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

就像我第一次接触勾股定理感觉。

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，学习著名定理案例和故事是相当有用。

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

他所作出结论真和欧几里得定理一样准确。

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

公元前 1800 年左右一块巴比伦石碑列出了15组满足该定理数字。

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

放弃对地球形状认识？对以太阳为中心宇宙认识？还是对勾股定理认识？对DNA结构认识？

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

相反，他们知道所有这些定理成立情况。

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

他思考了他在那里所感觉到在那里存在思维，并将其具体化在扬定理概念中。

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

那时他们还没有我们所说定理。

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

这就是中心极限定理妙处。

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

然而，不知何故，他提出了那些令人难以置信定理。

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.

从基本计数开始，一直到许多类型无穷大，最终达到康托尔定理深奥程度。

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

利用现有数学定理和逻辑，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延伸。

From there, its authors derived more and more complex theorems that corresponded with work being done across the field.

从那里，它作者推导出了越来越复杂定理，这些定理与整个领域所做工作相对应。