Finally, I have found online, a copy of the magnificent culmination of the 20th century’s most ambitious work of mathematics. The last page of Russel and Whitehead’s proof that 1+1=2. On page 378 (yes, three hundred and seventy eight!) of the Principia Mathematica.. Yes, it’s there. The whole thing: the entire Principia, in all of its hideous glory, scanned and made available for all of us to utterly fail to comprehend.
For those who are fortunate enough not to know about this, the Principia was, basically, an attempt to create the perfect mathematics: a complete formalization of all things mathematical, in which all true statements are provably true, all false statements are provably false, and no paradoxical statements can even be written, much less proven.
Back at the beginning of the 20th century, there was a lot of concern about paradox. Set theorists had come across strange things – things like the horrifying set of all sets that don’t contain themselves. (If it contains itself, then it doesn’t contain itself, but if it doesn’t contain itself, then it contains itself. And then really bad actors need to pretend to be robots short-circuiting while Leonard Nimoy looks on smugly.)
So some really smart guys named Bertrand Russell and Alfred North Whitehead got together, and spent years of their lives trying to figure out how to come up with a way of being able to do math without involving bad actors. 378 pages later, they’d managed to prove that 1+1=2. Almost.
Actually, they weren’t there yet. After 378 pages, they were able to talk about how you could prove that 1+1=2. But they couldn’t actually do it yet, because they hadn’t yet managed to define addition.
And then, along came this obnoxious guy by the name of Kurt Godel, who proceeded to show that it was all a big waste of time. At which point I assume Russell and Whitehead went off and had their brains explode, pretty much the same way that the bad actors would later pretend to do.