Conformal Field Theories (CFTs) are theories that are symmetric under changes of distance scale, like a fractal or a Russian doll. They are basic building blocks of more general Quantum Field Theories, which can describe how nature works at its most fundamental level. Despite their importance, the range of possible behavior in CFTs is poorly understood, and often the most interesting theories resist calculation with conventional perturbative methods. However, over the last few years, new techniques have emerged for mapping out the space of these important theories. I’ll explain how to use basic mathematical consistency conditions, techniques from optimization theory (a subfield of computer science), and a bit of CPU time, to place universal bounds on the behavior of CFTs that could be relevant for real world physics.