Ah yes, those university days, a heady mix of Ph.D-level pure mathematics and world debating championships, or, as I like to say, "Hello, ladies. Oh yeah." Didn't get much sexier than the Spence at university, let me tell you.
是啊,大學時代 充斥著博士級的純數學理論 和世界級的辯論冠軍, 換一種說法就是:" 你好,女士們,太棒了。" 沒人能比得上大學校園里的斯賓塞 我跟你們說。
It is such a thrill for a humble breakfast radio announcer from Sydney, Australia, to be here on the TED stage literally on the other side of the world. And I wanted to let you know, a lot of the things you've heard about Australians are true. From the youngest of ages, we display a prodigious sporting talent. On the field of battle, we are brave and noble warriors. What you've heard is true. Australians, we don't mind a bit of a drink, sometimes to excess, leading to embarrassing social situations. (Laughter) This is my father's work Christmas party, December 1973. I'm almost five years old. Fair to say, I'm enjoying the day a lot more than Santa was.
對一個來自澳洲雪梨 渺小的早間電臺播報員而言 能在世界的另一端 這個 TED 的講台上 讓我非常激動。 我想告訴大家 你們聽過的那些關於澳洲人的傳言 很多都是真的。 從很小的時候 我們就表現出 驚人的體育天分。 戰場上,我們是勇敢高貴的戰士。 你們聽說的那些是真的。 我們澳洲人,喝一杯並不算甚麼, 有時候喝過頭了 引發某些難堪的場面(笑聲) 這是在 1973 年 12 月,我父親的聖誕員工晚會上。 那時我將近五歲了。 說句公道話, 我的那一天過得比聖誕老人還快活。
But I stand before you today not as a breakfast radio host, not as a comedian, but as someone who was, is, and always will be a mathematician. And anyone who's been bitten by the numbers bug knows that it bites early and it bites deep.
可是我今天站在大家面前 不是來主持早間廣播的, 不是來表演喜劇的 我的角色過去式是,現在是, 也一直都會是一名數學家。 任何和數字打交道的人 都知道數字能在童年對人產生很深的影響。
I cast my mind back when I was in second grade at a beautiful little government-run school called Boronia Park in the suburbs of Sydney, and as we came up towards lunchtime, our teacher, Ms. Russell, said to the class, "Hey, year two. What do you want to do after lunch? I've got no plans." It was an exercise in democratic schooling, and I am all for democratic schooling, but we were only seven. So some of the suggestions we made as to what we might want to do after lunch were a little bit impractical, and after a while, someone made a particularly silly suggestion and Ms. Russell patted them down with that gentle aphorism, "That wouldn't work. That'd be like trying to put a square peg through a round hole."
回想我二年級時 在一個美麗的公立學校就讀 它叫波羅尼亞公園學校 在雪梨郊區地段 接近午餐時間時 我們的老師 拉塞爾女士向整個班級說道: "嘿,二年級學生們。你們午飯後想幹什麼? 我還沒有計劃。" 這是民主教育的一次實踐, 我完全支持 不過我們當時只有七歲。 所以我們提出的一些完後活動的想法 有點不切實際, 沒過多久 有人提出了個特別愚蠢的想法 而拉塞爾女士用她特有的方式 輕拍示意他們坐下,評價道 "那行不通的。 那就像試圖把一個方釘放入一個圓孔內。"
Now I wasn't trying to be smart. I wasn't trying to be funny. I just politely raised my hand, and when Ms. Russell acknowledged me, I said, in front of my year two classmates, and I quote, "But Miss, surely if the diagonal of the square is less than the diameter of the circle, well, the square peg will pass quite easily through the round hole." (Laughter) "It'd be like putting a piece of toast through a basketball hoop, wouldn't it?"
我不是想要顯示自己聰明。 也不想要搞笑。 我只是禮貌地舉起手, 當拉塞爾女士應聲我時, 當著所有二年級同學的面,我的原話是: "但小姐, 當然如果方形對角線 小於圓形直徑 那,方釘很容易就能穿過圓孔。" (笑聲) “就好像讓一片吐司通過籃球架,不是嗎?"
And there was that same awkward silence from most of my classmates, until sitting next to me, one of my friends, one of the cool kids in class, Steven, leaned across and punched me really hard in the head. (Laughter) Now what Steven was saying was, "Look, Adam, you are at a critical juncture in your life here, my friend. You can keep sitting here with us. Any more of that sort of talk, you've got to go and sit over there with them."
