Is there such a thing as an "unsolvable" question? There have been times throughout history where entirely new branches of mathematics have been created in service of puzzling out equations most mathematicians thought impossible to solve. Math is hard: sometimes, the same tools we use to ask a question aren't enough to answer it. So can we ever know if something is truly "unsolvable," or is there always just more, new math, out there waiting to be rearranged in ways that allow us to solve what we once thought impossible?

In your math education thus far, you may not have encountered any big, unsolved problems. But you've certainly encountered problems that were unsolvable to you until you learned the techniques necessary to figure them out.

In this section, we introduce some such problems -- and the techniques required to solve them.