OK, let's recap the vocabulary from this programme, starting with equation – a mathematical statement using symbols to show two equal things.

好的，让我们回顾一下本期节目中的词汇，首先是" 方程" ——用符号表示两个相等事物的数学句式。

A mathematical statement is simply true or false.

数学陈述只是真或假。

However, unlike the ambiguous sentence that inspired him, mathematical statements must be true or false.

然而，与启发他的模棱两可的句子不同，数学陈述必须是真或假。

But if a mathematical statement has a proof, then it must be true.

但是如果一个数学陈述有一个证明，那么它一定是真的。

This meant that mathematical statements written with those numbers were also expressing something about the encoded statements of mathematics.

这意味着用这些数字编写的数学语句也表达了一些关于数学编码语句的内容。

First, he translated mathematical statements and equations into code numbers so that a complex mathematical idea could be expressed in a single number.

首先，他将数学陈述和方程式翻译成代码数字，这样复杂的数学思想就可以用一个数字来表达。

Through this method, he was able to write: " This statement cannot be proved" as an equation, creating the first self-referential mathematical statement.

通过这种方法，他能够将：“这个命题无法证明”写成一个方程式，创造了第一个自指代的数学命题。