Asymptotically approaching the extreme of obsession...
"Erdös (pronounced 'air-dish') structured his life to maximize the amount of time he had for mathematics. He had no wife or children, no job, no hobbies, not even a home, to tie him down. He lived out of a shabby suitcase and a drab orange plastic bag from Centrum Aruhaz ('Central Warehouse'), a large department store in Budapest. In a never-ending search for good mathematical problems and fresh mathematical talent, Erdös crisscrossed four continents at a frenzied pace, moving from one university or research center to the next. His modus operandi was to show up on the doorstep of a fellow mathematician, declare, 'My brain is open,' work with his host for a day or two, until he was bored or his host was run down, and then move on to another home."
Erdös wrote or co-authored 1,475 academic papers. For the last 25 years of his life he put in nineteen-hour days, sustaining his frenzied pace via his fondest pharmacopeia: Benzedrine, Ritalin, and Caffeine (in tables and espressos).
A wild man of sorts. Eccentric and passionate; you should read the first chapter of Paul Hoffman's book about him.