Back in March the news was full of two teenage girls from New Orleans who had supposedly done the impossible: proved Pythagoras's theorem through trigonometry. There are many ways to prove Pythagoras's theorem from fundamental principles, mostly involving similar triangles, but you can't prove it "from trigonometry" because trigonometry - in the mathematical sense of the word - is derived from more fundamental results, including Pythagoras.
I waited for the proof to be revealed as bogus ... and waited ... and waited. The refutation never came. Of course there's a simple explanation as to why not: the girls, Calcea Johnson and Ne’Kiya Jackson, are black. Even now, googling the story reveals no dissenting voices. Their proof has never been published and is not available online, which of course is a huge red flag. A few mathematicians were asked to comment but they wisely said they'd have to see the proof published first. Right now they could practically claim 2 + 2 = 5 and not get called out on it.
So what did they do? Their proof has been reverse engineered from an image of a slide from a talk they gave. Basically they constructed an infinite series of triangles bolted onto the original whose total area converges to the expected answer. However this proof is invalid for a number of reasons. In formal logic a proof is a set of finite deductions from axioms. Translated into geometry this means any construction must have a finite number of steps. You can't have an infinite constructive proof. Furthermore in order to prove the convergence correct you need to invent a huge amount of theory on limits which comes from analysis. It's completely out of the domain of geometry.