當時也是這樣一陣尷尬的沉默 大多數同學一聲不吭, 直到我的一個朋友,他坐我旁邊 史蒂文,班上那種很酷的小朋友 靠過來 在我腦袋上狠狠打了一拳。 (笑聲) 史蒂文說:"你瞧,亞當, 你現在身處人生的關鍵節點,我的朋友 你可以繼續和我們坐在一起。 你再那樣說一句,你就要過去 和他們一起坐。
I thought about it for a nanosecond. I took one look at the road map of life, and I ran off down the street marked "Geek" as fast as my chubby, asthmatic little legs would carry me.
在一納秒中,我思考了一下, 審視了一下我的人生軌跡, 拖著我胖嘟嘟又帶哮喘的小身板 立馬跑到了對面“書呆子”的行列。
I fell in love with mathematics from the earliest of ages. I explained it to all my friends. Maths is beautiful. It's natural. It's everywhere. Numbers are the musical notes with which the symphony of the universe is written. The great Descartes said something quite similar. The universe "is written in the mathematical language." And today, I want to show you one of those musical notes, a number so beautiful, so massive, I think it will blow your mind.
我在很小的時候就愛上了數學。 我向我所有的朋友解釋數學。 數學是美妙的。 它很自然,普遍存在。 數字就如同音樂音符 構成了宇宙的交響樂章。 偉大的笛卡爾說類似的話。 他說宇宙 “是由數學語言編寫的。” 今天,我想要向大家展示一種音符, 這個數字如此美妙、宏大, 會讓你心醉神迷。
Today we're going to talk about prime numbers. Most of you I'm sure remember that six is not prime because it's 2 x 3. Seven is prime because it's 1 x 7, but we can't break it down into any smaller chunks, or as we call them, factors. Now a few things you might like to know about prime numbers. One is not prime. The proof of that is a great party trick that admittedly only works at certain parties.
今天我們要談的質數。 我想在座的大多數一定記得六不是質數 因為它2 x 3等於6。 七是質數因為它是1 x 7等於7, 但我們不能把它分成其他部份了, 或者也就是所謂的因子。 有幾個關於質數的有趣信息。 1不是質數。 關於這一點的證明其實是個很棒的派對節目 當然只能在某一特定派對中適用。
(Laughter)
(笑聲)
Another thing about primes, there is no final biggest prime number. They keep going on forever. We know there are an infinite number of primes due to the brilliant mathematician Euclid. Over thousands of years ago, he proved that for us. But the third thing about prime numbers, mathematicians have always wondered, well at any given moment in time, what is the biggest prime that we know about?
另一個關於質數的問題, 是極限最大質數不存在。 質數會不斷無限增大。 我們知道有無窮多個素質數 多虧了傑出的數學家歐幾裡德。 在幾千年前,他就證明了這一點。 但有關質數的第三點是, 也數學家們一直在思考的, 時時刻刻都是, 我們知道的最大質數是什麼?
Today we're going to hunt for that massive prime. Don't freak out. All you need to know, of all the mathematics you've ever learned, unlearned, crammed, forgotten, never understood in the first place, all you need to know is this: When I say 2 ^ 5, I'm talking about five little number twos next to each other all multiplied together, 2 x 2 x 2 x 2 x 2. So 2 ^ 5 is 2 x 2 = 4, 8, 16, 32. If you've got that, you're with me for the entire journey. Okay? So 2 ^ 5, those five little twos multiplied together. (2 ^ 5) - 1 = 31. 31 is a prime number, and that five in the power is also a prime number. And the vast bulk of massive primes we've ever found are of that form: two to a prime number, take away one. I won't go into great detail as to why, because most of your eyes will bleed out of your head if I do, but suffice to say, a number of that form is fairly easy to test for primacy. A random odd number is a lot harder to test. But as soon as we go hunting for massive primes, we realize it's not enough just to put in any prime number in the power. (2 ^ 11) - 1 = 2,047, and you don't need me to tell you that's 23 x 89. (Laughter) But (2 ^ 13) - 1, (2 ^ 17) - 1 (2 ^ 19) - 1, are all prime numbers. After that point, they thin out a lot.
