The 360-Page Proof That 1+1=2

Video written by Ben Doyle

[samuels]

This is what happens when the child keeps asking 'why' and the parent only breaks the discussion at 'because existence is assumed to be possible'

[TheSuperKnarf]

I can't believe you left out the best part! Accompanying the proof is the statement that 'the above [i.e. 1+1=2] is occasionally useful'

[evanmccarthy]

I have a degree in Mathematics. When he showed that first snippet of the proof I questioned my whole existence before he pointed out half of it was just old fashioned theorem references.

[ThatRandomFerarriFan]

Friend: What's 1 + 1?
Me: 2
Friend: No, it's 11!
Me: *Pulls out Prinicipia Mathematica*

[johnchessant]

Can't believe you didn't mention the fact that right after this proof, the authors write "The above proposition is occasionally useful"

[TrimutiusToo]

As far as I know 360 pages is where they got the basics needed to prove 1+1=2. The full rigorous proof itself took more than 300 pages on top of that

[eweccah.k.]

In my second-year real analysis class, we used "1 + 1" as our definition of 2. "Define 1" and "Define +" were two of those "laugh politely and stop talking to you forever" questions.
It looks like the authors of this book maybe had "Define 1" and "Define 2" among their "laugh politely and stop talking to you forever" questions, and a very long-winded answer for "Define +".

[alpheusmadsen]

As a mathematician, I have *never* liked proofs that used symbols like this. Some symbols *greatly* simplify things, but there's a certain line between making things easier to work with, and getting a headache trying to remember the heiroglyphics. Projects like this crossed that line a *long* time ago!

[beccylikesmonkeys]

As someone currently studying maths and physics, I think this video does a pretty good job by showing how complicated mathematical proofs can be. I hated them for my entire first semester because proofing theorems is not something you can learn in a day. It is a long time learning process and I am hoping to improve over time.

[csolisr]

As the saying goes, "to make an apple pie, one must first create the universe" - the universe here being the basic tenets of mathematics that had to be rigorously, logically defined before even being able to parse the concept of addition

[_-.-_-.-_-.-_-.]

What the teacher expects you to do when they say "Show your solution"

[soundpreacher]

"If two things exist, then one of them exists, and the other one exists." This is the single thing that kept me from my PhD in Mathematics. It's called the Axiom of Choice, or as I called it, "Duh."

[anidiotsguide]

Ah, this brings me back to takeing a crash course in logic a few years back. Loved it, understood nothing :)

[isuckatbedwars]

teacher: why didnt you use my strategy?
her strategy:

[jugemujugemugokonosurikire]

I remember my math teacher (i was about 13-16 at the time) telling the class about writing an essay that 1+1=2. I never believed that people would go ridiculous extents for such a simple problem. I guess I was wrong.

[sirreginaldfishingtonxvii]

Taking 300+ pages to prove 1+1=2, with lines like "if two things exist, they each exist" just sounds like the greatest work of procrastination in human history.

And you know what? I respect it.

[Michael-Hammerschmidt]

In Bertrand Russell's biography he is described in his later years recounting a nightmare he once had:
"Russell was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down books, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia Mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated…."

[hubertlenningrad]

Dude, I read this super old book on discrete mathematics and then tried to use it in class to prove something and no one knew what I was talking about. Took a second to realize the symbols were antiquated.

[KingHarambe_RIP]

Maybe I’m biased given my math degree but the proof description here is much more satisfying than the “this is so simple lol” jokes. In math, we can prove so much with so little. Most people accept 1+1=2 as a concept without much question but for those who question it, it can be proven. Most other fields can’t prove their widely accepted core concepts like this and most who can are based in math.

[falnica]

Principia Mathematica was very useful, even if it relies on principles which cannot be proven (axioms). It is basically the foundation of modern mathematic. Then Gödel came along and showed it was fine if you relied on principles which couldn't be proven