Placeholder Image

字幕列表 影片播放

  • Ah yes, those university days,

    是啊,大學時代

  • a heady mix of Ph.D-level pure mathematics

    充斥著博士級的純數學理論

  • and world debating championships,

    和世界級的辯論冠軍,

  • or, as I like to say, "Hello, ladies. Oh yeah."

    換一種說法就是:" 你好,女士們,太棒了。"

  • Didn't get much sexier than the Spence

    沒人能比得上大學校園里的斯賓塞

  • at university, let me tell you.

    我跟你們說。

  • It is such a thrill for a humble breakfast radio announcer

    對一個來自澳洲雪梨 渺小的早間電臺播報員而言

  • from Sydney, Australia, to be here on the TED stage

    能在世界的另一端 這個 TED 的講台上

  • literally on the other side of the world.

    讓我非常激動。

  • And I wanted to let you know, a lot of the things you've heard

    我想告訴大家 你們聽過的那些關於澳洲人的傳言

  • about Australians are true.

    很多都是真的。

  • From the youngest of ages, we display

    從很小的時候 我們就表現出

  • a prodigious sporting talent.

    驚人的體育天分。

  • On the field of battle, we are brave and noble warriors.

    戰場上,我們是勇敢高貴的戰士。

  • What you've heard is true.

    你們聽說的那些是真的。

  • Australians, we don't mind a bit of a drink,

    我們澳洲人,喝一杯並不算甚麼,

  • sometimes to excess, leading to embarrassing social situations. (Laughter)

    有時候喝過頭了 引發某些難堪的場面(笑聲)

  • This is my father's work Christmas party, December 1973.

    這是在 1973 年 12 月,我父親的聖誕員工晚會上。

  • I'm almost five years old. Fair to say,

    那時我將近五歲了。 說句公道話,

  • I'm enjoying the day a lot more than Santa was.

    我的那一天過得比聖誕老人還快活。

  • But I stand before you today

    可是我今天站在大家面前

  • not as a breakfast radio host,

    不是來主持早間廣播的,

  • not as a comedian, but as someone who was, is,

    不是來表演喜劇的 我的角色過去式是,現在是,

  • and always will be a mathematician.

    也一直都會是一名數學家。

  • And anyone who's been bitten by the numbers bug

    任何和數字打交道的人

  • knows that it bites early and it bites deep.

    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

    回想我二年級時

  • at a beautiful little government-run school

    在一個美麗的公立學校就讀

  • called Boronia Park in the suburbs of Sydney,

    它叫波羅尼亞公園學校 在雪梨郊區地段

  • and as we came up towards lunchtime, our teacher,

    接近午餐時間時 我們的老師

  • Ms. Russell, said to the class,

    拉塞爾女士向整個班級說道:

  • "Hey, year two. What do you want to do after lunch?

    "嘿,二年級學生們。你們午飯後想幹什麼?

  • I've got no plans."

    我還沒有計劃。"

  • It was an exercise in democratic schooling,

    這是民主教育的一次實踐,

  • and I am all for democratic schooling, but we were only seven.

    我完全支持 不過我們當時只有七歲。

  • So some of the suggestions we made as to what

    所以我們提出的一些完後活動的想法

  • we might want to do after lunch were a little bit impractical,

    有點不切實際,

  • and after a while, someone made a particularly silly suggestion

    沒過多久 有人提出了個特別愚蠢的想法

  • and Ms. Russell patted them down with that gentle aphorism,

    而拉塞爾女士用她特有的方式 輕拍示意他們坐下,評價道

  • "That wouldn't work.

    "那行不通的。

  • That'd be like trying to put a square peg through a round hole."

    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.

    我不是想要顯示自己聰明。

  • I wasn't trying to be funny.

