Just before Christmas in 1938, the young woman curator of a small South African museum spotted a strange-looking fish on a trawler's deck. It was five feet long, with steel-blue scales, luminescent eyes and remarkable limb-like fins, unlike those of any fish she had ever seen. Determined to preserve her unusual find, she searched for days for a way to save it, but ended up with only the skin and a few bones. A charismatic amateur ichthyologist,...