现代科学是从牛顿开始的，他是一位非常了不起的科学家。众所周知，他发现了万有引力定律还有牛顿力学，还是微积分发现人之一。从一个人对科学的贡献来讲，很少有人可以与牛顿相提并论，一生能如果做上述一件事，就能被称为非常伟大的科学家了，牛顿却做了三件。

Modern science began with Newton, a very remarkable scientist. As we all know, he discovered the law of universal gravity and Newton's mechanics, or one of the people who discovered calculus. In terms of a person's contribution to science, few people can be compared to Newton, who can be called a very great scientist if he can do one of these things in his life, but Newton did three.

关于牛顿，有一个家喻户晓的传说：牛顿在睡午觉的时候，一个苹果掉在他的头上，由此激发了他的灵感，从而发现了万有引力定律，这也是整个现代科学的起源。我的母校南京大学曾得到英国剑桥大学里这颗苹果树的种子，大家如果想看到这棵砸过牛顿的苹果树的后代，可以到南京大学的新校园。

About Newton, there is a household legend: Newton in the nap, an apple fell on his head, which inspired him to discover the law of gravity, which is the origin of the whole modern science. My alma mater, nanjing university, got the seeds of this apple tree at cambridge university in england. If you want to see the offspring of this newtonian apple tree, you can go to the new campus of nanjing university.

这幅漫画上有一段很有意思的笑话，大意是：我想下面更难的事，是怎么申请科研经费，总不能因为苹果掉在我头上就可以得到资助了。

There's an interesting joke in this cartoon to the effect that: I think the harder thing to do is to apply for research funding, the more money you can't get from dropping an apple on my head.

或许大家觉得牛顿发现万有引力是个偶然的幸运，但事实上并非如此，万有引力定律的发现经历了前人很多年的观测。

It may have been a coincidence that Newton was lucky enough to find universal gravity, but it wasn't. The discovery of the law of universal gravity has gone through years of observation.

类似的例子还有开普勒发现行星运动三大定律，（编者注：椭圆定律：所有行星绕太阳的轨道都是椭圆，太阳在椭圆的一个焦点上；面积定律：行星和太阳的连线在相等的时间间隔内扫过相等的面积；调和定律：所有行星绕太阳一周的恒星时间的平方与它们轨道长半轴的立方成比例。）开普勒三大定律的发现同样也不是偶然，不是灵机一现。

A similar example is kepler's discovery of the three laws of planetary motion (editor's note: elliptical law: all planets orbit the sun in an elliptical orbit, the sun in a focal point of the ellipse; area law: the line between the planets and the sun sweeps through an equal area at equal intervals; and harmonic law: the square of the stellar time around which all planets orbit the sun is proportional to the cubic axis of their orbit. ) The discovery of Kepler's three laws is not accidental, nor is it psychic.

开普勒发现了行星运动三大定律之前，有一位丹麦的数学家第谷·布拉赫，他花了很多时间去观察行星的运动，那时观测精度比较差，他又是用肉眼来观察行星的运动，因此花费了很多精力。

Before Kepler discovered the three laws of planetary motion, there was a Danish mathematician, Tigu Brah, who spent a lot of time observing the motion of the planet, when the accuracy was relatively poor, and he used the naked eye to observe the motion of the planet, so he spent a lot of energy.

丹麦皇帝甚至资助他在岛上修建天文台，花了很多钱来支持他的研究，有意思的是，当时他记录的纸都是一个专门的造纸厂提供的。

The danish emperor even helped him to build an observatory on the island, spending a lot of money to support his research. Interestingly, the paper he had recorded was supplied by a special paper mill.

第谷和皇帝关系很好，但是皇帝死后，继任皇帝不喜欢他，他就跑到布拉格去，那里的皇帝也非常支持他进行科学研究，第谷得以经常出没皇宫。有一次他在皇宫喝了很多酒，回家后就死掉了，大家一直猜测他是什么原因死亡，有一种猜测是被别人下毒，另一种猜测是喝多了被尿憋死，在他死后的四百多年，也就是2001年，有人决定把他的尸体挖出来，来确定他的死因，结果发现果然不是毒死的，而是被尿憋死的，第谷成了历史上第一个被尿憋死的科学家。

After the emperor's death, however, the succeeding emperor did not like him, and he went to Prague, where the emperor was also very supportive of his scientific research, and where he had frequented the palace. Once he drank a lot of wine at the palace and died when he got home, there was constant speculation about what the cause of his death was, one was poisoned by someone else, the other was that drinking too much was suffocated by urine, and in the four hundred years after his death, in 2001, someone decided to dig up his body to determine his cause of death, only to find out that it was not the poison, but the death of urine, the first scientist in the history of Gu Cheng.

