1 + 1 = 2

Many people are often confused with the Goldbach's conjecture with the problem 1+1=2.  The former is still unsolved, though there were considerable progress after Chen Jinrun (1973).  Chen is mentioned here is just because all introductions in Chinese about the conjecture stops at his work. 



The latter is literally proved by Whitehead and Russell in their 3 volume book, "Principia Mathematica".  The proposition 1+1=2 is defined in Volume 1, page 379( pp 362, 2ed or pp 360 in abridged version).  Then it is proved in volume 2, pp86, in 1ed.

Although I don't understand a thing, the proof is copied below:

 

There is also a blog article explaining this in details.