What Are Breakthroughs in Mathematics?

Call mathematics the purest form of knowledge, universal messaging anyone, anywhere, can understand. For math to advance, there must be breakthroughs, which may seem like magic. What are mathematical breakthroughs? How do they happen? How do they work?     Featuring interviews with Karen Uhlenbeck, Edward Witten, Michael Hopkins, Ivan Corwin, Gregory Chaitin, and Paul Davies.     For subscriber-only exclusives, register for free at closertotruth.com.