用已知的物理学无法证明大多数定理We Can’t Prove Most Theorems with Known Physics
布雷特：数学中绝大多数的定理，都是我们不可能证明的定理。这就是哥德尔定理，它也出自图灵的证明——关于什么可计算、什么不可计算的证明。
不可计算的事物，在数量上远远超过可计算的事物；而什么可计算，完全取决于我们在这个物理宇宙中能造出什么样的计算机。我们所能造出的计算机，必须遵守我们的物理定律。
如果物理定律有所不同，我们就能证明不同类型的数学。这也是数学家误解的又一部分：他们以为自己可以置身于物理定律之外。然而，他们的大脑不过是一台物理计算机，必须遵守物理定律。
如果他们生活在一个物理定律不同的宇宙里，就能证明不同的定理。但我们就存在于我们现在所处的这个宇宙中，所以受制于一大堆东西，其中尤以光速的有限性为甚。在抽象空间里，也许存在某些东西，如果我们能跳出物理定律的限制，就能对它们有更充分的理解。
幸运的是，目前我们无法证明的那些定理，没有一条本质上是有趣的。有些东西本质上就是枯燥乏味的——也就是所有这些我们既无法证明为真、也无法证明为假的定理。
这些定理在我们的物理宇宙中起不到任何作用，它们与我们的物理宇宙毫无关系，这正是我们说它们本质上索然无味的原因。而本质上索然无味的东西，其实非常多。
Brett: The overwhelming majority of theorems in mathematics are theorems that we cannot possibly prove. This is Gödel’s theorem, and it also comes out of Turing’s proof of what is and is not computable.
The things that are not computable vastly outnumber the things that are computable, and what is computable depends entirely upon what computers we can make in this physical universe. The computers that we can make must obey our laws of physics.
If the laws of physics were different, then we’d be able to prove different sorts of mathematics. This is another part of the mathematician’s misconception: They think they can get outside of the laws of physics. However, their brain is just a physical computer. Their brain must obey the laws of physics.
If they existed in a universe with different laws of physics, then they could prove different theorems. But we exist in the universe that we’re in, so we’re bound by a whole bunch of things, not least of which is the finite speed of light. There could be certain things out there in abstract space that we would be able to come to a fuller understanding of if we could get outside of the restrictions of the laws of physics.
Happily, none of those theorems that we cannot prove at the moment are inherently interesting. Some things can be inherently boring—namely, all of these theorems which we cannot possibly prove as true or false.
Those theorems can’t have any bearing in our physical universe. They have nothing to do with our physical universe, and this is why we say they’re inherently uninteresting. And there’s a lot of inherently uninteresting things.