Abstract: We live in a world with many pressing problems from climate change to sustainable development to social justice, to name just a few. However, in my experience, most people dealing with such momentous issues know very little mathematics. It is much harder to achieve clarity, to learn and to improve without mathematical thinking. For this reason, almost all of what we know in science from physics to ecology and evolution, to economics, uses mathematics as its language. In this talk, I want to demonstrate these statements through two mathematical concepts and their many uses in complex problems. First, I will discuss the concept of topology and its connection to graphs (networks) as the language of relationships. I will show how topology was invented to solve a very human problem of walking a path, and how we are using it today to support development in cities throughout the world. Second, I will discuss Bayes theorem, how it was introduced to discuss the existence of God, and how it is the basis today for models of epidemiology, and theories of the brain and artificial intelligence. I will close with some reflections on the essential role of mathematics for gaining traction in complex and unresolved challenges and for the synthesis, manipulation and generalization of ideas that can pave the path to transformative solutions.