Aug 132014
 


Maryam Mirzakhani, 37 岁, 刚刚在第二十七届国际数学家大会(ICM 2014)开幕式上, 从韩国女总统朴槿惠手中接过菲尔兹奖章. Mirzakhani 是首位荣获 fields medal 的女性.

Maryam Mirzakhani (R) was given the top mathematics award by South Korean president Park Geun-Hye (L)

Maryam Mirzakhani (R) was given the top mathematics award by South Korean president Park Geun-Hye (L)

Mirzakhani grew up in Iran and was at first more interested in reading and writing fiction than doing mathematics

Mirzakhani grew up in Iran and was at first more interested in reading and writing fiction than doing mathematics

Mirzakhani 在 IMO 表现杰出.

References

  1. Erica Klarreich, A Tenacious Explorer of Abstract Surfaces, August 12, 2014
Aug 132014
 
Maryam Mirzakhani

Maryam Mirzakhani

Fields Medals 2014

Artur Avila
Manjul Bhargava
Martin Hairer
Maryam Mirzakhani

At the opening ceremony of the International Congress of Mathematicians 2014 on August 13, 2014, the Fields Medals (started in 1936), the Nevanlinna Prize (started in 1982), the Gauss Prize (started in 2006), and the Chern Medal Award (started in 2010) were awarded. In addition, the winner of the Leelavati Prize (started in 2010) and the speaker of the ICM Emmy Noether Lecture (started in 1994) were announced.

Artur Avila

Artur Avila

Manjul Bhargava

Manjul Bhargava

Martin Hairer

Martin Hairer

Phillip Griffiths Chern Medalist 2014

Phillip Griffiths Chern Medalist 2014

ICM 2014

ICM 2014

Rolf Nevanlinna Prize 2014

Subhash Khot

Carl Friedrich Gauss Prize for Applications of Mathematics 2014

Stanley Osher

Chern Medal Award 2014

Phillip Griffiths

Leelavati Prize 2014

Adrián Paenza

ICM Emmy Noether Lecture 2014

The 2014 ICM Emmy Noether lecturer is  Georgia Benkart.

Maryam Mirzakhani

Mirzakhani was given the top mathematics award by South Korean president Park Geun-Hye

Mirzakhani was given the top mathematics award by South Korean president Park Geun-Hye

The Work of Maryam Mirzakhani

Stanford University, USA
[Maryam Mirzakhani is awarded the Fields Medal]
for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.

  • Maryam Mirzakhani has made stunning advances in the theory of Riemann surfaces and their moduli spaces, and led the way to new frontiers in this area. Her insights have integrated methods from diverse fields, such as algebraic geometry, topology and probability theory.
  • In hyperbolic geometry, Mirzakhani established asymptotic formulas and statistics for the number of simple closed geodesics on a Riemann surface of genus g. She next used these results to give a new and completely unexpected proof of Witten’s conjecture, a formula for characteristic classes for the moduli spaces of Riemann surfaces with marked points.
  • In dynamics, she found a remarkable new construction that bridges the holomorphic and symplectic aspects of moduli space, and used it to show that Thurston’s earthquake flow is ergodic and mixing.
  • Most recently, in the complex realm, Mirzakhani and her coworkers produced the long sought-after proof of the conjecture that – while the closure of a real geodesic in moduli space can be a fractal cobweb, defying classification – the closure of a complex geodesic is always an algebraic subvariety.
  • Her work has revealed that the rigidity theory of homogeneous spaces (developed by Margulis, Ratner and others) has a definite resonance in the highly inhomogeneous, but equally fundamental realm of moduli spaces, where many developments are still unfolding

Artur Avila

Avila was given the top mathematics award by South Korean president Park Geun-Hye

Avila was given the top mathematics award by South Korean president Park Geun-Hye

The Work of Artur Avila

CNRS, France & IMPA, Brazil
[Artur Avila is awarded a Fields Medal] for his profound contributions to dynamical systems theory have changed the face of the field, using the powerful idea of renormalization as a unifying principle.

  • Avila leads and shapes the field of dynamical systems. With his collaborators, he has made essential progress in many areas, including real and complex one-dimensional dynamics, spectral theory of the one-frequency Schródinger operator, flat billiards and partially hyperbolic dynamics.
  • Avila’s work on real one-dimensional dynamics brought completion to the subject, with full understanding of the probabilistic point of view, accompanied by a complete renormalization theory. His work in complex dynamics led to a thorough understanding of the fractal geometry of Feigenbaum Julia sets.
  • In the spectral theory of one-frequency difference Schródinger operators, Avila came up with a global de- scription of the phase transitions between discrete and absolutely continuous spectra, establishing surprising stratified analyticity of the Lyapunov exponent.
  • In the theory of flat billiards, Avila proved several long-standing conjectures on the ergodic behavior of interval-exchange maps. He made deep advances in our understanding of the stable ergodicity of typical partially hyperbolic systems.
  • Avila’s collaborative approach is an inspiration for a new generation of mathematicians.

Manjul Bhargava

Bhargava was given the top mathematics award by South Korean president Park Geun-Hye

Bhargava was given the top mathematics award by South Korean president Park Geun-Hye

The Work of Manjul Bhargava

Princeton University, USA
[Manjul Bhargava is awarded a Fields Medal]
for developing powerful new methods in the geometry of numbers and applied them to count rings of small rank and to bound the average rank of elliptic curves.

