Henry Kuttner's "The Creature From Beyond Infinity" aka "A Million Years to Conquer" (novel, free): Superfast evolution considered harmful
Story summary.There are actually two stories here.
First is of Ardath, the sole survivor of a group of super-advanced aliens shipwrecked on a pre-life earth while escaping doom of their own world, Kyria. He's, in fact, the sole survivor of his race. Passing the civilization of their race to something intelligent will become his mission in life. He can already foresee there will be intelligence on earth; his project is to collect individuals with good potential from various eras to eventually build a super-race here.
Over the eons, he will periodically awaken from hibernation - to choose a potential candidate for his future super race. We see three stories here: of a Roman hero, of a pristess from Atlantis, & of a war strategist from somewhere in Asia.
Second is of a plague. Sol is apparantly passing through some weird part of space, & a strange & highly contagious disease has began affecting individuals - their bodies go through future evolution at a superfast pace. Only, there is no time for them to mentally mature with their advanced body; they've become ... kind of ... monsters.
Stephen Court, a genius scientist will identify the disease & work towards eradicating it. Of course, he will be eventually helped by the alien guardian angel of earth.
Fact sheet.First published: Startling Stories, November 1940.
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Related: Stories of Henry Kuttner.