This short story, which takes place in a world where society is medieval and the sun is seen less than once per year, focuses on the mathematical advances brought about by the primary protagonist, Ganil. (It never addresses the obvious question of how food is produced without sunlight. ; ) Although everyone around them uses Roman notation for numbers and does arithmetic through rote memorization, a fellow machinist named Mede introduces him to the notion of zero and its symbol "0". With only a bit of coaching from Mede, Ganil discovers decimal notation. (Numerals like "2" rather than "II" are not entirely unknown, but are called "black numbers" and are taboo.) It is not long before he also develops algebra. Mede is pressing him to make progress on particular questions of interest such as "what is the curve that a projectile follows?" and understanding the dynamics of the solar system. Clearly these will require some calculus, though the story ends before we get there.
Presumably, this story takes place in a future, dystopian Earth where either nuclear war or environmental disaster has resulted in the sun only appearing rarely and society reverting to one that is agrarian and antiscientific. (I did not see anything that clearly indicated this, however.) There is a bit of romance in the story as Ganil courts a strong young woman. And, there is danger since the mathematics that Ganil is developing at Mede's request is considered heretical and subject to significant corporal punishment. However, unlike some works of mathematical fiction in which the math is in the background, these other subplots and themes appear to be scenery and the (re)discovery of the mathematics is the main feature.
Thanks to Fred Galvin and those involved in this thread at scifi.stackexchange.com for bringing it to my attention.