又过了十年，关于第谷又有一个很大的争议。第谷性格怪异，在二十几岁的时候跟堂兄争吵谁是更伟大的数学家，最后两人决定决斗，结果第谷的鼻子在决斗中被割掉，大家很长时间不知道他的鼻子是金子做的还是银子做的。2010年，大家决定再把他的棺材挖出来研究一下，结果发现他的鼻子是铜做的。

After another decade, there was another big controversy about the valley. Tigu had a strange character, arguing with his cousin in his twenties about who the greater mathematicians were, and finally the two decided to fight, only to have his nose cut off in the duel, and for a long time it was not known whether his nose was made of gold or silver. In 2010, people decided to dig up his coffin and study it again, only to find that his nose was made of copper.

第谷对天文学的观测奠定了开普勒的基础、奠定了万有引力定律的开始。作为他的学生，开普勒观测了火星运动。如果当初没有观测火星的话，大家会认为行星的轨道是圆形的，所以牛顿才终于发现了万有引力，而并不仅仅是因为一个苹果掉在他的头上。

The observation of astronomy in the valley laid the foundation for kepler and the beginning of the law of gravitation. As his student, Kepler observed the movement of Mars. If Mars had not been observed, it would have been assumed that the orbit of the planet was circular, so Newton finally discovered gravity, not just because an apple had fallen on his head.

当牛顿发现万有引力定律后，第一个问题是想解决多体问题，既有万有引力，又有牛顿力学，再加上微积分，这样的天文学问题变成了数学问题。

When Newton discovered the law of universal gravity, the first problem was to solve multibody problems, both gravitational and Newton's mechanics, plus calculus, such astronomical problems became mathematical problems.

如何根据这些物理定律来找到行星运动的轨道，精确地推算轨道。太阳和一个行星在一起就是二体问题，我们已经知道二体问题的轨道是稳定性轨道，而太阳与两个行星放在一起就叫三体问题，天体越多就变成越复杂的数学问题。三体问题花了很长时间，最终人们发现三体问题是不可解的。

how to find the orbit of the planetary motion according to these physical laws and accurately calculate the orbit. The sun is a two-body problem with one planet, and we already know that the orbit of the two-body problem is a stable orbit, while the sun and two planets together are called three-body problems, and the more celestial bodies become more complex mathematical problems. The trisomy problem took a long time, and eventually people found that the trisomy problem was insoluble.

太阳系远远超过三体，有太阳，有行星，行星还有卫星，还有其他很多小天体。整个太阳系是一个庞大的体系，远远超过三体，是更复杂的多体问题。既然三体问题都没法解，对于多体问题，用经典的方法去解决太阳系的运动，显然也是不太可能的。

The solar system far exceeds three bodies, with the sun, planets, planets and moons, and many other small objects. The whole solar system is a vast system, far more than three-body, and is a more complex multi-body problem. Since the three-body problem cannot be solved, it is obviously not possible to use classical methods to solve the motion of the solar system.

这里需要再提一下牛顿，他同样也是位“怪”人，上半辈子做了非常伟大的科学工作，但他是非常虔诚的基督徒，认为太阳系是不稳定的。人们会问太阳系既然不稳定，那人类怎么可能生存？牛顿的解释是，上帝每隔一段时间就来推一下行星或者球，让地球回到稳定的轨道上不会偏离太远。

It is important to mention newton, who is also a \"weird\" man who has done great scientific work for the first half of his life, but he is a very devout christian and believes that the solar system is unstable. How can humans survive if the solar system is unstable? Newton's explanation is that God pushes the planet or the ball every once in a while so that the Earth does not deviate too far from its stable orbit.

牛顿一直试图用数学的方法来证明上帝的存在，用数学公式去解开行星的轨道，现在看来非常荒唐的，所以有人开玩笑的说，牛顿被苹果砸了后，大脑其实不太好了。

Newton had been trying to mathematically prove the existence of God, using mathematical formulas to unravel the planet's orbit, now seems very absurd, so it was joked that Newton's brain wasn't really good after he was hit by an apple.

关于行星的稳定性，每一位伟大的科学家都会提出自己的见解，这些见解有时候介于数学分析，有时候介于猜测。

Every great scientist will come up with his own insights into the stability of planets, sometimes between mathematical analysis and sometimes between conjecture.

我刚才提到了，因为三体问题无法用经典方法把解写出来。三体是一个混沌系统，最重要的特征是不可预测。三体的运动，假如时间不够长，是不可能预测未来会如何变化。《三体》小说就是利用这种特征，描述了一个世界有三个太阳，三个太阳的运转处于非常不可预测的状态，可能三个太阳突然出现，使星球上的所有生命热死，很可能三个太阳一段时间都不出现，让星球很冷，把所有生命冻死，这就是《三体》小说里的科学原理。

As I mentioned earlier, the three-body problem cannot be solved classically. Three-body is a chaotic system, the most important feature is unpredictable. Three-body movement, if not long enough, is impossible to predict how the future will change. Using this feature, the novel describes a world in which there are three suns, which are in a very unpredictable state of motion. It is possible that the three suns suddenly appear and make all life on the planet hot, and it is likely that the three suns will not appear for a while, leaving the planet cold and freezing all life to death.