今天我們要尋找那龐大的質數。 不要驚慌。 你所需要知道的, 那些你學過的、 沒學會的、 死記硬背的,遺忘了的, 在一開始就沒明白過的數學知識, 你只需知道一點: 當我說2的5次方時, 我說的是5個2緊密排列 所有相乘, 2 x 2 x 2 x 2 x 2 所以2的五次方是 2 x 2 = 4 8、 16、 32 如果你明白這一點 那接下來的你都能聽得懂。好嗎? 所以 2的5次方 5個2相乘 (2 ^5)-1 = 31 31 是一個質數量, 而5次方 也是一個質數。 我們所發現的那些龐大的質數 都是同樣形式的: 2 的質數次方,再減去1 我不會解釋其中緣由, 否則大家腦袋都得想壞了, 但我只想說,這種形式的數字 要想證明其領先性並不難。 一個隨機的奇數反倒更難驗證。 但是,只要我們去搜尋龐大的質數, 我們會意識到 僅僅把質數放在次方上是不夠的。 (2 ^11)-1 = 2,047 不用我告訴你 23 x 89等於2047。 (笑聲) 但是 (2 ^13)-1,(2 ^17)-1 (2 ^19)-1,都是質數 在這個臨界點後, 質數越來越少。
And one of the things about the search for massive primes that I love so much is some of the great mathematical minds of all time have gone on this search. This is the great Swiss mathematician Leonhard Euler. In the 1700s, other mathematicians said he is simply the master of us all. He was so respected, they put him on European currency back when that was a compliment.
我喜歡去搜尋龐大質數的原因之一 是許多偉大的數學天才 花費其畢生精力在此之上。 這是偉大的瑞士數學家歐拉萊昂歐拉。 18 世紀時,其他數學家們認為 他的智慧高於所有人。 他如此受尊重, 人們把他的頭像印在歐洲貨幣上 那時這可算是一種讚譽。
(Laughter)
(笑聲)
Euler discovered at the time the world's biggest prime: (2 ^ 31) - 1. It's over two billion. He proved it was prime with nothing more than a quill, ink, paper and his mind.
歐拉當時發現了世界上最大的質數: (2 ^31)-1 數值大於20億。 他證明了它是世界上最大的質數 沒有比其更大的了。
You think that's big. We know that (2 ^ 127) - 1 is a prime number. It's an absolute brute. Look at it here: 39 digits long, proven to be prime in 1876 by a mathematician called Lucas. Word up, L-Dog.
你以為那算大麼。 我們知道,(2 ^127)-1 是一個質數。 那是絕對的當頭一擊。 看看這裡: 39 位數位長, 1876 年時有偉大的數學家盧卡斯 驗證為質數。 完全同意,盧兄
(Laughter)
(笑聲)
But one of the great things about the search for massive primes, it's not just finding the primes. Sometimes proving another number not to be prime is just as exciting. Lucas again, in 1876, showed us (2 ^ 67) - 1, 21 digits long, was not prime. But he didn't know what the factors were. We knew it was like six, but we didn't know what are the 2 x 3 that multiply together to give us that massive number.
但尋找龐大質數的偉大之處在於, 它不僅是為了尋找, 有時候證明一個質數並非最大確實激動人心。 盧卡斯在 1876 年 又向我們展示了 (2 ^67)-1 21 位數位長,不是質數。 但他不知道其中因子有哪些。 我們知道這就好像是6一樣 但我們不知道 是哪些2和3相乘 得出了這個龐大的數字。
We didn't know for almost 40 years until Frank Nelson Cole came along. And at a gathering of prestigious American mathematicians, he walked to the board, took up a piece of chalk, and started writing out the powers of two: two, four, eight, 16 -- come on, join in with me, you know how it goes -- 32, 64, 128, 256, 512, 1,024, 2,048. I'm in geek heaven. We'll stop it there for a second. Frank Nelson Cole did not stop there. He went on and on and calculated 67 powers of two. He took away one and wrote that number on the board. A frisson of excitement went around the room. It got even more exciting when he then wrote down these two large prime numbers in your standard multiplication format -- and for the rest of the hour of his talk Frank Nelson Cole busted that out. He had found the prime factors of (2 ^ 67) - 1. The room went berserk -- (Laughter) -- as Frank Nelson Cole sat down, having delivered the only talk in the history of mathematics with no words. He admitted afterwards it wasn't that hard to do. It took focus. It took dedication. It took him, by his estimate, "three years of Sundays."
