數(shù)學(xué)頂端的性別差距

Six hundred of the cleverest people in the world are sitting in a tent in Bath, in the west of England, listening to a man standing at a wooden lectern who is extolling their achievements.

600名世界上最聰明的人坐在位于英格蘭西部城市巴斯的帳篷內(nèi)，聆聽一個(gè)男人站在木質(zhì)講臺(tái)前贊揚(yáng)他們的成就。

He announces that there is a Fields medallist among them. Eager eyes try to spot the recipient of the world’s most prestigious prize in mathematics.

他宣稱，他們之中有一名菲爾茲(Fields)獎(jiǎng)得主。人們都用熱切的眼神試圖找出數(shù)學(xué)界世界最高獎(jiǎng)項(xiàng)的獲得者。

This is the closing ceremony of the 60th International Mathematical Olympiad, the annual world championship maths competition for secondary school-age students. It is late July, and 621 teenagers representing 112 countries are waiting for medals to be distributed. They have spent days working on mathematical problems that many university professors would fail to solve.

這是第60屆國(guó)際數(shù)學(xué)奧林匹克競(jìng)賽(International Mathematical Olympiad，以下簡(jiǎn)稱“國(guó)際數(shù)學(xué)奧賽”)的閉幕式，這場(chǎng)世界數(shù)學(xué)競(jìng)賽每年舉辦一次，參賽者為中學(xué)年齡段學(xué)生。時(shí)值7月末，代表112個(gè)國(guó)家的621名青少年正等待獎(jiǎng)牌頒發(fā)。他們已經(jīng)花費(fèi)數(shù)天時(shí)間解決數(shù)學(xué)問題，這些問題連許多大學(xué)教授也無(wú)法解出。

The man at the lectern, a mathematician and the president of the governing body of the Olympiad, gets to his punchline. There is a Fields medallist sitting in this room, “he just doesn’t know it yet”.

講臺(tái)上的男人是一名數(shù)學(xué)家，也是國(guó)際數(shù)學(xué)奧賽組委會(huì)主席，他抖開了包袱。房間里有一名菲爾茲獎(jiǎng)得主，“只不過(guò)他現(xiàn)在還不知道呢”。

Statistically Geoff Smith is right. Half of all Fields medallists are also IMO winners who have sat through similar ceremonies. Such is the calibre of this audience that its 52 new IMO gold medallists among them are 50 times more likely to go on to win the Fields Medal —“the Nobel for mathematics” — than someone with a PhD in mathematics from the University of Cambridge.

從統(tǒng)計(jì)學(xué)看，杰夫•史密斯(Geoff Smith)是對(duì)的。菲爾茲獎(jiǎng)得主有一半都是曾參加類似儀式的國(guó)際數(shù)學(xué)奧賽獲獎(jiǎng)?wù)?。這就是在座觀眾的水準(zhǔn)，他們之中的52名新晉奧賽金牌得主獲得菲爾茲獎(jiǎng)——“數(shù)學(xué)界的諾貝爾獎(jiǎng)”——的可能性是劍橋大學(xué)(University of Cambridge)數(shù)學(xué)系博士的50倍。

And though he will correct himself a few minutes later, Prof Smith is also right, at least statistically speaking, to use the masculine pronoun when he says, “he just doesn’t know it yet”. Of the 61 Fields medals awarded since 1936, only one has gone to a woman. Maryam Mirzakhani received hers in 2014 after winning gold for Iran at the IMOs of 1994 and 1995. She died two years ago.

雖然史密斯教授在幾分鐘之后糾正了自己，但他說(shuō)“只不過(guò)他現(xiàn)在還不知道”時(shí)用了男性的“他”也是對(duì)的，至少?gòu)慕y(tǒng)計(jì)上看是如此。自1936年以來(lái)，61名菲爾茲獎(jiǎng)得主中只有1名是女性。2014年菲爾茲獎(jiǎng)獲得者是瑪麗安•米爾札哈尼(Maryam Mirzakhani)，她曾在1994年和1995年代表伊朗獲得國(guó)際數(shù)學(xué)奧賽金牌。她于兩年前去世。

Looking across the audience, there are almost no girls in Prof Smith’s sightline. At the back is the UAE team of six girls and somewhere in the front sits 17-year-old Jelena Ivancic of Serbia, the only girl to score high enough on the problems that make up the competition to win a gold medal at the games.