对人类而言，我们没必要担心太阳系是否稳定，科学家计算过，几百万年，甚至上亿年内都没有问题，即使不稳定，也要几亿年后才会出现的事了。

For humans, there is no need to worry about the stability of the solar system. Scientists have calculated that for millions of years, even hundreds of millions of years, there will be no problem.

人类为什么要关心太阳系的稳定性呢？我想说科学的发展并不是从实用性的角度出发的。现代科学从牛顿力学而来，牛顿力学又从天体力学而来，而天体力学刚开始是满足人类的好奇心，但是科学给人类的生活带来革命性的发展与技术不一样，技术是竞技性的，科学是革命性的，现代的生活，所有一切是由于科学的发展，故而用功利性的眼光去看科学研究是错误的。

Why should humans care about the stability of the solar system? I would say that the development of science is not from the perspective of practicality. Modern science comes from newtonian mechanics, and newtonian mechanics comes from celestial mechanics, which at first satisfies human curiosity, but science brings revolutionary development and technology to human life, technology is competitive, science is revolutionary, modern life, all due to the development of science, so it is wrong to look at scientific research with a utilitarian view.

数学家有一个非常深刻的理论，叫KAM理论（编者注：KAM理论是经典力学里讨论近可积保守系统：哈密顿系统，可逆系统，保体积映射的动力学性态的著名的理论。K，A，M分别代表公认的于上个世纪五六十年代创立该理论的三位数学家，他们是：俄罗斯数学家Kolmogorov和Arnold，以及德国数学家Moser），有很多数学家为此做出了很大的贡献。人们对力学系统所关心的问题之一，是运动过程的长期行为和它最终会达到的状态。动力系统的长时间行为可能有多种形式：平衡或不动点、周期振动、准周期运动、混沌，它们都是定常态。

Mathematicians have a very profound theory called KAM Theory (Editor's Note: KAM Theory is a well-known theory in classical mechanics that discusses the dynamics of nearly integrable conservative systems: Hamiltonian systems, reversible systems, and volume-preserving maps. K, A, and M represent the three recognized mathematicians who founded the theory in the 1950s and 1960s: Russian mathematicians Kolmogorov and Arnold, and German mathematician Moser. One of the concerns of the mechanical system is the long-term behavior of the motion process and the state it will eventually reach. The long-term behavior of a dynamical system may take many forms: equilibrium or fixed point, periodic vibration, quasi-periodic motion, chaos, they are all stationary states.

牛顿力学的确定论观点曾因解决太阳系行星运行问题的成功而在很长时期占统治地位，但是，力学中的三体问题和重刚体绕固定点的运动问题成为困扰人们近一个世纪的难题，KAM定理通过对弱不可积系统运动稳定性条件的证明，说明了三维以上非线性系统的运动轨道出现混沌现象具有普遍性。

Newton's deterministic view of mechanics was dominated for a long time by the success of solving the problem of planetary motion in the solar system. However, the three-body problem in mechanics and the motion of the heavy rigid body around the fixed point have become a difficult problem for nearly a century.

稳定性的对立面就是混沌，认知的进步使我们认识到世界越来越多元，越来越发现稳定性的可能性不大，大部分情况是动态的稳定，或者是混沌的系统。

The opposite of stability is chaos, and the progress of cognition makes us realize that the world is becoming more and more pluralistic, and the possibility of stability is more and more small, most of the situation is dynamic stability, or chaotic system.

上图是挪威的皇帝奥斯卡二世，这是唯一的一位数学家皇帝，本科读了数学，一直喜欢科学和艺术，定期在皇宫组织科学讲堂。他在位时，创立了一本数学杂志：《ActaMathematica》，现在仍是数学领域的四大杂志之一。

Above is the emperor oscar ii of norway, the only mathematician emperor who has studied mathematics, has always loved science and art, and regularly organizes science lectures at the palace. When he was in office, he founded a math magazine, ActaMatica, which is still one of the four major magazines in mathematics.

1887年，有一位数学家MitagLefler建议他设立一个科学大奖：谁能解决三体问题，就把这个奖颁给他。虽然现在我们知道三体问题不可解，但当时大家并不知道。

In 1887, a mathematician, Mitag Leffler, suggested that he set up a science prize: whoever could solve the three-body problem would give it to him. Although we now know that the three-body problem cannot be solved, but we did not know at that time.

MitagLefler何许人也？我给大家讲一个故事，诺贝尔奖为什么没有数学家呢？传说是因为诺贝尔的情人被一位数学家拐骗走了，那位数学家就是MitagLefler。

Mitag Lefler Who? I tell you a story. Why didn't the Nobel Prize have a mathematician? Legend has it that Nobel's lover was abducted by a mathematician who was called Mitag Leffler.

