Okay.

好的

As a child, were you good at mathematics?

你小時候數學好嗎？

Like, was mathematics a natural thing for you?

數學對你來說是天生的嗎？

Yeah, it was very natural.

是的，非常自然。

And I always liked it.

我一直都很喜歡。

I liked counting.

我喜歡數數。

I liked continually multiplying things by two.

我喜歡不斷地把東西乘以二。

Although by the time I got to a thousand twenty-four or whatever it is, I had enough of it.

不過，當我讀到一千二百二十四還是什麼的時候，我已經讀夠了。

But I liked math.

但我喜歡數學。

I discovered as a very young kid, maybe four, something called Zeno's Paradox.

我很小的時候，大概四歲，就發現了一個叫芝諾悖論的東西。

Did you ever hear of Zeno's Paradox?

你聽說過芝諾悖論嗎？

My father told me that the car could run out of gas.

父親告訴我，汽車可能會沒油。

And I was disturbed by that notion.

我對這種想法感到不安。

It never occurred to me.

我從沒想過

But then I thought, well, it shouldn't run out.

但我又想，嗯，應該用不完。

It could always use half of what it has, and then it could use half of that and then half of that, and it could go on forever, and so it would never run out.

它總是可以用掉一半，然後再用掉一半，再用掉一半，這樣可以一直用下去，永遠用不完。

So, now, it didn't occur to me, yes, but it wouldn't get very far either.

所以，現在我沒有想到這一點，是的，但也不會走得太遠。

But the idea that, in principle, you didn't have to run out of gas was kind of a profound thought for a very little boy.

但是，對於一個小男孩來說，"原則上，你不需要耗盡汽油 "這個想法實在是太深奧了。

Did it feel like this was where your career was going to take you, or were you like another boy who dreamed of being a baseballer or something?

你是否覺得這就是你的職業發展方向，還是說你就像另一個夢想成為棒球運動員的男孩？

Oh, no, no, no.

哦，不，不，不

The only thing I thought about was I would be a mathematician, whatever exactly that meant.

我唯一想到的是我將成為一名數學家，不管這究竟意味著什麼。

I didn't know quite what it meant, except that mathematics was the only subject I really liked.

我不知道這意味著什麼，只知道數學是我唯一喜歡的科目。

They wanted me to go to Berkeley and get away from MIT, meet some new faculty, because I was quite close to the MIT faculty, and they thought, I think they didn't want to get rid of me so much as they thought I was probably pretty good, so I should get exposed to a certain guy named Churn, who was just coming to Berkeley that year.

他們想讓我去伯克利，遠離麻省理工學院，認識一些新的教師，因為我和麻省理工學院的教師關係很好，他們認為，我想他們並不是想擺脫我，而是覺得我可能還不錯，所以我應該去接觸一個叫楚恩的人，他那年剛來伯克利。

And I got this very nice fellowship, and I went there.

我得到了一份很不錯的獎學金，就去了那裡。

I was very eager to work with Churn, meet Churn, except he wasn't there.

我很想和楚恩一起工作，見見楚恩，但他不在。

He celebrated his first year at Berkeley.

他慶祝了在伯克利的第一年。

He had just come to Berkeley, and he celebrated that first year by taking a sabbatical, so he wasn't there.

他剛剛來到伯克利，為了慶祝第一年的到來，他休了公休假，所以不在那裡。

So I worked with another guy, which was fine, and by the time Churn came in the second year,

所以我和另一個人一起工作，這很好，到了第二年《攪局者》出現的時候、

I was already pretty far along with the thesis project.

我的論文項目已經進展得相當順利了。

I was giving a seminar at the beginning of my second year at Berkeley, and in walked this tall Chinese guy, and I said to the guy next to me, who's that?

在伯克利的第二年年初，我正在舉辦一個研討會，一個高個子中國人走了進來，我對旁邊的人說，那是誰？

He said, oh, that's Churn.

他說，哦，那是 Churn。

I said, that's Churn?

我說，那是 Churn？

I didn't know he was Chinese.

我不知道他是中國人。

I thought Churn was probably short for Chernowski or something, or he was probably some Polish guy who had shortened his name to Churn.

我想 Churn 可能是 Chernowski 或其他什麼的簡稱，或者他可能是某個波蘭人把自己的名字簡稱為 Churn。

If it had been Chen or Chan, I would have known it was Chinese, but Churn with the R, I didn't know.

