Experiments in Mathematics: Fact, Fiction, or the Future?

In this chapter, the possibility of experiments in mathematics is examined. A general scheme is proposed as a tool to handle the different forms of experiments that are being used in mathematical practices: computations, “experimental mathematics” as a new research domain in mathematics and computer science, real-world experiments, and thought experiments. In a final section, extensions of the scheme are proposed that further support the conclusion that mathematical experiments are indeed facts and the future.