1895年，皇帝请巴黎大学的数学家潘勒维到皇宫做讲座，当时潘勒维提出了一个猜测，现在叫潘勒维猜测，该猜测经过不到一百年，最后在我的博士论文里面用混沌问题得出了解。

In 1895, the emperor invited the university of paris's mathematician, panlwi, to give a lecture at the palace when he made a conjecture, now called panlvi's conjecture, which, after less than a hundred years, was finally understood in my phd thesis with a question of chaos.

大家可能要问为什么会花这么长时间呢？因为我们对科学的理解是一步一步发展的，庞加莱跟潘勒维是同期的数学家，其实我证明的猜测是庞加莱和潘勒维共同探讨的猜测，庞加莱写了关于如何解三体问题的一篇文章，虽然并没有解出来，但是获奖委员会最后还是决定给了他一个大奖。但有意思的是结果他的学生发现文章里面有错误，庞加莱又重新写了一篇文章，在这篇文章里，混沌的概念第一次在数学里被正确描述。

Why would it take so long? Because our understanding of science has evolved step by step, Pangale and Panlwi are mathematicians in the same period, I actually prove that the guess is that Pangale and Panlwe discussed together, Pangale wrote an article on how to solve the three-body problem, although not solved, but the award-winning committee finally decided to give him a prize. But what's interesting is that his students found a mistake in the article, and Pangala rewrote an article in which the concept of chaos was first correctly described in mathematics.

下面这个故事相信很多人都听过，一位数学家发明了国际象棋，皇帝非常高兴问他想要什么样的奖赏，数学家说很简单，你在棋盘里面第一格放1颗麦子，第二格放2颗麦子，第三格放4颗麦子，第四格放8颗麦子，再下面一格放16颗麦子，用这种方式把棋盘放满就够了。皇帝认为数学家的要求不是很高，只不过要了几颗麦子而已，当即答应了。实际总共需要多少颗麦子呢？棋盘一共是64格，第一格是1，最后一格是2的63次方，一共是2的64次方减1，大约是140万亿升的麦子。由此可见，几何级的增长速度特别快，这也是混沌里最基本的一个概念。

The Emperor was pleased to ask him what kind of reward he wanted, and the mathematician said it was simple enough to fill the board with one grain for the first, two for the second, four for the third, eight for the fourth, and 16 for the next. The emperor thought that the demands of mathematicians were not very high, but only a few wheat, and immediately agreed. How many grains of wheat do you actually need? The board consists of 64 squares, the first is 1, the last is 63 squares of 2, and the total is 64 squares of 2 minus 1, about 140 trillion liters of wheat. Thus, the geometric growth rate is particularly fast, which is also the most basic concept in chaos.

我们看上图这个盒子，一个盒子里面放入气体分子，分子在盒子里运动速度非常快，假如有一个小的误差，第一秒就加倍，第二秒又加倍，第三秒又加倍，60秒后，2的60次方，原先再小的误差都被刚才的这种方式加倍，由此可见，分子运动带来的后果是非常大的，而混沌的量有多少，取决于多长时间加倍一次。

We look at the box, a box into the gas molecules, the molecules move very fast in the box, if there is a small error, the first second double, the second double, the third double,60 seconds later, the second 60 square, the original small error is doubled by this way, it can be seen that the effect of the molecular motion is very large, and the amount of chaos depends on how many times.

在空气动力学中，空气移动比较快，可能零点几秒钟就加倍。太阳系运动相对较慢，误差加倍时间可能需要几十年、几百年，但有一个共同的性质存在，误差在一次一次的加倍！时间拉长后，你没法知道它原先的状态，因为一次次加倍带来的后果是将来不可预测，这就是将来不可预测原理。

In aerodynamics, the air moves faster, possibly doubling in a few seconds. The solar system is moving relatively slowly, and the error doubling time may take decades, hundreds of years, but there is a common property that exists, and the error is doubled at a time! As time goes by, you don't know its original state, because the consequence of doubling over and over is that the future is unpredictable.

气象系统是最典型的混沌系统。大家可能都遇到过，准备周末出去玩，一看气象预报是晴天，到周末却开始下大雨，大家可能都会指责气象台预报的不准，事实上气象是一个非常混沌的系统，基本没有办法长时间预测。本来广州应该晴空万里，但有一只蝴蝶在美国芝加哥挥了挥翅膀，它对空气的影响可能一秒钟以后就会加倍，两个星期以后就会影响着广州的气候。

The meteorological system is the most typical chaotic system. Everyone may have met, ready to go out for the weekend, to see the weather forecast is sunny, to the weekend but began to rain, everyone may blame the weather station forecast is inaccurate, in fact, the weather is a very chaotic system, there is no way to predict for a long time. Guangzhou was supposed to be clear, but a butterfly waved its wings in Chicago, USA, and its impact on the air could double in a second and affect the city's climate in two weeks.