向觀眾席望去，史密斯教授的視線中幾乎沒有女孩。后排坐著阿聯(lián)酋隊(duì)的6名女孩，前排某個(gè)角落坐著塞爾維亞17歲的耶萊娜•伊萬(wàn)契奇(Jelena Ivancic)，她是唯一一名在競(jìng)賽中答題得分高到足以贏得金牌的女孩。

Most countries, particularly those in the top ranks, have a rigorous gender-blind national competition programme to pick the six members of their IMO team. Of the top 25 ranking nations at this year’s competition, 148 team members were boys and two were girls.

大多數(shù)國(guó)家，特別是那些排名高的國(guó)家，都會(huì)舉辦嚴(yán)格的、不分性別的全國(guó)競(jìng)賽，挑選6名選手組建國(guó)際數(shù)學(xué)奧賽參賽隊(duì)伍。今年競(jìng)賽排名前25的國(guó)家中，有148名選手是男孩，2名選手是女孩。

The divide at the top of mathematics is so stark that it is difficult to think of a comparable gender-blind data set that is global and spans 60 years.

數(shù)學(xué)頂端的性別差距如此嚴(yán)峻，以至于很難在不分性別的情況下再找出一個(gè)同樣的全球性、跨越60年、性別差距如此之大的數(shù)據(jù)組。

Almost no one, from neuroscientists and geneticists to educationalists and mathematicians, suggests the reason for this discrepancy is down to inherent differences in ability between the sexes. If that is correct, it means that all across the world, girls are being put off maths.

從神經(jīng)科學(xué)家、遺傳學(xué)家到教育學(xué)家、數(shù)學(xué)家，幾乎沒有人認(rèn)為造成這種差距的原因是兩性天生的能力差別。如果他們是正確的，那就意味著全世界女孩的數(shù)學(xué)能力都被耽誤了。

That matters, not only because the top minds go on to win Fields medals and advance the field of mathematics, but because they also go on to work in computer science and write the algorithms that will define our future in an artificial intelligence-driven world.

這很重要，不但因?yàn)轫敿馊瞬拍苴A得菲爾茲獎(jiǎng)、推動(dòng)數(shù)學(xué)領(lǐng)域的進(jìn)步，而且因?yàn)樗麄兛赡軙?huì)去計(jì)算機(jī)科學(xué)領(lǐng)域工作、寫出算法定義我們未來(lái)靠人工智能驅(qū)動(dòng)的世界。

Top mathematicians also follow careers in finance that will determine the stability of economies and they move into medicine and science to work on the world’s most pressing problems. When women are not present, biases are baked into systems. This is especially potent in AI.

頂尖數(shù)學(xué)家也可能進(jìn)入金融業(yè)工作，他們的工作將決定經(jīng)濟(jì)的穩(wěn)定;他們還可能進(jìn)入醫(yī)學(xué)和科學(xué)領(lǐng)域工作，解決世界上最緊迫的問題。若女性不參與其中，這些體系中就會(huì)產(chǎn)生偏差。在人工智能領(lǐng)域尤其如此。

Doug Gurr, head of Amazon UK, says mathematical skills will be important for almost all jobs in the future world of work. At Amazon, he says, “We see mathematical ability as essential to all our day-to-day work at all levels: from impact measurement to accounting, to machine learning, robotics and AI.”

英國(guó)亞馬遜(Amazon UK)總裁葛道遠(yuǎn)(Doug Gurr)表示，數(shù)學(xué)技能對(duì)于未來(lái)的幾乎所有工作都很重要。對(duì)于亞馬遜，他表示：“我們認(rèn)為數(shù)學(xué)能力在各層級(jí)的日常工作中都至關(guān)重要：從影響衡量到會(huì)計(jì)，到機(jī)器學(xué)習(xí)、機(jī)器人科學(xué)和人工智能。”

Numeracy is vital for everyone. But according to Alain Dehaze, chief executive of Adecco, the world’s biggest recruiting company, the most valuable mathematical skills in a more automated future, especially for those people who can also communicate them to generalists, are the ability to spot patterns; to problem solve logically; and to work with statistics, probability and large data sets to see into the future.

