A liver fluke describes its life (from hatching from an egg to its final moments) to an alien who is recording it. As it turns out, these trematatode parasites are not as dumb as we think. In fact, they are smarter than humans, and resent the dominance we have over the planet just because of our long life, and hands, and other unfair advantages like that.
They flukes seemingly share prior knowledge with the next generation telepathically, and they can learn from humans in the same way. What they like to do with their time, when they are not busy trying to find a host body to inhabit, is math. Because of their limited experience with the physical world, they prefer pure to applied math:
(quoted from By a Fluke)
Although I solve easily all varieties of differential equations, including some that have baffled the human experts, it is, for me, a purely formal process, and for that reason less intriguing than problems in the theory of numbers, which most of us prefer. In the latter field, the mathematics is all: no practical relation is implied. With applied analysis, one works in a vacuum. For example, I have solved the problem of n bodies moving in a gravitational field, but have no real feeling for the result.

In addition to having solved the "Nbody Problem", the narrator claims to have proved Goldbach's conjecture and the Riemann Hypothesis.
Interestingly, he also found two values of n for which Fermat's Last Theorem is false. This story was written many years before FLT was proved, and so it was reasonable at the time to imagine there might be counterexamples. In a way, this makes the story dated but quaint. The same fate may befall my story in which a counterexample is found to Goldbach's Conjecture (written many years before I read "By a Fluke").
This story first appeared in the October 1955 issue of The Magazine of Fantasy and Science Fiction. I am grateful to Fred Galvin for mentioning its existence to me.