这就是蝴蝶效应，也是为什么说气象系统是典型的混沌系统，假如要想精确预告天气，你必须知道芝加哥的每一只蝴蝶在两个星期之前干了什么，但有很多比蝴蝶更大的影响因素，比如汽车、飞机、人，想预告广州两个星期后的气候，就必须知道在地球另外一边发生的所有现象，这几乎是不可能的，所以短期气象预告可以的，但长期只能从概率上去预告。

This is the butterfly effect, and why the weather system is a typical chaotic system, if you want to accurately predict the weather, you have to know what each butterfly in Chicago did two weeks ago, but there are many more factors than butterflies, such as cars, planes, people, want to predict the climate after two weeks in Guangzhou, you have to know all the phenomena that happen on the other side of the earth, which is almost impossible, so the short-term weather forecast can only be predicted from probability in the long term.

大家都知道混沌非常地糟糕，那是不是就代表着不好？我讲一个代表混沌系统好的例子。现在中国、美国、印度等国家，大家都想进行太空探测，上月球、上火星，所以要发射很多卫星探测器。

We all know that chaos is very bad, does that mean bad? I give a good example of a chaotic system. Now China, the United States, India and other countries, we all want to do space exploration, on the moon, on Mars, so we have to launch a lot of satellite probes.

1991年4月，日本发射了HiTen的月球探测器，上天后才发现燃料不够，大家可能觉得这种问题不应该出现，这是因为发射过程有很多不定因素，放太多的燃料，重量就会增加，多放一斤燃料就要少放一斤科学仪器，而燃料刚好够，但是遇到特殊情况就可能出现燃料不足的情况。美国加州理工大学JPL实验室，派了一位数学家叫Belbruno，协助日本人重新设计轨道。

In April 1991, Japan launched the HiTen's lunar probe, only to find that there was not enough fuel, and it may be felt that the problem should not arise, because the launch process has many uncertainties, too much fuel, the weight will increase, one more kilo of fuel will be less scientific equipment, and the fuel will be just enough, but in special cases there may be a shortage of fuel. The JPL Lab at the California Institute of Technology sent a mathematician named Belbruno to help the Japanese redesign their orbits.

解决方案是利用有限的燃料把探测器送到混沌区域，混沌区域的将来不定，可能会出现在任何地方，到达有利地点就让它过去，不利的地点就稍微花一些燃料推动一下，1991年10月份，科学家用这种方式，最后成功地把探测器送到了月球轨道。

The solution is to use a limited amount of fuel to send the probe to the chaotic region, where the future is uncertain, where it may appear anywhere, to get to the vantage point to let it pass, and the unfavorable place to use a little fuel to propel it, in october 1991, when scientists succeeded in sending the probe to the lunar orbit.

某一天Belbruno给我打电话，说读了我的一篇文章，他在找混沌区域时，花了一个月的时间，如果先读了我的那篇关于混沌的文章，可能不用一个月就可以很快找到相应的区域，我听后非常高兴，没想到自己发表论文居然会有所应用。

One day Belbruno called me and said he had read one of my articles and that he had spent a month looking for a chaotic area, and if he had read my article about chaos first, it would probably take me less than a month to find the corresponding area soon.

本来以为这种事情日本发生了一次，以后就不太可能再发生了。谁知7年以后，1998年美国Hughe公司的一个探测器也遇到了同样的问题，发射后发现燃料不够，这时他们又找道Belbruno，很快，Belbruno帮他们重新设计了一条新的轨道，让探测器又成功抵达了原先的轨道。（注：文字信息未经夏志宏审校，图片来源于夏志宏演讲PPT）

This was supposed to happen once in Japan, and it is unlikely to happen again. Seven years later, a probe by the United States company Hughe encountered the same problem in 1998, when they found that there was not enough fuel after the launch, when they went to Belbruno, who soon helped them redesign a new track that allowed the probe to reach its original orbit. (Note: The text is from PPT)

新浪科技：您认为数学在中国科学中处于什么样的地位？近期四部委发布《关于加强数学科学研究工作方案》的文件，您是怎么看待这个方案的？

Sina science and technology: what kind of position do you think mathematics is in in Chinese science? What do you think of the recent publication by the four ministries of the Programme of Work on Strengthening Scientific Research in Mathematics?

中国对基础科学非常关注，但对数学的投入还是少了些，数学是所有学科的基础，尤其数学对提高大众的社会素质非常重要，它包含着分析能力、逻辑推理能力、简单的抽象思维能力，对公民素质的评价非常重要。

China is very concerned about basic science, but the investment in mathematics is still less, mathematics is the basis of all subjects, especially mathematics is very important to improve the social quality of the public, it contains analytical ability, logical reasoning ability, simple abstract thinking ability, the evaluation of the quality of citizens is very important.