    也不想要搞笑。

  • I just politely raised my hand,

    我只是禮貌地舉起手,

  • and when Ms. Russell acknowledged me, I said,

    當拉塞爾女士應聲我時,

  • in front of my year two classmates, and I quote,

    當著所有二年級同學的面,我的原話是:

  • "But Miss,

    "但小姐,

  • surely if the diagonal of the square

    當然如果方形對角線

  • is less than the diameter of the circle,

    小於圓形直徑

  • well, the square peg will pass quite easily through the round hole."

    那,方釘很容易就能穿過圓孔。"

  • (Laughter)

    (笑聲)

  • "It'd be like putting a piece of toast through a basketball hoop, wouldn't it?"

    “就好像讓一片吐司通過籃球架,不是嗎?"

  • And there was that same awkward silence

    當時也是這樣一陣尷尬的沉默

  • from most of my classmates,

    大多數同學一聲不吭,

  • until sitting next to me, one of my friends,

    直到我的一個朋友,他坐我旁邊

  • one of the cool kids in class, Steven, leaned across

    史蒂文,班上那種很酷的小朋友 靠過來

  • and punched me really hard in the head.

    在我腦袋上狠狠打了一拳。

  • (Laughter)

    (笑聲)

  • Now what Steven was saying was, "Look, Adam,

    史蒂文說:"你瞧,亞當,

  • you are at a critical juncture in your life here, my friend.

    你現在身處人生的關鍵節點,我的朋友

  • You can keep sitting here with us.

    你可以繼續和我們坐在一起。

  • Any more of that sort of talk, you've got to go and sit

    你再那樣說一句,你就要過去

  • over there with them."

    和他們一起坐。

  • I thought about it for a nanosecond.

    在一納秒中,我思考了一下,

  • I took one look at the road map of life,

    審視了一下我的人生軌跡,

  • and I ran off down the street marked "Geek"

    拖著我胖嘟嘟又帶哮喘的小身板

  • as fast as my chubby, asthmatic little legs would carry me.

    立馬跑到了對面“書呆子”的行列。

  • I fell in love with mathematics from the earliest of ages.

    我在很小的時候就愛上了數學。

  • I explained it to all my friends. Maths is beautiful.

    我向我所有的朋友解釋數學。 數學是美妙的。

  • It's natural. It's everywhere.

    它很自然,普遍存在。

  • Numbers are the musical notes

    數字就如同音樂音符

  • with which the symphony of the universe is written.

    構成了宇宙的交響樂章。

  • The great Descartes said something quite similar.

    偉大的笛卡爾說類似的話。

  • The universe "is written in the mathematical language."

    他說宇宙 “是由數學語言編寫的。”

  • And today, I want to show you one of those musical notes,

    今天,我想要向大家展示一種音符,

  • a number so beautiful, so massive,

    這個數字如此美妙、宏大,

  • I think it will blow your mind.

    會讓你心醉神迷。

  • Today we're going to talk about prime numbers.

    今天我們要談的質數。

  • Most of you I'm sure remember that six is not prime

    我想在座的大多數一定記得六不是質數

  • because it's 2 x 3.

    因為它2 x 3等於6。

  • Seven is prime because it's 1 x 7,

    七是質數因為它是1 x 7等於7,

  • but we can't break it down into any smaller chunks,

    但我們不能把它分成其他部份了,

  • or as we call them, factors.

    或者也就是所謂的因子。

  • Now a few things you might like to know about prime numbers.

    有幾個關於質數的有趣信息。

  • One is not prime.

    1不是質數。

  • The proof of that is a great party trick

    關於這一點的證明其實是個很棒的派對節目

  • that admittedly only works at certain parties.

    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.

    另一個關於質數的問題, 是極限最大質數不存在。

  • They keep going on forever.

    質數會不斷無限增大。

  • We know there are an infinite number of primes

    我們知道有無窮多個素質數

  • due to the brilliant mathematician Euclid.

    多虧了傑出的數學家歐幾裡德。

  • Over thousands of years ago, he proved that for us.

    在幾千年前,他就證明了這一點。

  • But the third thing about prime numbers,

    但有關質數的第三點是,

  • mathematicians have always wondered,

    也數學家們一直在思考的,

  • well at any given moment in time,

    時時刻刻都是,

  • what is the biggest prime that we know about?

