Once, in a nation that spanned many stars, a robot made its home in the City of Ravens Feasting. It was a small city, as cities went, upon a world of small repute. But in the city dwelled a girl who liked to walk by the sea. Her parents had no reason to believe she would come to harm taking the shuttle down to the shore, and she often made the trip alone in the evenings, after she had completed her homework and chores.

The robot had the task of cleaning up detritus on the shore. Most of the city’s denizens didn’t litter, but there were always exceptions. And, of course, the sea itself cast junk and treasure alike onto the sands. So the robot gathered up everything from abandoned shoes to lost meditation-pendants, spent and dented bullets to bent styluses. To amuse itself during its work, it used its unoccupied grippers (it had many grippers) to write nonsense equations in the sand.

The other robots who worked by the seashore regarded this behavior with amusement. Why not real math? they would ask it. What good does nonsense math do anyone?

The robot only flashed serene green lights at them in response and continued its usual habits.

The girl who liked to walk by the sea would sometimes accompany the robot in its duties. At first the robot took no particular notice of this. In its experience, humans ignored its kind–it was no accident that the humans called them “servitors”–and the girl would eventually grow bored and go away. At least she wasn’t one of the ones who threw rocks at it, or attempted to turn it turtle, or shove it underwater. The robots had protocols for such instances, which mostly involved waiting for a technician to shoo away the prankster. While the human authorities didn’t precisely have a high regard for the robots, they appreciated that the robots would complete their tasks more easily without interference.

Then one day the girl addressed the robot, in oddly accented high language: “Excuse me,” she said.

The robot didn’t realize at first that she was speaking to it, and continued doodling a mangled version of the quadratic equation next to some washed-up strands of dark and pungent kelp.

The girl squatted next to it, fished a stylus out of her pocket–a bent and sandscratched one, likely scavenged from the shore before anyone could clean it up–and wrote a corrected version in tidy handwriting.

The robot stopped and blinked at her, lights vacillating between pink and violet with amusement and confusion.

“Do you need help?” the girl asked, a little anxiously. “I’m still learning math, but I’ve been studying the things you write down and I think I can teach you some of these.”

The robot refrained for flashing even more brightly pink, for it didn’t want to laugh at the girl’s obvious sincerity. Like all of its kind, it had greater knowledge of the mathematical arts than many humans except specialists. On the other hand, it considered that it wouldn’t mind company while it went about its work; certainly it had seen the girl plenty of times before.

After a moment’s thought, the robot wrote out a polynomial and deliberately misfactored it.

The girl’s brow furrowed, and she patiently began writing out a correction, explaining her method as she went, as though to a child even smaller than herself.

The robot couldn’t help a pink-yellow flicker of satisfaction as it accepted the lesson. From then on, the two of them could often be seen exchanging such impromptu lessons, on topics that grew ever more advanced as the girl’s facility increased. And if anyone minded that the shore was messier than it had been in the past, they kept it to themselves.

For cohomology. Prompt: servitor math glitch/comedy.