Turing reasoned if there existed a program, whose halting behavior was not decidable by age, it would mean the halting problem is unsolvable.

推断，如果存在一个程序，其停机行为不能由年龄决定，则意味着停机问题无法解决。

And number three, is math decidable?

第三, 数学是可以决定吗?

But Turing's ideas about computability came from his concept of the Turing machine, which came from thinking about Hilbert's question, is math decidable?

但是关于可计算性来自于他机概念，而机概念又来自于对希尔伯特问题考：数学是可判定吗？