If geniuses thrive on clutter, John Milnor has a lot to work with. His office – once described as a “maze of papers and notes stacked feet high atop his desk and neighboring couch” – has hosted countless breakthroughs in topology, the study of what happens to the properties of geometric shapes when they are twisted or disfigured.

Milnor, a professor at Stony Brook University, demonstrated proof of the existence of the 7-dimensional sphere. From his discovery emerged the field of differential topology, which applies mathematical concepts to studying manifolds.

This accomplishment earned Milnor the Abel Prize for “profound ideas and fundamental discoveries have largely shaped the mathematical landscape of the second half of the 20th century.”

“I’ve never had much of a record as to predicting what will happen next,” he said in 2011. “I just tend to sit back and try to learn what’s happening and enjoy it.”