Knowledge of unprovably true statements inspired key innovations in early computers.

无法证明真实陈述的知识激发了早期计算机的关键创新。

No matter how many axioms you add, there will always be unprovably true statements in your system.

无论你添加多少公理，你的系统中总会有无法证明的真实陈述。

But as more classical problems were proven to be unprovably true, some began to worry their life's work would be impossible to complete.

但随着越来越多的经典问题被证明是无法证明的真实性，一些人开始担心他们毕生的工作将无法完成。

Even if you account for these unprovable statements by adding them as new axioms to an enlarged mathematical system, that very process introduces new unprovably true statements.

即使你通过将这些无法证明的陈述作为新的公理添加到一个扩大的数学系统中来解释这些无法证明的陈述，这个过程也会引入新的无法证明的真实陈述。