我经常举好多简单的例子，经过数学推理逻辑思维培训的人有很多方面的优势，对分析能力、以后的发展都非常有用。数学教育的一个误解是希望培养专业的数学家，其实数学教育不仅仅是培养数学家，这只是小小的一部分，数学素质的培养是对整个民族素质，不仅是理工科的，对文科都是非常重要的。

I often give a lot of simple examples. Those trained in mathematical reasoning logic thinking have many advantages, which are very useful for analysis ability and future development. One misunderstanding of mathematics education is the hope of cultivating professional mathematicians. In fact, mathematics education is not only a training mathematician, but it is a small part. Mathematics quality training is very important to the whole national quality, not only in science and technology.

国家现在开始重视数学教育，作为一个数学家我觉得非常高兴，这是一个非常大的机遇，也是一个很大的挑战。

The country is now beginning to attach importance to mathematics education, as a mathematician I feel very happy, this is a very big opportunity, but also a great challenge.

挑战是什么呢？国家人才的培养应该是多层次的，鼓励做研究本来是好事，但数学教育不仅仅是研究，有些学校没有足够的研究水平和能力，但也在拼命追求写文章，做一些毫无意义的研究工作，而且以论文作为一个指标，这样对于整个数学的发展是很不利的。

What is the challenge? The cultivation of national talents should be multi-level, encouraging to do research is a good thing, but mathematics education is not only research, some schools do not have enough research level and ability, but also desperately pursue writing articles, do some meaningless research work, and take the paper as an indicator, which is very unfavorable to the development of the whole mathematics.

另外一个挑战，国家会投入更大的财力物力去支持数学研究，我希望看到的是更多支持年轻的、非常活跃的一些数学家，把资源充分地给他们，鼓励他们研究。

Another challenge, the state will invest more money and resources to support mathematical research, and what I'd like to see is more support for young, very active mathematicians, giving them the full resources to encourage them to study.

资助的方式也应该有很多不同的层次，除了政府还有民间，政府有不同的机构，资助的方式也不一样，可以多元化一起来做。

There should also be many different levels of funding, in addition to the government and the private sector, the government has different institutions, funding is not the same way, can be diversified to do together.

新浪科技：现在很多前沿研究都属于交叉的学科，因此产生一种说法，认为数学是学好其他学科的基础，您是怎么看待这个说法？

Sina science and technology: now a lot of frontier research is a cross-disciplinary subject, so there is a saying that mathematics is the basis of learning other subjects, what do you think of this statement?

夏志宏：数学研究本身非常重要，但数学教育启发学生的好奇心，对于任何学科都有帮助，它作为所有学科的基础，尤其逻辑推理能力、分析应用能力以及量化分析能力、抽象思维能力，这些都是一些基础素质，比方说你想做好物理、工程，哪怕做社会科学，都需要这些简单的技能。所以提高数学研究，提高数学老师本身的数学培养，这样可以提高学生基本素质。

Xia zhihong: mathematics research itself is very important, but mathematics education inspires the curiosity of students, it is helpful for any subject, it is the basis of all subjects, especially logical reasoning ability, analytical application ability, quantitative analysis ability, abstract thinking ability, these are some basic qualities, for example, you want to do well in physics, engineering, even social science, all need these simple skills. So improve the mathematics research, improve the mathematics teacher's own mathematics training, so as to improve the basic quality of students.

谈公民素质的时候我一直想强调公民的数学素质，一个社会的进步依赖于所有的公民有比较好的各方面素质，但数学素质往往可能是被忽略的。

When talking about the quality of citizens, I always want to emphasize the mathematical quality of citizens. The progress of a society depends on all citizens to have better qualities in all aspects, but the quality of mathematics may often be ignored.

新浪科技：不管是数学，一种新的研究成果出来，民众更感兴趣的是这个研究成果有什么用，以后能应用到什么地方，面对科学功利化，您怎么看？您又是怎么看待应用数学研究和基础数学研究之间关系？

Sina science and technology: whether it is mathematics, a new research results come out, people are more interested in this research results what use, later can be applied to where, in the face of scientific utilitarianism, how do you think? What do you think of the relationship between applied and basic mathematical research?

夏志宏：应用研究和基础研究没法人为地分开，有些数学研究刚开始是没有任何应用，也看不出任何的应用，比方说现代科学的起源，是从牛顿开始的，你可以说牛顿仰望星空去看行星的运动，是一件很不着边际的事，但就是牛顿跟科学家们，对一些大家觉得可能觉得毫无实用价值的科学研究，带来了现代科学的发展，而现代科学对人类的文明、生活带来的影响是巨大的，现代科学都是从无用开始的，到现在才变成现代生活完全不可或缺的部分。

Xia zhihong: applied research and basic research cannot be artificially separated, some mathematical research is at first no application, also cannot see any application, for example, the origin of modern science, starting from newton, you can say that newton looking up at the stars to see the movement of planets, is a very unlimited thing, but it is newton and scientists, to some scientific research that may feel that may be of no practical value, bring the development of modern science, and modern science is a great impact on human civilization, life is a huge, modern science is from the beginning of useless to become a part of modern life.

