And this means mathematics is undecidable.

这意味着数学是不可判定的。

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

直到最近的 2015 年，数学家才证明隙问题一般是不可判定的。

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.

管功能强大， 但是每个图灵完备系统都存在缺陷，即其自身的停机问题类似物，以及系统的一些不可判定性质。