將近 40 年我們都不知道 直到弗蘭克 · 納爾遜 · 科爾的出現。 在一次美國著名數學家的集會上 他走到黑板前,拿起一隻粉筆, 開始書寫2的次方: 2、 4、 8、 16 — — 來吧,和我一起來,你知道怎麼接下去 — — 32、 64、 128、 256 512、 1,024、 2,048 我這是在書呆子天堂。 我們先停一小會兒。 弗蘭克 · 納爾遜 · 科爾並未就此停止。 他不斷地繼續 計算出了2的67次方 他去掉了一位並在黑板上書寫了這個數字 房間內瞬時充滿了興奮的騷動。 當他以標準格式寫下這個兩個龐大的質數時 房間內的人們更為興奮 而在接下來的演講中 弗蘭克 · 納爾遜 · 科爾徹底地突破了。 他找到了那個質數因子 (2 ^67)-1 房間裡變得狂暴起來 — — (笑聲)- 當弗蘭克 · 納爾遜 · 科爾坐下, 發表了數學史上 唯一一次無聲的演講。 他後來承認其實並不難。 只需要集中精神,不斷付出。 他估計,這花了他, "三年的星期天那麼長"。
But then in the field of mathematics, as in so many of the fields that we've heard from in this TED, the age of the computer goes along and things explode. These are the largest prime numbers we knew decade by decade, each one dwarfing the one before as computers took over and our power to calculate just grew and grew.
但然後在數學界, 以及TED涵蓋的各個領域, 電腦技術普及,信息爆炸。 這些事幾十年來我們所發現的最大質數 每一個都把前任比的體無完膚 這得益於電腦科技的發展 我們的計算能力不斷增強。
This is the largest prime number we knew in 1996, a very emotional year for me. It was the year I left university. I was torn between mathematics and media. It was a tough decision. I loved university. My arts degree was the best nine and a half years of my life.
這是1996 年時我們所知的最大質數, 那對我而言是情緒波動的一年。 那是我離開大學的一年。 我面對著數學與媒體兩種選擇。 它是個艱難的決定。 我愛大學生活。 我取得文學學位的求學路 是我人生中最好的九年半
(Laughter)
(笑聲)
But I came to a realization about my own ability. Put simply, in a room full of randomly selected people, I'm a maths genius. In a roomful of maths Ph.Ds, I'm as dumb as a box of hammers. My skill is not in the mathematics. It is in telling the story of the mathematics.
但我對我自己的能力有了新的認識。 簡而言之,在一屋子的隨機挑選的人中, 我算是一個數學天才。 在滿屋子的數學博士裡, 我笨得想一盒子錘子。 我的技能並不在於數學。 而是講述數學的故事上。
And during that time, since I've left university, these numbers have got bigger and bigger, each one dwarfing the last, until along came this man, Dr. Curtis Cooper, who a few years ago held the record for the largest ever prime, only to see it snatched away by a rival university. And then Curtis Cooper got it back. Not years ago, not months ago, days ago. In an amazing moment of serendipity, I had to send TED a new slide to show you what this guy had done.
那段時間,自從我離開了大學後, 這些數位變得越來越大。 一個超過一個, 直到這個人出現,柯帝士 · 庫珀博士, 他幾年其保持了史上最大質數的紀錄, 後來卻被一個對手大學搶走了。 然後柯帝士 · 庫珀又搶回了紀錄。 不是幾年前,不是幾個月前 而是幾天天前 我突發靈感, 必須給TED發一張幻燈片 向大家展示這個傢伙的成就。
I still remember -- (Applause) -- I still remember when it happened. I was doing my breakfast radio show. I looked down on Twitter. There was a tweet: "Adam, have you seen the new largest prime number?" I shivered -- (Laughter) -- contacted the women who produced my radio show out in the other room, and said "Girls, hold the front page. We're not talking politics today. We're not talking sport today. They found another megaprime." The girls just shook their heads, put them in their hands, and let me go my own way.
