A father cleans up after his toddler and imagines a cup that won’t spill. An engineer watches people using walkie-talkies and has an idea. A doctor figures out how to deliver patients to the operating room before they die. By studying inventions like these—the sippy cup, the cell phone, and an ingenious hospital bed —we can learn how people imagine their way around “impossible” problems to discover groundbreaking answers. Pagan Kennedy reports on how these enduring methods can be adapted to the twenty-first century, as millions of us deploy tools like crowdfunding, big data, and 3-D printing to find hidden opportunities.