    我們知道的最大質數是什麼?

  • Today we're going to hunt for that massive prime.

    今天我們要尋找那龐大的質數。

  • Don't freak out.

    不要驚慌。

  • All you need to know, of all the mathematics

    你所需要知道的,

  • you've ever learned, unlearned, crammed, forgotten,

    那些你學過的、 沒學會的、 死記硬背的,遺忘了的,

  • never understood in the first place,

    在一開始就沒明白過的數學知識,

  • all you need to know is this:

    你只需知道一點:

  • When I say 2 ^ 5,

    當我說2的5次方時,

  • I'm talking about five little number twos next to each other

    我說的是5個2緊密排列

  • all multiplied together,

    所有相乘,

  • 2 x 2 x 2 x 2 x 2.

    2 x 2 x 2 x 2 x 2

  • So 2 ^ 5 is 2 x 2 = 4,

    所以2的五次方是 2 x 2 = 4

  • 8, 16, 32.

    8、 16、 32

  • If you've got that, you're with me for the entire journey. Okay?

    如果你明白這一點 那接下來的你都能聽得懂。好嗎?

  • So 2 ^ 5,

    所以 2的5次方

  • those five little twos multiplied together.

    5個2相乘

  • (2 ^ 5) - 1 = 31.

    (2 ^5)-1 = 31

  • 31 is a prime number, and that five in the power

    31 是一個質數量, 而5次方

  • is also a prime number.

    也是一個質數。

  • And the vast bulk of massive primes we've ever found

    我們所發現的那些龐大的質數

  • are of that form:

    都是同樣形式的:

  • two to a prime number, take away one.

    2 的質數次方,再減去1

  • I won't go into great detail as to why,

    我不會解釋其中緣由,

  • because most of your eyes will bleed out of your head if I do,

    否則大家腦袋都得想壞了,

  • but suffice to say, a number of that form

    但我只想說,這種形式的數字

  • is fairly easy to test for primacy.

    要想證明其領先性並不難。

  • A random odd number is a lot harder to test.

    一個隨機的奇數反倒更難驗證。

  • But as soon as we go hunting for massive primes,

    但是,只要我們去搜尋龐大的質數,

  • we realize it's not enough

    我們會意識到

  • just to put in any prime number in the power.

    僅僅把質數放在次方上是不夠的。

  • (2 ^ 11) - 1 = 2,047,

    (2 ^11)-1 = 2,047

  • and you don't need me to tell you that's 23 x 89.

    不用我告訴你 23 x 89等於2047。

  • (Laughter)

    (笑聲)

  • But (2 ^ 13) - 1, (2 ^ 17) - 1

    但是 (2 ^13)-1,(2 ^17)-1

  • (2 ^ 19) - 1, are all prime numbers.

    (2 ^19)-1,都是質數

  • After that point, they thin out a lot.

    在這個臨界點後, 質數越來越少。

  • And one of the things about the search for massive primes

    我喜歡去搜尋龐大質數的原因之一

  • that I love so much is some of the great mathematical minds

    是許多偉大的數學天才

  • of all time have gone on this search.

    花費其畢生精力在此之上。

  • This is the great Swiss mathematician Leonhard Euler.

    這是偉大的瑞士數學家歐拉萊昂歐拉。

  • In the 1700s, other mathematicians said

    18 世紀時,其他數學家們認為

  • he is simply the master of us all.

    他的智慧高於所有人。

  • He was so respected, they put him on European currency

    他如此受尊重, 人們把他的頭像印在歐洲貨幣上

  • back when that was a compliment.

    那時這可算是一種讚譽。

  • (Laughter)

    (笑聲)

  • Euler discovered at the time the world's biggest prime:

    歐拉當時發現了世界上最大的質數:

  • (2 ^ 31) - 1.

    (2 ^31)-1

  • It's over two billion.

