Is there a word/phrase/idiom for when you're working on a challenging problem and you can't stop thinking about it or put it down? It's like "having an itch." Would that be an appropriate phrase?
You might consider the idiomatic phrase absent-minded professor.
The phrase "absent-minded professor" is also commonly used more generally in English to describe people who are so engrossed in their "own world" that they fail to keep track of their surroundings. It is a common stereotype that professors get so obsessed with their research that they pay little attention to anything else.
It's often used to refer to a character in a story, but as the paragraph above indicates, it's also commonly used to describe a person so obsessed with their own curiosities and theories that they fail to perform other necessary life functions.