“Be grateful when solutions exist, because of Brouwer’s Fixed Point Theorem” offers a introduction to a mathematical theorem asserting the existence of solutions to problems in engineering, medicine, economics, and other fields, as long as certain criteria are satisfied. The discussion is illustrated with numerous hand-drawn sketches. While this theorem assures the existence of a solution—a “fixed point”—it does not provide insight on how to find it. Still, it can be reassuring to know that a solution exists. For example, economist John von Newmann used this theorem in his 1937 economic model establishing that there exist prices at which supply equals demand. Mathematics students and enthusiasts are encouraged to be grateful for knowledge that a solution exists in mathematical and life pursuits, even when the solution itself remains elusive. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.