    數值大於20億。

  • He proved it was prime with nothing more

    他證明了它是世界上最大的質數

  • than a quill, ink, paper and his mind.

    沒有比其更大的了。

  • You think that's big.

    你以為那算大麼。

  • We know that (2 ^ 127) - 1

    我們知道,(2 ^127)-1

  • is a prime number.

    是一個質數。

  • It's an absolute brute.

    那是絕對的當頭一擊。

  • Look at it here: 39 digits long,

    看看這裡: 39 位數位長,

  • proven to be prime in 1876

    1876 年時有偉大的數學家盧卡斯

  • by a mathematician called Lucas.

    驗證為質數。

  • Word up, L-Dog.

    完全同意,盧兄

  • (Laughter)

    (笑聲)

  • But one of the great things about the search for massive primes,

    但尋找龐大質數的偉大之處在於,

  • it's not just finding the primes.

    它不僅是為了尋找,

  • Sometimes proving another number not to be prime is just as exciting.

    有時候證明一個質數並非最大確實激動人心。

  • Lucas again, in 1876, showed us (2 ^ 67) - 1,

    盧卡斯在 1876 年 又向我們展示了 (2 ^67)-1

  • 21 digits long, was not prime.

    21 位數位長,不是質數。

  • But he didn't know what the factors were.

    但他不知道其中因子有哪些。

  • We knew it was like six, but we didn't know

    我們知道這就好像是6一樣 但我們不知道

  • what are the 2 x 3 that multiply together

    是哪些2和3相乘

  • to give us that massive number.

    得出了這個龐大的數字。

  • We didn't know for almost 40 years

    將近 40 年我們都不知道

  • until Frank Nelson Cole came along.

    直到弗蘭克 · 納爾遜 · 科爾的出現。

  • And at a gathering of prestigious American mathematicians,

    在一次美國著名數學家的集會上

  • he walked to the board, took up a piece of chalk,

    他走到黑板前,拿起一隻粉筆,

  • and started writing out the powers of two:

    開始書寫2的次方:

  • two, four, eight, 16 --

    2、 4、 8、 16 — —

  • come on, join in with me, you know how it goes --

    來吧,和我一起來,你知道怎麼接下去 — —

  • 32, 64, 128, 256,

    32、 64、 128、 256

  • 512, 1,024, 2,048.

    512、 1,024、 2,048

  • I'm in geek heaven. We'll stop it there for a second.

    我這是在書呆子天堂。 我們先停一小會兒。

  • Frank Nelson Cole did not stop there.

    弗蘭克 · 納爾遜 · 科爾並未就此停止。

  • He went on and on

    他不斷地繼續

  • and calculated 67 powers of two.

    計算出了2的67次方

  • He took away one and wrote that number on the board.

    他去掉了一位並在黑板上書寫了這個數字

  • A frisson of excitement went around the room.

    房間內瞬時充滿了興奮的騷動。

  • It got even more exciting when he then wrote down

    當他以標準格式寫下這個兩個龐大的質數時

  • these two large prime numbers in your standard multiplication format --

    房間內的人們更為興奮

  • and for the rest of the hour of his talk

    而在接下來的演講中

  • Frank Nelson Cole busted that out.

    弗蘭克 · 納爾遜 · 科爾徹底地突破了。

  • He had found the prime factors

    他找到了那個質數因子

  • of (2 ^ 67) - 1.

    (2 ^67)-1

  • The room went berserk --

    房間裡變得狂暴起來 — —

  • (Laughter) --

    (笑聲)-

  • as Frank Nelson Cole sat down,

    當弗蘭克 · 納爾遜 · 科爾坐下,

  • having delivered the only talk in the history of mathematics

    發表了數學史上

  • with no words.

    唯一一次無聲的演講。

  • He admitted afterwards it wasn't that hard to do.

    他後來承認其實並不難。

  • It took focus. It took dedication.

    只需要集中精神,不斷付出。

  • It took him, by his estimate,

    他估計,這花了他,

  • "three years of Sundays."

