I will discuss two central challenges in theoretical physics. The first is dealing with strong coupling: many interesting and important physical systems are strongly-coupled and resist
traditional computational methods. The second challenge is making predictions for quantum gravity in the absence of a complete microscopic theory of quantum gravity. Surprisingly, these two problems are connected, and both can be attacked with a strategy called the "bootstrap": using symmetries and consistency conditions to carve out the space of theories. To illustrate the connection, I will describe recent applications of bootstrap methods to the superfluid
transition in liquid helium, and to constraining corrections to Einstein's theory of General Relativity.