[momentoftop]

There isn't a serious proof that 1+1=2, because it's near enough axiomatic. In the last 150 years or so, we've been trying to find very general logical systems in which we can encode "1", "2" and "+" and for which 1+1=2 is a theorem, and the derivations are sometimes non-trivial, but they are ultimately mere sanity checks that the logical system can capture basic arithmetic.

[tomrod]

If this is new, then you're one of today's luck 10,000![2] Serious logical foundations take a lot of time and exposition to start from fundamentals. Dismissing them as non-serious because GP's argument failed to consider them is misguided, IMHO.

[0] The classic reference: https://en.wikipedia.org/wiki/Principia_Mathematica -- over 1,000 pages, Betrand Russell

[1] https://cmartinez.web.wesleyan.edu/documents/FP.pdf -- a bit more modern, relying on other mathematics under the hood (like DRY reduces the base count), 11 pages

[2] https://xkcd.com/1053/

[3] Some reasonable review https://blog.plover.com/math/PM.html

[momentoftop]

Yes, as I said: systems such as Russell's encoded "1", "2" and "+" in such a way that the theorem "1 + 1 = 2" is non-trivial to prove. This doesn't say anything about the difficulty of proving that 1 + 1 = 2, but merely the difficulty of proving it in a particular logical encoding. Poincare ridiculed the Principia on this point almost immediately.

And had Russell failed to prove that 1 + 1 = 2 in his system, it would not have cast one jot of doubt on the fact that 1 + 1 = 2. It would only have pointed to the inadequacy of the Principia.

[whiskiss]

Am I the only one that always felt like that xkcd post came from a place of insane intellectual elitism?

I teach multiple things online and in person... language like that seems like a great to lose a student. I'd quit as a student, it's so condescending sounding. It's only lucky because you get to flex ur knowledge!(jk, pushing it I know lol but i can def see it being taken that way)

Keep in mind I know you're just having fun.

[tomrod]

I can't be too condescending with the number of typos I have to edit :D

I actually really like the message for 1 in 10,000. As a social outsider for much of my life, it helped me to learn that the way people dismissed my questions about common (to them) topics was more about their empathy and less about me.

But, these sorts of things are difficult to communicate via text media, so we thus persist.

[whiskiss]

Yeah I guess I've had only a few people be the other person that treated me right as the 1 - I feel ya on being an outsider having things dismissed. Does make sense. Another person gave me a good alternate view as well.

On a side note my couple of times I thought I was treating someone to some great knowledge they should already know I'm pretty sure I came across as condescending. Not bc they didn't know it - i always aim to be super polite - just being young, stupid, and bad at communicating, heh.

[fragmede]

The key thing to focus on with XKCD 1053, is that the alternative before that comic was to make fun of the person who didn't know there's a proof for, eg 1 + 1 = 2. "Oh, you didn't know there's a proof for that? are you an idiot? who doesn't know the proof for 1 + 1 = 2 by Alfred North Whitehead and Bertrand Russell?", to which I think you could agree would put possible students off more by that than being told they're in luck today.

[whiskiss]

Ah okay that's a good read. I'm just always on edge about my language and sometimes view the worst possible interpretation rather than what most would read. I'm not a negative person... just goes back to some "protecting myself" instincts I unfortunately had to develop. Thanks for that view.