計(jì)算能力對(duì)于每個(gè)人來(lái)說(shuō)都十分重要。但是，據(jù)世界最大的人才招聘企業(yè)德科(Adecco)的首席執(zhí)行官阿蘭•德海茲(Alain Dehaze)說(shuō)，在更加自動(dòng)化的未來(lái)，最有價(jià)值的數(shù)學(xué)技能——特別是對(duì)于那些能將數(shù)學(xué)技能傳授給跨領(lǐng)域人才的人們——是發(fā)現(xiàn)模式的能力;運(yùn)用邏輯解決問題的能力;利用統(tǒng)計(jì)學(xué)、概率和大數(shù)據(jù)預(yù)測(cè)未來(lái)的能力。

Po-Shen Loh, a maths professor at Carnegie Mellon University in Pittsburgh, and the coach of the US IMO team, believes that there is “absolutely no difference in ability” between girls and boys.

羅博深(Po-Shen Loh)是匹茲堡卡內(nèi)基梅隆大學(xué)(Carnegie Mellon University)的數(shù)學(xué)教授，也是美國(guó)的奧數(shù)隊(duì)教練，他認(rèn)為女孩與男孩之間“絕對(duì)沒有能力差別”。

“I think that the average girl hears from various sides, various angles through their life that girls are not as good in maths and science,” he says.

他說(shuō)：“我認(rèn)為，普通女孩一生中會(huì)從各種方面、各種角度聽說(shuō)女孩不那么擅長(zhǎng)數(shù)學(xué)和科學(xué)的觀點(diǎn)。”

This is particularly potent in maths, where an answer is either right or wrong and everyone eventually runs into a problem they cannot solve. When one’s culture and a dearth of role models send out the message that girls are not as good at maths, it is a lot easier to give up and turn to other subjects and endeavours.

在數(shù)學(xué)領(lǐng)域尤為如此。在數(shù)學(xué)中，答案要么對(duì)要么錯(cuò)，而且每個(gè)人最終都會(huì)遇到自己無(wú)法解決的問題。當(dāng)一個(gè)人的文化背景以及缺乏榜樣釋放出女孩相對(duì)不擅長(zhǎng)數(shù)學(xué)的訊息時(shí)，她就更容易放棄，轉(zhuǎn)向其他學(xué)科和工作。

The US team has not sent a girl to the Olympiad in 12 years and some of its members worry that the gender gap in ability is widening. So far, attempts such as girls-only competitions and camps have made little difference in the statistics.

美國(guó)隊(duì)已有12年沒有派女孩參加國(guó)際數(shù)學(xué)奧賽，團(tuán)隊(duì)中一些成員擔(dān)心能力上的性別差距在擴(kuò)大。到目前為止，為女孩專門舉辦競(jìng)賽和夏令營(yíng)等嘗試都沒有在統(tǒng)計(jì)數(shù)據(jù)上帶來(lái)什么改變。

Dame Celia Hoyles, one of Britain’s best known maths educationalists, says that the fear of making mistakes is holding people back, especially girls. “We’d love to change this view. It’s really quite deeply ingrained and one generation is passing it on to another.”

英國(guó)最知名的數(shù)學(xué)教育家之一西莉亞•霍伊爾斯女爵(Dame Celia Hoyles)表示，對(duì)犯錯(cuò)的恐懼阻止了人們前進(jìn)，尤其是女孩。“我們很愿意改變這種觀念。它確實(shí)根深蒂固，代代相傳。”

Educationalists call this fear “maths anxiety” and have tried for decades to tackle it.

教育家把這種恐懼稱為“數(shù)學(xué)焦慮癥”，幾十年來(lái)一直嘗試解決它。

Progress has been slow, but Dame Celia notes that there has been some improvement in the number of girls taking A level maths and choosing it at degree level. Efforts to make maths less gender biased have increased over the past decade. But cultural biases that start at birth, including expectations that undermine girls’ willingness to make mistakes, are harder to change, as is the way teenage girls approach learning.

雖然進(jìn)展很緩慢，但是西莉亞女爵指出，中學(xué)選修A level數(shù)學(xué)、并在讀大學(xué)學(xué)位時(shí)選擇數(shù)學(xué)的女生數(shù)量已有提升。在過(guò)去十年中，降低數(shù)學(xué)領(lǐng)域性別差異的努力增多了。但是生來(lái)就存在的文化偏見——例如讓女孩不愿犯錯(cuò)的期望——更難改變。女孩在青少年時(shí)期的學(xué)習(xí)方式也是如此。

When asked why she thinks there are so few girls studying maths Ms Ivancic, the Serbian IMO gold medallist, says: “I worked really hard and I worked alone when I was younger because I loved it . . . 

