WikiColdplay states that the song The Scientist, from Coldplay's 2002 album A Rush of Blood to the Head, "shows strong allusion to the short story The Birthmark by Nathaniel Hawthorne." The story appears in Hawthorne's 1846 collection Mosses from an Old Manse.
Hawthorne's tale concerns Aylmer, a dedicated scientist who marries a young woman named Georgiana. Georgiana's beauty is very nearly perfect, except for a small birthmark on her cheek. She is accustomed to the mark and gives it no thought, but Aylmer feels that it keeps his wife from attaining true perfection. He becomes increasingly obsessed with removing the birthmark, and it soon becomes a source of discord between them. In the end, Georgiana agrees to submit to Aylmer's treatment and he prepares a solution for her, which she drinks. It successfully removes the birthmark, but kills Georgiana in the process.
The narrator of the song seems to also be a scientist (I was just guessing/At numbers and figures/Pulling the puzzles apart) and who also seems to have lost a loved one (It's such a shame for us to part), perhaps as a result of his devotion to science:
Questions of science,Science and progress,Do not speak as loud as my heart.Tell me you love me,Come back and haunt me,Oh, what a rush to the start.
So the song certainly seems to share some themes with the story, but there is nothing to specifically link the two. Unfortunately, WikiColdplay offers no documentation for the claim that the one alludes to the other, and we have been unable to locate any supporting evidence.
Chris Martin is one guy who would know for sure, but his explanation of the song isn't very helpful. ""That's just about girls," he said in Billboard. "It's weird that whatever else is on your mind, whether it's the downfall of global economics or terrible environmental troubles, the thing that always gets you most is when you fancy someone."
Mosses From An Old Manse (Kindle Edition)