如果是 Chen 或 Chan，我會知道它是中文，但 Churn 帶 R，我就不知道了。

But anyway, so I met Churn then, and we became friends.

總之，我在那時認識了楚恩，我們成了朋友。

Of course, I was much younger than he, but we became friends, and later collaborators.

當然，當時我比他年輕得多，但我們成了朋友，後來又成了合作者。

So we worked together, and we came up with these results, this whole structure.

是以，我們共同努力，取得了這些成果和整個結構。

In fact, that's the slides of the presentation that Churn made at the International Congress in the early 70s.

事實上，這就是 Churn 在 70 年代初國際大會上發言的幻燈片。

It was very nice geometry.

幾何形狀非常漂亮。

I pushed on with it, and we defined some things called differential characters, which was another chapter, working with a guy named Cheeger.

我繼續研究，我們定義了一些叫做微分字元的東西，這是另一章，是和一個叫切格的人合作完成的。

But the Churn-Simons invariance, about 10 years later, the physicists got a hold of it, and it seemed to be very good for what ailed them, or whatever might have ailed them.

但大約10年後，物理學家們掌握了 "楚恩-西蒙斯不變性"，它似乎很好地解決了困擾他們的問題，或任何可能困擾他們的問題。

And it wasn't just string theory, as I subsequently developed.

這不僅僅是弦理論，正如我後來發展的那樣。

It was kind of all areas of physics, including condensed matter theory.

它涉及物理學的所有領域，包括凝聚態理論。

Even some astronomers seemed to want to look at those terms.

甚至一些天文學家似乎也想看看這些術語。

That's really what's great about basic science, in this case mathematics.

這就是基礎科學（這裡指數學）的真正偉大之處。

I mean, I didn't know any physics.

我是說，我根本不懂物理。

It didn't occur to me that this material that Churn and I had developed would find use somewhere else altogether.

我沒有想到，我和楚恩開發的這些材料會在其他地方派上用場。

This happens in basic science all the time, that one guy's discovery leads to someone else's invention and leads to another guy's machine.

這種情況在基礎科學中時有發生，一個人的發現導致了其他人的發明，並導致了另一個人的機器。

Actually, in the middle of my mathematics career, which ended when I was about 37 or 38, was that I spent four years at a place called the Institute for Defense Analyses, down in Princeton, which was a super-secret, government-based,

實際上，在我數學生涯的中期，也就是我37或38歲時，我在普林斯頓一個叫國防分析研究所的地方工作了四年，那是一個超級機密的政府機構、

National Security Agency-based place for code cracking.

設在國家安全局的密碼破解場所。

But I also learned about computers and algorithms, and I did one thing there that was quite good, because I can't tell you what it was.

但我也學習了計算機和算法，我在那裡做了一件相當不錯的事情，因為我不能告訴你那是什麼。

It's all classified.

這都是機密。

So I had a good career there, both doing mathematics and learning about the fun of computer modeling.

是以，我在那裡度過了美好的職業生涯，既從事數學研究，又瞭解到計算機建模的樂趣。

My father had made a little bit of money, and I had the opportunity to try investing it.

我父親賺了一點錢，我有機會嘗試投資。

And that was interesting, and I thought, you know, I'm going to try another career altogether.

這很有趣，於是我想，我要嘗試另一種職業。

And so I went into the money management business, so to speak.

就這樣，我進入了理財行業。

So you started with some of your dad's money, and that got you a taste for an interest in it?

所以你是用你父親的一些錢開始的，這讓你對它產生了興趣？

Yeah, some family money.

是啊，家裡有些錢。

And then some other people put up some money, and I did that.

後來又有一些人出了一些錢，我就這麼做了。

But no models. No models for the first two years.

但沒有模特。頭兩年沒有模特。

So what were you doing then?

那你當時在做什麼？

You were just using cunning and, you know, just like normal people do.

你只是在使用狡猾，你知道，就像正常人一樣。

Like normal people do.

像正常人一樣

And I brought in a couple of people to work with me, and we were extremely successful.

我找了幾個人和我一起工作，我們非常成功。

I think it was just plain good luck, but nonetheless, we were very successful.

我認為這只是運氣好而已，但儘管如此，我們還是非常成功。

But I could see that this was a very gut-wrenching business.

