During my time as the Technical Director of the Imaging Research Center @ UMBC, we piloted a app that attempted to visualize set theory mathematics. UMBC President, Freeman Habrowski often utilized a elementary set theory problem during live events to showcase the role of creativity in mathematics. The problem is as follows:

29 children are in a classroom. 20 have dogs, and 15 have cats. How many students have a dog and a cat?

Due to nature of set theory, the answer to this problem is variable depending on how you assign cats and dogs to the children in the classroom. The app needed to allow users to easily assign the pets to characters on screen, and see how their choices affects the total number of students with dogs and cats. I lead the development team and was responsible for the UI design. The video below showcases this functionality.

Despite being a problem at the 7th grade level, rigid perceptions of mathematics prevent many adults from answering the problem. Can you!?