Gödel's incompleteness theorems are two fundamental theorems of mathematical logic which state inherent limitations of sufficiently powerful axiomatic systems for mathematics. The theorems were proven by Kurt Gödel in 1931, and are important in the philosophy of mathematics. Roughly speaking, in proving the first incompleteness theorem , Gödel used a modified version of the liar paradox, replacing "this sentence is false" with "this sentence is not provable", called the "Gödel sentence G". Thus for a theory "T", "G" is true, but not provable in "T". The analysis of the truth and provability of "G" is a formalized version of the analysis of the truth of the liar sentence. 
After becoming a teacher it became pretty clear that no one outside of education can understand just how brutal and time-consuming it is to be a teacher — especially when it comes to grading essays. But on the flip-side most teachers don't know how or where technology can help them. Or worse, they're surrounded by all this awful technology that's been forced upon them. My district's attendance system required three separate logins! Three! Argghh! Last year I had four sections of the same Senior English prep. That meant 96 papers would come in all at once. I was super-passionate about getting these regular-level students ready for the rigors of college so I would find myself spending 15, 20, 30 minutes per paper. That multiplied by 96 is insane. That's where came from — as a teacher I felt the same pain you're feeling but my programming background allowed me to see where a little bit of technology could go a long way.