我還記得 — — (掌聲)- 我還記得當時的場景。 我正在做早間廣播節目。 我低頭看了眼 Twitter 有一個推特資訊 "亞當,你見過最新的最大質數?" 我顫抖起來 — — (笑聲)- 聯繫了在隔壁房間的 我的廣播節製作人 說道"姑娘們,留白頭條專欄。 我們今天不討論政治。 我們今天不討論體育。 他們發現另一個超級質數。” 那些姑娘們只是搖頭, 用手捂著頭 任由我行事
It's because of Curtis Cooper that we know, currently the largest prime number we know, is 2 ^ 57,885,161. Don't forget to subtract the one. This number is almost 17 and a half million digits long. If you typed it out on a computer and saved it as a text file, that's 22 meg. For the slightly less geeky of you, think about the Harry Potter novels, okay? This is the first Harry Potter novel. This is all seven Harry Potter novels, because she did tend to faff on a bit near the end. (Laughter) Written out as a book, this number would run the length of the Harry Potter novels and half again. Here's a slide of the first 1,000 digits of this prime. If, when TED had begun, at 11 o'clock on Tuesday, we'd walked out and simply hit one slide every second, it would have taken five hours to show you that number. I was keen to do it, could not convince Bono. That's the way it goes.
正是歸功於柯帝士 · 庫珀, 我們知道了先今最大的質數, 是 2 ^57等於 885,161 別忘了要減去1。 這一數位是將近 17,500,000位數長。 如果你把它輸入電腦存檔, 文檔有 22 梅格大。 對於在座比較不那麼書呆子的各位, 試想一下哈利 · 波特小說好嗎? 這是哈利 · 波特系列的第一部。 這是所有七部哈利 · 波特系列, 因為作者寫到最後是有點冗長了。 (笑聲) 把所有數位寫成一本書 它將有哈利 · 波特系列的1.5倍長 這是這個質數前1000位的幻燈展示 如果TED 大會開始於星期二上午11, 我們每秒切換一張幻燈片, 要5個小時才能完成所有數位顯示。 我是很想這麼做 但波諾不同意 這也是沒法子的事。
This number is 17 and a half thousand slides long, and we know it is prime as confidently as we know the number seven is prime. That fills me with almost sexual excitement. And who am I kidding when I say almost?
這個數字有17,000張幻燈長度, 我們堅信那是一個質數 就好比我們確信7是質數一樣。 這讓我幾乎有點性興奮了。 說“幾乎”這是要糊弄誰呢?
(Laughter)
(笑聲)
I know what you're thinking: Adam, we're happy that you're happy, but why should we care? Let me give you just three reasons why this is so beautiful.
我知道你們在想什麼: 亞當,我們很高興能看到你快樂 但我們為什麼要在乎? 讓我給你列舉三個理由說明其每秒之處。
First of all, as I explained, to ask a computer "Is that number prime?" to type it in its abbreviated form, and then only about six lines of code is the test for primacy, is a remarkably simple question to ask. It's got a remarkably clear yes/no answer, and just requires phenomenal grunt. Large prime numbers are a great way of testing the speed and accuracy of computer chips.
首先,正如之前解釋的,要問一台電腦 ”那個數字是質數嗎?",鍵入其縮寫形式 然後僅約六行代碼是用來測試領先性的, 這是一個十分簡單的問題。 答案很簡單,是或者不是, 只需大聲說出來就行。 大的質數是很好的 測試電腦晶片速度和準確度的方法。
But secondly, as Curtis Cooper was looking for that monster prime, he wasn't the only guy searching. My laptop at home was looking through four potential candidate primes myself as part of a networked computer hunt around the world for these large numbers. The discovery of that prime is similar to the work people are doing in unraveling RNA sequences, in searching through data from SETI and other astronomical projects. We live in an age where some of the great breakthroughs are not going to happen in the labs or the halls of academia but on laptops, desktops, in the palms of people's hands who are simply helping out for the search.
但第二,如柯帝士 · 庫珀 一直在尋找的那個終極質數一樣, 他不是唯一一個在搜尋的人。 我家裡的筆記本電腦自己也在搜尋 四個潛在的候選質數 全世界各地都有愛好人士 通過電腦有組織地進行搜尋。 發現這個質數類似於 人們解析RNA圖譜 從外太空文明搜尋計畫 和其他天文項目中搜尋數據 我們生活的時代,那些偉大的發現 並不在實驗室或是學院大廳裡發生 但在筆記本上、 在台式機上, 在人們的掌心上 只是幫忙搜尋而已。
But for me it's amazing because it's a metaphor for the time in which we live, when human minds and machines can conquer together. We've heard a lot about robots in this TED. We've heard a lot about what they can and can't do. It is true, you can now download onto your smartphone an app that would beat most grandmasters at chess.
