It's like when I first encountered the Pythagorean Theorem.

就像我第一次接触勾股定理的感觉。

And it turns out there's a variety of proofs of the Pythagorean Theorem.

其实有很多种证明勾股定理的方法。

And we did that in kind of the intuition behind the binomial theorem videos.

我们是在利用二项式定理的方法来解决问题。

It's actually quite useful to have case studies or stories, which are these famous theorems.

事实上，学习著名定理的案例和故事是相当有用的。

His conclusions were as infallible as so many propositions of Euclid.

所作出的结论真和欧几里得的定理一样的准确。

A Babylonian tablet from around 1800 B.C. lists 15 sets of numbers that satisfy the theorem.

公元前 1800 年左右的一块巴比伦石碑列出了15组满足该定理的数字。

The shape of the earth? The heliocentric universe? The Pythagorean theorem? The structure of DNA?

放弃对地球形状的认识？对以太阳为中心的宇宙的认识？还是对勾股定理的认识？对DNA结构的认识？

Instead, they knew all these particular cases where the theorem held true.

相反，们知道所有这些定理成立的特殊情况。

He thought about the mentality that he felt there was there and crystallized it in this concept of Janteloven.

考了在那里所感觉到的在那里存在的维，并将其具体化在扬特定理的概念中。

Now they didn't have what we call the theorem.

那时们还没有我们所说的定理。

And that is a neat thing about the central limit theorem.

这就是中心极限定理的妙处。

And yet, somehow, he came up with these incredible theorems.

然而，不知何故，提出了那些令人难以置信的定理。

I am tired of people who treat this like math.

我烦透了那些将之视作刻板数学定理的人。

Because I want to show you the power of the central limit theorem.

因为我想向你展示中心极限定理的威力。

So this is what's super cool about the central limit theorem.

所以这就是中心极限定理的超级酷之处。

You might remember the Pythagorean theorem from school like what the formula is?

你可能还记得在学校学的勾股定理，比如公式是什么？

Start with basic counting and work your way up to the many types of infinity culminating in the profundity of Cantor's theorem.

从基本的计数开始，一直到许多类型的无穷大，最终达到康托尔定理的深奥程度。

If you, don't a positive integer the binomial theorem, Newton's binomial theorem will give you an infinite sum.

如果你不知道二项式定理中的正整数，牛顿二项式定理将给出一个无穷和。

Proofs use existing mathematical rules and logic to demonstrate that a theorem must hold true all the time.

利用现有的数学定理和逻辑，我们可以证明该定理总是成立。

So, the law of cosines is an extension of the pythagorean theorem to the arbitrary angles...

所以余弦定律是勾股定理对任意角度的延伸。