世间聪明的头脑有很多

Q168

本文为与《时代》杂志的合作内容，原文发表在Time.com网站。
    约翰•纳什是2001年奥斯卡获奖影片《美丽心灵》的主人公原型。美国警方称，纳什与妻子上周六乘出租车在新泽西州高速公路遭遇车祸，双双身亡。纳什生前长住新泽西州普林斯顿大学，因博弈论的研究荣获1994年诺贝尔经济学奖。
    很多人认识约翰•纳什是因为那部由他真实经历改编的电影，以及他的研究对经济学所产生的深远影响。但别忘了最重要的是，纳什首先是名数学家。在回顾他的生平时，我希望我们能逐渐了悟的一点是：世间聪明的头脑有很多，但纳什是非常特别的一类。

his post is in partnership with Time. This post was originally published at Time.com.
    John Forbes Nash Jr., the subject of the 2001 Oscar-winning film A Beautiful Mind, and his wife were killed Saturday in a taxi crash on the New Jersey Turnpike, police said. Nash, a longtime resident of Princeton Junction, N.J., won the 1994 Nobel Prize in Economics for his work on game theory.
    Many people know John Nash because of his life story and because his work impacted economics in such a profound way. But first and foremost, he was a mathematician. I hope one thing will become clear when we look back on Dr. John Nash’s life: there are many brilliant minds, but he was a very special kind.

Q168

我记得很清楚，上世纪80年代末到90年代初，从某种意义上说，他还沉浸在自己的世界中，但纳什的精神分裂症趋于缓和，他得以重返普林斯顿从事学术工作。那段时间，只要坐车去城里，就会在那列“Dinky”小火车上碰到纳什。他是车上的常客，总是坐在那儿听别人聊天。后来到90年代初，他终于从分裂症中挣脱，让所有人都为之震惊。突然之间，他仿佛重获新生了。
    以我观察所见，在纳什与病魔奋战的几十年里，最了不起的一件事就是，他一直被同事们包容接纳，他们从未遗忘过他。我认为，这是普林斯顿的一项美好品质，所有人都把纳什视为我们当中的一员。

I remember well the period in the late 1980s and early 1990s, when he was still, in some sense, in his own world. At that time, Nash’s schizophrenia was diminishing, allowing him to return to academic work at Princeton University. You would meet him in the “Dinky” train you’d take to go into town. He was a very frequent visitor, sitting there, listening to people. In the early 1990s, he emerged out of that period, and it was such a surprise to everyone. He suddenly came back alive again.
    One of the great things I’ve observed through the many decades Nash was struggling, was that he was always accepted by his colleagues, who never forgot who he was. I think that’s a terrific quality here at Princeton; he was accepted as one of us.

Q168

纳什成就斐然，却格外谦逊。他行事谨慎，作风低调，兴趣广泛。他极少向别人提起自己的工作和贡献，即便谈起，他也将其置入大背景中，淡化个人。我觉得，这或许也是纳什给我们最大的启示之一，他能看到其他人看不到的深远之处，但他深知前方路上亦有艰难险阻。
    纳什的研究传递了一个重要的信息——从周围纷繁复杂的世界中，发掘数学规律以及捕捉现象背后的本质是可能的。他的博弈论明显做到了，不仅如此，他的非线性偏微分方程也达到了这个目标。使用非线性偏微分方程后，任何物理现象、任何物理学定律都可以用微分方程阐述。纳什与数学家路易斯•尼伦伯格合著的论文获得了阿贝尔奖，他们的研究成果为阐释世间万物打下了基础。

Nash was on the one hand such an impressive figure, but also so incredibly modest. He was very careful, very low profile and interested in many things. He was always the last person to educate others about his own work and contributions. He always sold it as part of a much bigger story. I think that might be one of the greatest inspirations: he was somebody who saw much further than others, but was always very much aware of what big problems were still out there.
    Nash’s work projects a powerful message, namely, that it is possible in the great complexity of the world you see around us, to discover mathematical laws and capture the essence of phenomenon. He did this, of course, with his work in game theory, but as another bookend were his results in nonlinear differential equations. Any physical phenomenon, any physical law, is formulated in terms of differential equations. The result of his and mathematician Louis Nirenberg’s work, which was awarded the Abel Prize, underpins almost everything we see around us.

Q168

纳什做研究有个特点，他总是探索大家认为不可能的，或是困难重重让人失望的领域。纳什思考的问题不同凡响，都是数学领域最重大的那些问题。人们往往认为有些问题已经非常难了，每个人都在致力于此，完全没有勇气去解决更重大的问题。纳什曾因此饱受折磨，他是真正有勇气推动思维走向深处的数学家，远远超过常人有胆量触及的范围。
    业界有个非常精到的短语就和纳什有关：数学的合理有效性。这种理念可以通过不断应用获得印证。多年来纳什不断付出，获得的成果在每次应用后都更加强大。这也正是纳什研究的核心。

    本文作者罗伯特•迪格拉夫是一位数学物理学家，现任普林斯顿大学高等研究所主任兼里昂•列维基金会荣誉教授。

One consistent element of Nash’s work was that he was always going in directions that were either thought to be impossible, or actively discouraged. It’s amazing the problems he was thinking of. They were really the biggest problems in mathematics. People think that there are these very big problems that everyone’s working on, but people simply cannot find the internal courage to address the bigger issues. Nash suffered for that; he was really a mathematician that pushed his mind to go far, far beyond where other peoples’ would dare to go.
    There was this wonderful phrase that was once coined about him: the reasonable effectiveness of mathematics. It’s that the same idea can be applied again and again and again. He keeps on giving, and the result only becomes more powerful with every application. And that is really the core of Nash’s work.
    Robbert Dijkgraaf is the Director of the Institute for Advanced Study and Leon Levy Professor in Princeton, New Jersey, where he is a mathematical physicist.