还有，数论可能大家觉得是一个毫无用处的学科，为什么关心数数，为什么要关注几个数字之间的规律，但是没有数论就没有现代的编码学，就没有现在的因特网，现在网络所有的交流、基本的保密加密方法都是从数论中来的，没有数论就没有办法在网上做任何交易，因为没有办法使网上的交易能保密，这是数学非常妙的地方。

Besides, number theory may be regarded as a useless subject, why we care about numbers, why we should pay attention to the law between several numbers, but without number theory, there is no modern coding, there is no Internet now, all the communication of the network, the basic secret encryption method are from number theory, there is no way to make any transactions on the Internet without number theory, because there is no way to keep online transactions confidential, which is very good for mathematics.

新浪科技：这种美妙的事情是不是可以认为是数学里潜在的美学价值，普通人可能学数学，看到一堆公式觉得很枯燥，作为一个数学家您是怎么看待这种美学价值？

Sina technology: this wonderful thing can be considered as the potential aesthetic value of mathematics, ordinary people may learn mathematics, see a bunch of formulas feel very boring, as a mathematician how do you think of this aesthetic value?

夏志宏：这种美学价值不是生来俱有的，一方面美是一开始就有，这是慢慢对数学的研究、对数学进一步了解以后会看到，比方说对称性，比方说非常美妙的剪辑方法来描述整个世界，比方说爱因斯坦的场方程就是非常美妙的数学方程，这种美真正要你进入后慢慢培养，跟现代艺术也有类似的地方，要沉浸进去，要有充分的了解，是后天培养出来的。

Xia zhihong: the aesthetic value of this kind of aesthetic value is not all born, on the one hand, beauty is there from the beginning, this is to slowly study mathematics, the further understanding of mathematics will see later, for example, symmetry, for example, the very wonderful editing method to describe the whole world, for example, Einstein's field equation is very wonderful mathematical equation, this beauty really needs you to enter the post-cultivation slowly, similar to modern art, to be immersed in, to have a full understanding, is the cultivation of the day after tomorrow.

新浪科技：学好数学有什么秘诀吗？如果要成为一名数学家，需要数学方面有天分，还是说通过后天的努力也可以达到？

Sina science and technology: what secret does study mathematics have? If you want to be a mathematician, you need a talent in mathematics, or you can do it through hard work?

夏志宏：数学有好多方面，而每个人的技能也是不一样的，不要认为某一方面不行可能数学就不行，数学面非常广，如果代数、抽象的公式不行，但是你可能几何很好，或者空间概念很好，我相信大部分人都可以找到所能激发他兴趣的某个方向的。

Xia zhihong: there are many aspects of mathematics, and everyone's skills are different, don't think that a certain aspect is not possible math is not, mathematics is very wide, if algebra, abstract formula is not good, but you may be good geometry, or space concept is good, I believe most people can find the direction that can stimulate his interest.

抽象思维是需要慢慢培养的，很多人数学学不好是没有适应抽象思维的方式，没有进入的足够顺利，我想大家其实都有简单抽象思维的能力，人要抓住一个事情的本质，需要把它抽象出来，需要把它简单化，这样才能真正地看透这些事情。

Abstract thinking needs to be cultivated slowly, a lot of people are not good enough to adapt to the way of abstract thinking, not enough to enter smoothly, I think everyone actually has the ability of simple abstract thinking, people want to grasp the essence of a thing, need to abstract it out, need to simplify it, in order to really see through these things.

夏志宏：美国的培养方式更注重的是学生的兴趣，中国的培养方式是注重技巧和基本技能，我们国家对学生培养的过程，是让学生花很多时间去演算，而美国学校的教育更多是启发学生，所以在考试的时候美国学生绝对考不过中国学生。

Xia Zhihong: The American way of training is more focused on students'interest, the Chinese way of training is to pay attention to skills and basic skills, the process of training students in our country is to let students spend a lot of time to calculate, and the American school education is more to inspire students, so the American students absolutely fail the Chinese students in the examination.

但美国学生假如想做数学，他是真的对数学感兴趣，即使告诉他将来会非常辛苦，他仍然去做。中国有时虽然你也感兴趣做数学，但是更多的情况下，一个更好的机会你可能就去做其他东西了。

But if an American student wants to do math, he is really interested in it, and even if he is told that it will be very hard in the future, he will still do it. China is sometimes interested in doing math, but more often than not, you might have a better chance of doing something else.

所以大家都在问为什么开始考试的时候都很厉害，做研究的时候反而不是那么特殊，当然中国也有很多非常优秀的中国科学家，但是相比我们整体的中学教育和考试的水平，这个数字相对少一些。

So we're all asking why they're so good at starting exams, and the research isn't that special. Of course, there are a lot of very good Chinese scientists in China, but it's a relatively small number compared to our overall level of secondary education and exams.