當(dāng)被問起她認(rèn)為為什么學(xué)數(shù)學(xué)的女孩這么少時(shí)，塞爾維亞的奧數(shù)金牌得主伊萬(wàn)契奇表示：“我真的非常努力，我小時(shí)候獨(dú)自一人學(xué)數(shù)學(xué)，因?yàn)槲姨珢蹟?shù)學(xué)了……

I don’t think they [girls] are not capable. Maybe they don’t try enough or think they are not good enough.”

“我不認(rèn)為她們(女孩們)做不到。也許她們只是嘗試得不夠多，或者自認(rèn)為不夠好。”

Lisa Sauermann, the most decorated female IMO contestant ever, suggests that the attitude of parents and culture can have a profound effect, especially early in life. Ms Sauermann’s mother grew up in the former DDR (East Germany) where, culturally, she says it was normal for women to be scientists and mathematicians.

得獎(jiǎng)最多的女性國(guó)際數(shù)學(xué)奧賽選手莉薩•紹爾曼(Lisa Sauermann)認(rèn)為，父母和文化的態(tài)度會(huì)產(chǎn)生深刻的影響，特別在一個(gè)人的人生初期。紹爾曼的母親成長(zhǎng)于前民主德國(guó)(東德)，她說(shuō)，在那里的文化中，女性成為科學(xué)家和數(shù)學(xué)家是很正常的。

A study published last year by IZA Institute of Labor Economics concludes that European socialism has had lasting benefits on girls’ mathematical achievements.

德國(guó)IZA勞動(dòng)經(jīng)濟(jì)研究所(IZA Institute of Labor Economics)去年發(fā)表的一項(xiàng)研究顯示，前歐洲社會(huì)主義國(guó)家持續(xù)受益于女性的數(shù)學(xué)成就。

But the big rise has been that of Asia, in particularly China. Of the two winning teams, the US and China, all but one of the boys was of Asian descent. South and North Korea placed third and fourth respectively and of the top 15 nations all but the US are Asian or former socialist states, with only the Serbian and Polish teams including girls.

但是后起之秀在亞洲，特別是中國(guó)。今年的兩支獲勝隊(duì)伍——美國(guó)隊(duì)與中國(guó)隊(duì)中，所有選手只有一人不是亞洲血統(tǒng)。韓國(guó)和朝鮮分列第三、第四名。在排名前15的國(guó)家中，除了美國(guó)以外，全是亞洲國(guó)家或前社會(huì)主義國(guó)家，只有塞爾維亞隊(duì)與波蘭隊(duì)有女孩參賽。

“This is not about particular ethnic groups having more capability. I think that’s bogus,” says Prof Loh, himself a child of Chinese parents. “If you want to have a very strong ability in something, it takes a lot of time and dedication. When one talks about the Chinese culture, this idea of focusing on studies has always been something that has been very pervasive.”

“這不是由于某些民族的能力更強(qiáng)。我認(rèn)為那是無(wú)稽之談。”父母都是中國(guó)人的羅博深表示，“如果你想要在某一領(lǐng)域獲得很強(qiáng)的能力，那需要大量的時(shí)間和投入。談到中國(guó)文化，這種專注學(xué)習(xí)的觀念總是普遍存在的。”

Prof Loh, who spends a significant amount of time trying to bring maths to the masses, notes there is a higher purpose to it than winning medals.

羅博深投入了大量時(shí)間，嘗試把數(shù)學(xué)普及至大眾。他指出，這樣做的目的不只是為了贏得獎(jiǎng)牌。

“Mathematics teaches you how to question, how to be very confident that you have pushed your logical conclusion through and then you actually believe in what you are doing. Then you have a world with discourse. And a world with discourse is one in which we as a society — I am talking about all 7bn of us — can get along much better.”

“數(shù)學(xué)教會(huì)你如何提問，如何獲得自信——你用邏輯推導(dǎo)出了結(jié)論，然后你確實(shí)相信自己所做的事情。然后我們才有一個(gè)能夠?qū)υ挼氖澜纭Ｒ粋€(gè)能對(duì)話的世界是我們作為一整個(gè)社會(huì)——我是指全球70億人——能更加和諧相處的世界。”

The author is the former recruitment editor of the FT and is founder of the non-profit organisation Maths Teams

本文作者是前英國(guó)《金融時(shí)報(bào)》職場(chǎng)編輯，也是非營(yíng)利組織Maths Teams創(chuàng)始人