但我看得出，這是一件非常令人揪心的事情。

You know, you come in one morning, you think you're a genius, the markets are for you.

你知道，有一天早上你來了，你覺得自己是個天才，市場是為你準備的。

We were trading currencies and commodities and financial instruments and so on.

我們交易貨幣、商品和金融工具等等。

Not stocks, but those kinds of things.

不是股票，而是這類東西。

And the next morning you come, and you feel like a jerk, the market's against you.

第二天早上，你來了，你覺得自己像個混蛋，市場對你不利。

It was very gut-wrenching.

這讓人非常揪心。

And in looking at the patterns of prices,

在研究價格模式時、

I could see that there was something we could study here, that there were maybe some ways to predict prices, mathematically or statistically.

我可以看到，我們可以在這裡研究一些東西，也許有一些方法可以用數學或統計學的方法來預測價格。

And I started working on that, and then brought in some other people, and gradually built models.

我開始著手這項工作，然後找來其他人，逐漸建立起模型。

And the models got better and better, and finally the models replaced the fundamental stuff.

模型變得越來越好，最後模型取代了基本的東西。

So it took a while.

所以花了一段時間。

I would have thought, with your background, a mathematician, this would have almost occurred to you immediately, like you would have straightaway seen this.

我本以為，以你的數學家背景，你會立刻想到這一點，就像你會直接看到這一點一樣。

What was the two-year delay?

延遲兩年的原因是什麼？

Well, two things.

有兩件事

I saw it pretty early, but...

我很早就看到了，但...

And I brought in a guy who was a wonderful guy, also from the code-cracking place.

我還找來了一個很棒的傢伙，他也來自破解代碼的地方。

And he was...

他...

I thought, together we'll start building models.

我想，我們一起開始製作模型吧。

That was fairly early, but it wasn't right away.

那是相當早的時候，但不是馬上。

But he got more interested in the fundamental stuff, and he says, the models aren't going to be very strong, and so on and so forth.

但他對基本的東西更感興趣，他說，模型不會很強，諸如此類。

So we didn't get very far.

所以我們沒走多遠。

But I knew there were models to be made.

但我知道有模型可以製作。

Then I brought in another mathematician, and a couple more, and a better computer guy.

後來，我又請來了一位數學家，又請來了幾位，還有一位更好的計算機專家。

And then we started making models, which really worked.

然後我們開始製作模型，這真的很有效。

But, you know, the general...

但是，你知道，一般...

There's something called the efficient market theory, which says that there's nothing in the data, let's say price data, which will indicate anything about the future, because the price is sort of always right.

有一種叫做有效市場理論的東西，說的是數據（比方說價格數據）中沒有任何東西能預示未來，因為價格總是對的。

The price is always right, in some sense.

從某種意義上說，價格總是對的。

But that's just not true.

但事實並非如此。

So there are anomalies in the data, even in the price history data.

是以，即使是價格歷史數據也存在異常。

For one thing, commodities especially used to trend, not dramatically trend, but trend.

首先，商品尤其習慣於趨勢，不是大幅趨勢，而是趨勢。

So if you could get the trend right, you'd bet on the trend, and you'd make money more often than you wouldn't, whether it was going down or going up.

是以，如果你能把握趨勢，你就會在趨勢上下注，不管是下跌還是上漲，你都會比不下注的人賺得更多。

That was an anomaly in the data.

這是數據中的異常現象。

But gradually we found more and more and more and more anomalies.

但漸漸地，我們發現了越來越多的異常現象。

None of them is so overwhelming that you're going to clean up on a particular anomaly, because if they were, other people would have seen them.

沒有任何一種異常情況會讓你手足無措，因為如果有的話，其他人早就看到了。

So they have to be subtle things.

是以，它們必須是微妙的東西。

And you put together a collection of these subtle anomalies, and you begin to get something that will predict pretty well.

把這些微妙的異常現象集合在一起，你就會開始得到一些能很好預測的東西。

It's what's called machine learning.

這就是所謂的機器學習。

So you find things that are predictive.

是以，你要找到具有預測性的東西。

You might guess, oh, such and such should be predictive, might be predictive, and you test it out on the computer, and maybe it is, and maybe it isn't.

你可能會猜測，哦，這樣那樣的東西應該是有預測性的，可能是有預測性的，然後你在電腦上測試一下，也許是，也許不是。

What discipline of mathematics, or disciplines, is it multidisciplinary, or are we talking...