但對我而言這棒極了, 因為這是對我們生活時代的比喻, 當人腦和機器可以合作征服世界。 我們在TED聽到過很多關於機器人的演講。 我們聽說了很多可以什麼和不能做什麼。 真的,你現在可以下載一款應用到你的手機 可以打敗大多數的象棋大師。
You think that's cool. Here's a machine doing something cool. This is the CubeStormer II. It can take a randomly shuffled Rubik's Cube. Using the power of the smartphone, it can examine the cube and solve the cube in five seconds.
你覺得這很酷。 這裡有一個很酷的機器。 它叫魔方暴風者二代。 它可以將打亂的魔方規整。 僅憑智能手機的力量, 它可以檢查魔方並規整 只需5秒鐘的時間。
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That scares some people. That excites me. How lucky are we to live in this age when mind and machine can work together?
這樣會嚇到一些人 但這使我興奮 我們生活在這個時代是有多么幸運 人腦和機器可以一起合作
I was asked in an interview last year in my capacity as a lower-case "c" celebrity in Australia, "What was your highlight of 2012?" People were expecting me to talk about my beloved Sydney Swans football team. In our beautiful, indigenous sport of Australian football, they won the equivalent of the Super Bowl. I was there. It was the most emotional, exciting day. It wasn't my highlight of 2012. People thought it might have been an interview I'd done on my show. It might have been a politician. It might have been a breakthrough. It might have been a book I read, the arts. No, no, no. It might have been something my two gorgeous daughters had done. No, it wasn't. The highlight of 2012, so clearly, was the discovery of the Higgs boson. Give it up for the fundamental particle that bequeaths all other fundamental particles their mass.
我在去年在澳洲的 一次採訪中以小名人的身份 接受了一次訪問 "你的2012年的亮點什麼?" 人們都以為我要談一談 我心愛的雪梨天鵝橄欖球隊 在我們美麗、 本土的澳式足球聯賽裡, 他們贏得了冠軍,意義相當於超級盃。 我也在場 它是最情緒化的、 令人興奮的一天 但這不是我2012年的亮點。 人們認為可能是我在節目裡做了某次採訪。 可能是某位政客 或是某一項突破 可能是我讀的一本書 不,不,不 可能是我那兩個可愛的女兒做了什麽事。 不,不是 我2012 年的亮點,很明顯 是希格斯玻色子的發現。 為這一造就了所有基本粒子的 希格斯玻色子鼓掌吧。
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And what was so gorgeous about this discovery was 50 years ago Peter Higgs and his team considered one of the deepest of all questions: How is it that the things that make us up have no mass? I've clearly got mass. Where does it come from? And he postulated a suggestion that there's this infinite, incredibly small field stretching throughout the universe, and as other particles go through those particles and interact, that's where they get their mass. The rest of the scientific community said, "Great idea, Higgsy. We've got no idea if we could ever prove it. It's beyond our reach." And within just 50 years, in his lifetime, with him sitting in the audience, we had designed the greatest machine ever to prove this incredible idea that originated just in a human mind.
這一項發現的美妙之處在於 50 年前彼得 · 希格斯和他的團隊 思考了最深奧的問題之一? 爲什麽造就我們的元素沒有質量呢? 我顯然是有質量的 那這是從哪裡來的呢? 他提出了一個假想 有這樣一個無限,非常小的欄位 貫穿整個宇宙 當其他粒子穿過它們時 與之交互,也就形成了質量 科學界的其他人認為, "好主意,Higgsy“ 我們完全不知道怎麼去證明它。 它在我們的能力範圍之外。” 而僅僅過了 50 年, 他的有生之年,他作為旁觀, 人們設計出了有史以來最大的機器 證明這個令人難以置信的想法 最初僅存在於人們的腦海中。
That's what is so exciting for me about this prime number. We thought it might be there, and we went and found it. That is the essence of being human. That is what we are all about. Or as my friend Descartes might put it, we think, therefore we are.
這就是我對於質數如此興奮的原因。 我們以為它可能存在, 於是我們去尋找並發現它。 這是作為人的本質。 這是我們存在的意義。 或像我的朋友笛卡爾所說的, 我思, 故我在。
Thank you.
謝謝。
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