Before he left Ireland for Harvard in 2009, John Collison had to promise his mother he would not drop out. His older brother, Patrick, had ditched MIT not long before, after just a few months in college. Promise and all, John never made it past freshman. He dropped out to join his brother to create Stripe, an online- and mobile-payments company that two years later is processing billions in transactions, counts PayPal’s three founders (Peter Thiel, Max Levchin, and Elon Musk) as investors, and is growing at a dizzying speed. With scores of hot startups like Lyft, Foursquare, and Squarespace using it to handle payments, Stripe has emerged as the buzziest new payments company since Jack Dorsey’s Square turned iPhones into credit card readers. Now John, 23, and Patrick, 25, are about to go head to head with online-payments giant PayPal, which in September agreed to spend $800 million to buy Stripe’s older and larger rival, a Chicago-based startup called Braintree. “John and Patrick are two of the sharpest characters that we’ve ever partnered with,” says Stripe investor Mike Moritz of Sequoia Capital, who is no stranger to sharp characters, having backed the founders of Google, Yahoo, PayPal, and countless other tech icons.