The Proof For '1+1=2′ Is 300 Pages Long

为了证明1+1=2，数学家用了300多页纸来计算

The equation 1+1=2 is probably the very first bit of math that most of us learned, because addition and subtraction are probably the simplest concepts in mathematics. If you have one apple and somebody gives you another, you have two apples. By the same logic, if you have two apples and someone takes one away, you only have one apple. It's a universal fact of life that transcends barriers like language or race. Which is what makes the following sentence so unbelievable: The proof for 1+1=2 is well over 300 pages long and it wasn't conclusively proven until the 20th century.

1+1=2这个等式或许是我们大多数人最先学到的数学知识，因为加法和减法也许是数学中最简单的概念。如果你有一个苹果，某人又给了你一个，那么你就有两个苹果。同样的逻辑，如果你有两个苹果，某人拿走了一个，那么你就剩一个苹果了。这是生活中普遍存在的一个事实。也许人们语言不通，种族不同，但他们都认同这一等式。正因为道理如此简单，才得使下面这句话令人难以置信：1+1=2的证明用了300多页纸，并且直到20世纪才被完全证实。四级考前答案

As Stephen Fry explains in this handy clip, in the early 20th century, Bertrand Russell wanted to conclusively prove that mathematics worked, so he decided to start with the simplest concept we know of and went right ahead and proved 1+1=2. However, what sounds like an incredibly simple task actually took the mathematician and philosopher 372 pages of complex sums. The mammoth solution was published as Principia Mathematica across three volumes, which we invite you to read if you aren't planning on doing anything for the next few weeks.

正如斯蒂芬?弗雷在这个有用的视频片段中所解释的那样，20世纪早期，伯特兰?罗素想要结论性地证明数学的原理，所以他决定从我们所知道的最简单的概念开始，然后再进一步深入，由此他证明了1+1=2。虽然这个任务听上去无比简单，却让这位数学家和哲学家用了372页纸来进行复杂的计算。这一繁杂的验证步骤发表在《数学原理》1上，贯穿全书全三卷的内容。如果接下来的几周你没有什么事情要做的话，我们推荐你去读一读这本书。

(责任编辑：田学江)