數學的哪一門學科，或哪幾門學科，它是多學科的，還是我們所說的...

It's mostly statistics.

主要是統計數據。

It's mostly statistics and some probability theory.

主要是統計學和一些概率論。

But I can't get into what things we do use and what things we don't use.

但是，我不能說我們用什麼東西，不用什麼東西。

We reach for different things that might be effective.

我們尋求不同的可能有效的方法。

I would imagine lots of people want to be financially successful.

我想很多人都希望在經濟上取得成功。

Most people want that, of course.

當然，大多數人都希望如此。

I suppose.

我想是的

And lots of people are good at mathematics and know a lot about computers, at your level, I would imagine.

我想，很多人都精通數學，對計算機也很瞭解，就像你這樣的水準。

Why did you do it? Why didn't someone else do it?

你為什麼要這麼做？為什麼別人不這麼做？

I don't know.

我不知道。

Well, first of all, some other people have done it.

首先，其他人已經做到了。

I think that our firm is better.

我認為我們公司更勝一籌。

But nonetheless, I'm pretty sure of that.

但儘管如此，我還是非常確定這一點。

But nonetheless, other people have done some very good modeling, and so we're not alone.

儘管如此，其他人也做了一些非常好的模型，所以我們並不孤單。

But it's not easy to do, and there's a big barrier to entry.

但要做到這一點並不容易，而且門檻很高。

For example, huge data sets that we've collected over the years, programs that we've written to make it really easy to test hypotheses and so on.

例如，我們多年來收集的龐大數據集，我們為測試假設而編寫的程序等等。

The infrastructure is exceptionally good, so everything is tuned right.

這裡的基礎設施特別好，一切都調整得恰到好處。

It took years to learn how to do that.

我花了很多年才學會怎麼做。

I know you guys made the model, so you do have the ownership of it and feel proud of it.

我知道模型是你們做的，所以你們擁有它的所有權，併為它感到自豪。

But is it hard to follow the model religiously?

但是，虔誠地遵循這一模式很難嗎？

Is it hard for your ego to think all the success is because of the computer?

如果你認為所有的成功都是電腦的功勞，這對你的自尊心來說是否很困難？

And I just sat there and watched?

我就坐在那裡看著？

No, the computer is just a tool that we use.

不，電腦只是我們使用的一種工具。

A good cabinetmaker doesn't say, it's all because of my wonderful chisel.

一個好的櫥櫃匠不會說，這都是我的鑿子的功勞。

You may have great film equipment, but that's not why you're a success at doing what you're doing.

你可能有很好的電影設備，但這並不是你成功的原因。

You're working with good equipment, but another guy would make a mess of it with the same equipment.

你用的是好設備，但另一個人用同樣的設備就會弄得一團糟。

So no, we don't feel, oh, the computer is doing everything.

所以，我們不會覺得，電腦在做所有的事情。

The computer does what you tell it to do.

電腦會按照你的指令行事。

Given that you will put some of it down to luck, what are you more proud of, all of this and the business, or the mathematics from that first half of your career?

既然你會把其中的一些原因歸結為運氣，那麼你更引以為豪的是什麼？是所有這些和業務，還是你職業生涯前半段的數學？

Oh, to the extent that I'm proud,

哦，我很自豪、

I think I'm proud of both.

我為這兩件事感到驕傲。

I think, you know, I've done some mathematics, and some of it's had a positive effect, so I guess I'm proud of that.

我想，你知道，我做了一些數學研究，其中一些產生了積極的影響，所以我想我為此感到自豪。

And I've built a nice business, and I'm proud of that.

我建立了一個不錯的企業，我為此感到自豪。

I don't say I'm prouder of one than the other.

我並不為其中一個而感到驕傲。

And now for the last number of years,

現在是最近幾年、

I've been working with my wife on this foundation, which she started actually in 1994 with my money, but nonetheless she started the foundation, and then I joined.

我一直在和我的妻子一起籌建這個基金會，實際上是她在 1994 年用我的錢創辦的，但不管怎麼說，是她創辦了基金會，然後我也加入了。

I got more and more involved with the foundation as time went on, and now that's my main thing, so I'm very proud of the foundation.

