And this means mathematics is undecidable.

这意味着数学是不可判。

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

近 2015 年，数学家才证明隙问题一般是不可判。

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，以及系统一些不可判性质。