In his 2017 Christmas lecture (https://news.ycombinator.com/item?id=15898919 https://news.ycombinator.com/item?id=15898919), Donald Knuth mentions at around the

In his 2017 Christmas lecture (https://news.ycombinator.com/item?id=15898919 https://news.ycombinator.com/item?id=15898919), Donald Knuth mentions at around the 5-minute mark: > You know, people think that mathematicians have been working for hundreds of years, and now there's tens of thousands or hundreds of thousands of mathematicians all spending every day working on problems, so how could you possibly still find a simple down-to-earth problem that hasn't already been studied, you know, way too much? And the answer is: those problems aren't rare at all, they keep coming up several times a year, and this is an example where even this very basic problem of rectangle into rectangles has all kinds of stones not yet turned. You can see in the talk where he starts simple and just keeps working on it, until he gets something that seems new (a conjecture, which he proposed as a problem in the American Mathematical Monthly). Of course, this particular problem is now solved, but if you just keep exploring you'll pretty soon hit the limits of what's known. (Potential exercise that I haven't tried: load random sequences on OEIS http://oeis.org/ http://oeis.org/ until you hit one where there are only conjectures, and not much research.)