Today we're gonna talk about Fermat's Last Theorem.

今天我們來談談費馬最後定理

He had a hobby. A passion for math.

費馬對數學有極大的興趣與熱忱

So he would go back home and write his theorems and conjectures.

他會回家然後把他的定理跟推測寫下來

Fermat's notebook had lots of conjectures.

費馬的筆記本裡有非常多假設

He would write down saying,

他會寫下來然後想說

"Oh I know some proof of this, but I have no time to write it."

「噢我知道它們的證明，但我現在沒空寫」

Over the centuries, mathematicians went through this book and found proof to all his conjectures,

好多世紀以來，他的猜測都被數學家得證

apart from the last theorem.

除了最後一個

The last theorem was very interesting.

最後一個假設很有趣

Many people attempted the solution, and thought they found it, but then somebody proved them wrong.

許多人都嘗試解它，並認為自己找到了，然後被人推翻

Andrew Wiles discovered this theorem when he was 10 years old and became obsessed with it.

安德魯·懷爾斯在十歲時認識了這個定理且著迷於它

He worked in secret because so many people attempted and failed.

他偷偷地嘗試解開，因為有非常多人試過且失敗了

He found a solution and he presented to the public and he was acclaimed worldwide.

他找到了一個解，並且告知大眾，接受了全世界的表揚

The Queen knighted him and it was a great success

那是個無與倫比的成功，英國女王甚至將他封為騎士

until somebody actually found an error in his proof.

直到某天有人找到了一個錯誤

He was not gonna give up that easily and he worked for another year, full time,

他沒那麼容易放棄，於是又努力了一年

and he found a solution.

找到了解答

And it goes like this:

是這樣的：

If you have X to the n plus Y to the n equal Z to the n.

X 的 n 次方加上 Y 的 n 次方等於 Z 的 n 次方

If n is a positive integer greater than 2,

如果 n 是大於二的整數

this equation is never true.

那這個式子永遠不會成立

It looks very simple, but the mathematics proving that something doesn't exist,

看似簡單，但數學家若想證明某東西不存在

is always harder than proving that something exists.

比證明它存在難非常多

This is a variety of application in cryptography.

這是密碼學中的各種運用方式

Writing encryptions and codes and all of that, you know, secret stuff.

編寫密碼、代碼等等，那些秘密的東西

And it opened up a whole new world for mathematics, a whole new branch of mathematics.

它打開了數學家的另一個世界，讓他們認識了全新的數學領域