they could find was a small note that said, “don’t drink and derive,” a spot on the ground marked as “local minimum,” and Crane’s horse eating some grass on a misshapen patch of the road. Vandermonde and Wronskian married, and remember the strange visitor to their town with a calculus-themed party every year (no one else in Empty Interior has yet attended).
