Are you doing an REU this summer like Patrick Orchard? Or are you just thinking about math on your own time? Either way, no doubt you’re looking for some new theorems.
Well, look no further! David Simmons-Duffin has an automated theorem writing machine available here. Even better, the theorems come pre-proven! For example:
Okay, now that you have your theorems (with proof!), you need a journal to publish them in. Fortunately, thanks to Kimball Martin, et. al. there is no such thing as unpublishable mathematics: