Paul Erdős didn't own a house.

He spent most of his life living with just a suitcase. He would travel from one mathematician's home to another, knock on the door, and say, "my brain is open." Then they'd spend days doing math together. Coffee, eighteen-hour work sessions, nonstop problem solving. Then he'd leave and move to the next place.

He published around 1,500 papers this way, working with hundreds of collaborators. He's probably the most productive mathematician ever.

But he also left behind something else: thousands of math problems. These were questions even he couldn't solve, but thought were beautiful enough that someone should. He handed them out almost like gifts. Sometimes he even attached prize money to them.. a few dollars for easier ones, and hundreds or thousands for the really difficult problems.

He died in 1996. Many of those problems are still unsolved today.