A technological solution, at least to that last problem, may lie 2,600 miles east of Silicon Valley, in a computer-science laboratory at Dartmouth College. Prof. Hany Farid, chairman of the department, creates algorithms that can sweep digital networks and automatically purge extremist content—if only the tech companies will adopt them. “If you look at recent attacks, from Orlando to San Bernardino to Nice to Paris to Brussels,” Mr. Farid says, “all of those attackers had been radicalized online. They weren’t going to Syria. They watched YouTube videos.”