I have Turing's famous paper listed as one of my favorite books on Facebook. I love theoretical computer science, but since college I've mostly worked "in industry" and been pretty distant from anything resembling serious math. That recently changed, though, when I started working through a textbook on computational complexity, problem by problem .
At the end of chapter one, I felt renewed excitement for the subject, accompanying my renewed understanding. But along with this came a negative feeling: that I'd been wrong to have kept that paper on my Facebook profile. I'd understood the paper when I added it (in college), but in the intervening years, as my understanding  faded, my claim on it had faded into an identity statement for mere identity's sake. It felt like I'd been posing. The new me, knowing the interim me's level of understanding, was disdainful.
I don't know whether that's fair or not. But it made me think about how much of our identities, whether expressed on Facebook or just felt internally, might be similar — conclusions stored without their proof. Do we really still like that thing? How often do you have to check?
For that matter, how much of anything we believe can we justify? Consider politics, ethical questions, or feelings about a person. Direct understanding quickly gives way to shortcuts, post hoc reasoning, and believing our own superficial rhetoric. The prospect of living awash in a mix of stubbornly held falsehoods on one hand, or opinions surrendered too weakly on the other, is scary. I in particular don't have a great memory, so I feel especially susceptible, but we must all be living like this to an extent. My answer, for now, is to make things, because something, once made, is incontrovertible.
 You can track my progress on GitHub.
 I mean "understanding" in a broad sense. Not just the mechanics of the paper, but its implications for the world.