新浪科技：2019年7月20日是阿波罗工程登月50周年，前段时间中国也宣布火星车已建好，印度也发射了月船2号探测器，世界各国掀起了新一轮的外太空探索热潮，您对天体方面的研究也比较多，您觉得遥远的天体研究对于目前的外太空探索有哪些帮助或指导意义？

Sina Science and Technology: July 20,2019 is the 50th anniversary of the Apollo project, China also announced that the Mars vehicle has been built some time ago, India has also launched the lunar ship 2 detector, the world has set off a new wave of outer space exploration upsurge, you also have more research on celestial bodies, what do you think the distant celestial body research is helpful or instructive to the current exploration of outer space?

夏志宏：一个人对外太空或天文的兴趣是一种求知欲，这种兴趣是人类智慧的一个特征，对未知事件的探索，正是因为这些科学使人的生活更丰富，科学探索从物质上也许没有用，但对人的心理是非常有用的。我们知道一些好像不实用的知识，但这些知识满足了我们的求知欲。所以科学永远是满足求知欲，对未知事物的探索，无论有无用，对科学家来讲这也是一种感受，这并不亚于物质享受，未必比一顿美食要差。

Xia Zhihong: a person's interest in outer space or astronomy is a kind of thirst for knowledge, this interest is a feature of human wisdom, the exploration of unknown events, precisely because these sciences make people's lives richer, scientific exploration may not be physically useful, but very useful to the human mind. We know something that seems impractical, but it satisfies our thirst for knowledge. So science is always satisfied with the desire for knowledge, the exploration of unknown things, whether useless, for scientists it is also a feeling, this is no less than material enjoyment, not necessarily worse than a meal of food.

从另外的角度，因为这种探索有时候给我们一些惊喜，突然发现有很多用处，现代科学的发展也证明了这一点，我们对世界的探索给我们带来了很多有用的东西，也许现在登月计划可能没有多少物质上实用的东西，但对整个人类的精神上的满足不容忽视，它是一个非常重要的事件。

From another point of view, because this kind of exploration sometimes gives us some surprise, suddenly found to have a lot of use, the development of modern science also proves this, our exploration of the world has brought us a lot of useful things, perhaps now the moon landing plan may not have much material practical things, but the spiritual satisfaction of the whole human being cannot be ignored, it is a very important event.

科学的发展从开始无用，突然发现有很多有用的东西，然后花更多的精力去做有用的研究，例如又再次返回太空去进行火星计划、月球计划，这是一个好的回归科学，人类再给自己一个挑战，看我们能做些什么，这也许是没有用的，但也许又会给将来科学发展新的推动。

The development of science from the beginning useless, suddenly found that there are a lot of useful things, and then spend more energy to do useful research, such as return to space to carry out the Mars plan, the moon plan, this is a good return to science, human beings give themselves a challenge to see what we can do, it may be useless, but it may give new impetus to the development of science in the future.

人类作为共同体，大家接受这种挑战，而且各个国家，不仅是中国，美国、印度，都在主动地接受挑战，这对于科学发展来讲是一个非常好的事情，也是一个非常好的机遇。

Human beings as a community, people accept this challenge, and countries, not only China, the United States, India, are taking the initiative to accept the challenge, which is a very good thing for scientific development, but also a very good opportunity.

新浪科技：看到您出席过很多类似于GMIC这样的学界和商业界间的交流大会，您觉得什么原因吸引到您？您觉得科学家在产业界和学界之间扮演着哪种角色？发挥什么样的作用？

Sina technology: see you have attended a lot of academic and business circles like GMIC, what reason do you think attract you? What role do you think scientists play between industry and academia? What role do you play?

夏志宏：科学家跟企业家在一起参加活动，这是一个非常好的现象，现在企业家们对科学关心得比较多，企业家谈的都是非常基础的数学，中国企业家们非常关心中国科学发展，也对基础科学感兴趣，企业家毕竟是中国新兴的一个群体，这个群体对科学能做出贡献，在美国很多私立大学主要的经济来源是捐赠，比方说哈佛大学他们有300多亿美元的基金是完全捐赠的，我所在的西北大学大概有100多亿的捐赠基金，这些基金就是来支撑学校，在美国私立学校的发展主要是依赖于这些捐赠资金。

Xia zhihong: it's a very good phenomenon for scientists to participate in the activities with entrepreneurs. Now entrepreneurs care more about science, entrepreneurs talk about very basic mathematics, Chinese entrepreneurs are very concerned about the development of science in China, and they are also interested in basic science. After all, entrepreneurs are a new group in China, which can contribute to science. In many private universities in the United States, the main source of economics is donations, for example, Harvard University, whose $30 billion fund is a total endowment.

我国的私立大学西湖大学，也接受社会捐赠，用全民的力量来办一个研究型的大学，我希望西湖大学能发展起来，有更多的企业家关注、去捐赠促进大学的发展。

The private university of our country, the west lake university, also accepts the social donation, uses the national strength to run a research type university, I hope the west lake university can develop, has more entrepreneurs to pay attention to, goes to the donation to promote the university development.