这一结果唯一合理的数学解释就是哈代悖论。

The only mathematically consistent explanation known for this result is therefore Hardy's.

youdao

如果用数学解释，给它一个数字，给它一个零。

That's going to presumably be given — mathematically if we gave it a number, we'd slap a zero on that.

youdao

但是这个例子这说明了，为什么得到的具体答案是数学解释而不是物理解释。

But the explanation is to why it comes up with that particular answer is a mathematical explanation not a physical one.

youdao

That's going to presumably be given--mathematically if we gave it a number, we'd slap a zero on that.

如果用数学解释,给它一个数字，给它一个零。

耶鲁公开课 - 死亡课程节选

It seems like a very compelling account of what's going on in mathematics.

似乎对于数学的解释,这是一种很有说服力的说法

耶鲁公开课 - 死亡课程节选

So, what we're dealing here with is a situation where the ancient Greeks were very much into mathematics as a way of explaining the world and explaining music in particular And they thought these ratios were primary.

那么,我们现在要潜心琢磨,古希腊人热衷于,用数学来解释世界,尤其是音乐的这种情形,他们认为这些比例才是基础

耶鲁公开课 - 聆听音乐课程节选