    "三年的星期天那麼長"。

  • But then in the field of mathematics,

    但然後在數學界,

  • as in so many of the fields that we've heard from in this TED,

    以及TED涵蓋的各個領域,

  • the age of the computer goes along and things explode.

    電腦技術普及,信息爆炸。

  • These are the largest prime numbers we knew

    這些事幾十年來我們所發現的最大質數

  • decade by decade, each one dwarfing the one before

    每一個都把前任比的體無完膚

  • as computers took over and our power to calculate

    這得益於電腦科技的發展

  • just grew and grew.

    我們的計算能力不斷增強。

  • This is the largest prime number we knew in 1996,

    這是1996 年時我們所知的最大質數,

  • a very emotional year for me.

    那對我而言是情緒波動的一年。

  • It was the year I left university.

    那是我離開大學的一年。

  • I was torn between mathematics and media.

    我面對著數學與媒體兩種選擇。

  • It was a tough decision. I loved university.

    它是個艱難的決定。 我愛大學生活。

  • My arts degree was the best nine and a half years of my life.

    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.

    但我對我自己的能力有了新的認識。

  • Put simply, in a room full of randomly selected people,

    簡而言之,在一屋子的隨機挑選的人中,

  • I'm a maths genius.

    我算是一個數學天才。

  • In a roomful of maths Ph.Ds,

    在滿屋子的數學博士裡,

  • I'm as dumb as a box of hammers.

    我笨得想一盒子錘子。

  • My skill is not in the mathematics.

    我的技能並不在於數學。

  • It is in telling the story of the mathematics.

    而是講述數學的故事上。

  • And during that time, since I've left university,

    那段時間,自從我離開了大學後,

  • these numbers have got bigger and bigger,

    這些數位變得越來越大。

  • each one dwarfing the last,

    一個超過一個,

  • until along came this man, Dr. Curtis Cooper,

    直到這個人出現,柯帝士 · 庫珀博士,

  • who a few years ago held the record for the largest ever prime,

    他幾年其保持了史上最大質數的紀錄,

  • only to see it snatched away by a rival university.

    後來卻被一個對手大學搶走了。

  • And then Curtis Cooper got it back.

    然後柯帝士 · 庫珀又搶回了紀錄。

  • Not years ago, not months ago, days ago.

    不是幾年前,不是幾個月前 而是幾天天前

  • In an amazing moment of serendipity,

    我突發靈感,

  • I had to send TED a new slide

    必須給TED發一張幻燈片

  • to show you what this guy had done.

    向大家展示這個傢伙的成就。

  • I still remember -- (Applause) --

    我還記得 — — (掌聲)-

  • I still remember when it happened.

    我還記得當時的場景。

  • I was doing my breakfast radio show.

    我正在做早間廣播節目。

  • I looked down on Twitter. There was a tweet:

    我低頭看了眼 Twitter 有一個推特資訊

  • "Adam, have you seen the new largest prime number?"

    "亞當,你見過最新的最大質數?"

  • I shivered --

    我顫抖起來 — —

  • (Laughter) --

    (笑聲)-

  • contacted the women who produced my radio show out in the other room,

    聯繫了在隔壁房間的 我的廣播節製作人

  • and said "Girls, hold the front page.

    說道"姑娘們,留白頭條專欄。

  • We're not talking politics today.

    我們今天不討論政治。

  • We're not talking sport today.

    我們今天不討論體育。

  • They found another megaprime."

    他們發現另一個超級質數。”

  • The girls just shook their heads,

    那些姑娘們只是搖頭,

  • put them in their hands, and let me go my own way.

    用手捂著頭 任由我行事

  • It's because of Curtis Cooper that we know,

    正是歸功於柯帝士 · 庫珀,

  • currently the largest prime number we know,

    我們知道了先今最大的質數,

  • is 2 ^ 57,885,161.

    是 2 ^57等於 885,161

  • Don't forget to subtract the one.

    別忘了要減去1。