隨著時間的推移，我越來越多地參與基金會的工作，現在這是我的主要工作，所以我為基金會感到非常自豪。

Let me focus you more on the mathematics versus the business then.

那就讓我把重點放在數學和業務上吧。

Would you trade any or all of your business success for being the man who cracked the Riemann hypothesis, or something like that?

你是否願意用你事業上的任何或所有成功來換取成為破解黎曼假設的人，或者類似的東西？

No, that's a good question.

不，這是個好問題。

Would I trade that for...

我會用它來換...

Well, I'd probably trade some of it,

好吧，我可能會換一些、

I mean, for the Riemann hypothesis.

我是指黎曼假設。

It would certainly, I guess, be a thrill to solve the Riemann hypothesis.

我想，解決黎曼假設肯定會讓人興奮不已。

I'm pleased mostly with the way my career has gone, so would I trade part of it for something?

我對自己的職業生涯感到非常滿意，那麼我會用其中的一部分來交換什麼嗎？

I don't know.

我不知道。

I've never looked back and said,

我從來沒有回過頭來說

I wish, at least in business,

我也希望如此，至少在生意場上是這樣、

I wish I hadn't done that, or I wish I had done this and not that, whatever it is.

我希望我沒有那麼做，或者我希望我做了這個而不是那個，不管是什麼。

I've never looked back that way.

我再也沒有回頭看過。

The foundation is focused on support of scientific research, primarily basic science, but not completely because we have a large autism project, which involves a lot of basic science, but treatments are a goal.

基金會的重點是支持科學研究，主要是基礎科學研究，但也不完全是，因為我們有一個大型自閉症項目，其中涉及很多基礎科學研究，但治療也是我們的一個目標。

But the rest is support of mathematics, physics, computer science, biology of all sorts, neuroscience, genetics.

但剩下的就是數學、物理學、計算機科學、各種生物學、神經科學和遺傳學的支持了。

We support basic science, and that's what we like to do.

我們支持基礎科學，這也是我們喜歡做的事情。

There's a certain amount of outreach.

有一定的外聯活動。

We have Math for America Pro.

我們有《美國專業數學》。

We spend maybe 10 or 15 percent on outreach, outreach and education, but 80, 85 percent is support of basic science.

我們可能將 10% 或 15% 用於外聯、推廣和教育，但 80% 或 85% 用於支持基礎科學。

You put a lot of money into mathematics, and you've got some right to comment on it.

你在數學上花了很多錢，你有權對它發表意見。

How are you feeling about it?

你感覺如何？

Oh, I think mathematics is really going quite well worldwide, the research end of it.

哦，我認為數學在世界範圍內發展得非常好，研究方面也是如此。

A lot of new ideas are coming up.

許多新想法正在萌生。

New fields sort of are flourishing.

新的領域正在蓬勃發展。

It feels like a pretty healthy enterprise to me.

我覺得這是一個相當健康的企業。

What's not healthy is the state of mathematics education in our country.

不健康的是我們國家的數學教育現狀。

It's very unhealthy for young people.

這對年輕人來說非常不健康。

That's why we started this thing called Math for America and so on.

這就是為什麼我們發起了 "美國數學 "等活動。

But we don't have enough teachers of mathematics who know it, who know the subject, and even of science.

但是，我們沒有足夠的懂數學、懂這門學科甚至懂科學的教師。

And that's for a simple reason.

原因很簡單。

30, 40 years ago, if you knew some mathematics enough to teach, let's say, in high school, there weren't a million other things you could do with that knowledge.

30 年或 40 年前，如果你懂得一些數學知識，足以在高中任教，比方說，你可以用這些知識做的事情並不多。

Oh, yeah, maybe you could become a professor, but let's suppose you're not quite at that level, but you were good at math and so on.

哦，是的，也許你可以成為一名教授，但假設你還沒有達到那個水準，但你擅長數學等等。

Being a math teacher was a nice job.

當數學老師是一份不錯的工作。

But today, if you know that much mathematics, you could get a job at Google, you could get a job at IBM, you could get a job at Goldman Sachs.

但今天，如果你懂那麼多數學，你可以在谷歌找到工作，可以在 IBM 找到工作，可以在高盛找到工作。

I mean, there's plenty of opportunities that are going to pay more than being a high school teacher, right?

我的意思是，比當高中老師工資高的機會多得是，對嗎？

There weren't so many when I was going to high school, such things.