And this means mathematics is undecidable.

这意味着数学是定。

Only recently, in 2015, did mathematicians prove that in general the spectral gap question is undecidable.

直到最 2015 ，数学家才证明隙问题一般是定。

Although they are powerful, every Turing-complete system comes with a catch, its own analog of the halting problem, some undecidable property of the system.

尽管功能强大， 但是每个图灵完备系统都存在缺陷，即其自身停机问题类似物，以及系统一些定性质。