Jaime Lerner reinvented urban space in his native Curitiba, Brazil. Along the way, he changed the way city planners worldwide see what's possible in the metropolitan landscape.

Eduardo Paes is the mayor of Rio de Janeiro, a sprawling, complicated, beautiful city of 6.5 million. He shares four big ideas about leading Rio -- and all cities -- into the future, including bold (and do-able) infrastructure upgrades and how to make a city "smarter."