More or less a normal Saturday, which my family treats as a "work day" as a mental reminder to treat the following day as a "rest day."
But since it's also Pi day, my work today must include some math. At this time I am focused on a creation of my own that I have labeled "arrangements." These Chinese Remainder Theorem analogues have some interesting properties, but so far they haven't provided any earth-shattering insights, and today was no exception. I started my theorizing session by properly defining my terms around a small sub-idea that at certain lengths, arrangements could be guaranteed to be unique. At the end of the day I had definitely concluded that while some arrangements could be unique, the vast majority of them would not be. This conclusion brought a decisive end to one avenue for possibly approaching Legendre's Conjecture.
But that's just one avenue, and now I have a stronger understanding of how these objects really work. This negative progress is still progress.