  • Bhargava’s thesis provided a reformulation of Gauss’s law for the composition of two binary quadratic forms. He showed that the orbits of the group \(SL(2, \Bbb Z)3\) on the tensor product of three copies of the standard integral representation correspond to quadratic rings (rings of rank \(2\) over \(\Bbb Z\)) together with three ideal classes whose product is trivial. This recovers Gauss’s composition law in an original and computationally effective manner. He then studied orbits in more complicated integral representations, which correspond to cubic, quartic, and quintic rings, and counted the number of such rings with bounded discriminant.
  • Bhargava next turned to the study of representations with a polynomial ring of invariants. The simplest such representation is given by the action of \(PGL(2, \Bbb Z)\) on the space of binary quartic forms. This has two independent invariants, which are related to the moduli of elliptic curves. Together with his student Arul Shankar, Bhargava used delicate estimates on the number of integral orbits of bounded height to bound the average rank of elliptic curves. Generalizing these methods to curves of higher genus, he recently showed that most hyperelliptic curves of genus at least two have no rational points.
  • Bhargava’s work is based both on a deep understanding of the representations of arithmetic groups and a unique blend of algebraic and analytic expertise.

Martin Hairer

Hairer was given the top mathematics award by South Korean president Park Geun-Hye

Hairer was given the top mathematics award by South Korean president Park Geun-Hye

The Work of Martin Hairer

University of Warwick, UK
[Martin Hairer is awarded a Fields Medal]
for his outstanding contributions to the theory of stochastic partial differential equations, and in particular created a theory of regularity structures for such equations.

  • A mathematical problem that is important throughout science is to understand the influence of noise on differential equations, and on the long time behavior of the solutions. This problem was solved for ordinary differential equations by Itó in the 1940s. For partial differential equations, a comprehensive theory has proved to be more elusive, and only particular cases (linear equations, tame nonlinearities, etc.) had been treated satisfactorily.
  • Hairer’s work addresses two central aspects of the theory. Together with Mattingly he employed the Malliavin calculus along with new methods to establish the ergodicity of the two-dimensional stochastic Navier-Stokes equation.
  • Building on the rough-path approach of Lyons for stochastic ordinary differential equations, Hairer then created an abstract theory of regularity structures for stochastic partial differential equations (SPDEs). This allows Taylor-like expansions around any point in space and time. The new theory allowed him to construct systematically solutions to singular non-linear SPDEs as fixed points of a renormalization procedure.
  • Hairer was thus able to give, for the first time, a rigorous intrinsic meaning to many SPDEs arising in physics.

Subhash Khot

Khot was given the Rolf Nevanlinna Prize by South Korean president Park Geun-Hye

Khot was given the Rolf Nevanlinna Prize by South Korean president Park Geun-Hye

Subhash Khot

New York University, USA
[Subhash Khot is awarded the Nevanlinna Prize]
for his prescient definition of the “Unique Games” problem, and his leadership in the effort to understand its complexity and its pivotal role in the study of efficient approximation of optimization problems, have produced breakthroughs in algorithmic design and approximation hardness, and new exciting interactions between computational complexity, analysis and geometry.

  • Subhash Khot defined the “Unique Games” in 2002 , and subsequently led the effort to understand its complexity and its pivotal role in the study of optimization problems. Khot and his collaborators demonstrated that the hardness of Unique Games implies a precise characterization of the best approximation factors achievable for a variety of NP-hard optimization problems. This discovery turned the Unique Games problem into a major open problem of the theory of computation.
  • The ongoing quest to study its complexity has had unexpected benefits. First, the reductions used in the above results identified new problems in analysis and geometry, invigorating analysis of Boolean functions, a field at the interface of mathematics and computer science. This led to new central limit theorems, invariance principles, isoperimetric inequalities, and inverse theorems, impacting research in computational complexity, pseudorandomness, learning and combinatorics. Second, Khot and his collaborators used intuitions stemming from their study of Unique Games to yield new lower bounds on the distortion incurred when embedding one metric space into another, as well as constructions of hard families of instances for common linear and semi- definite programming algorithms. This has inspired new work in algorithm design extending these methods, greatly enriching the theory of algorithms and its applications.

Phillip Griffiths

Phillip Griffiths was  given the Chern Medal by South Korean president Park Geun-Hye

Phillip Griffiths was given the Chern Medal by South Korean president Park Geun-Hye

Institute for Advanced Study, USA
[Phillip Griths is awarded the 2014 Chern Medal]
for his groundbreaking and transformative development of transcendental methods in complex geometry, particularly his seminal work in Hodge theory and periods of algebraic varieties.

  • Phillip Griffiths’s ongoing work in algebraic geometry, differential geometry, and differential equations has stimulated a wide range of advances in mathematics over the past 50 years and continues to influence and inspire an enormous body of research activity today.
  • He has brought to bear both classical techniques and strikingly original ideas on a variety of problems in real and complex geometry and laid out a program of applications to period mappings and domains, algebraic cycles, Nevanlinna theory, Brill-Noether theory, and topology of K¨ahler manifolds.
  • A characteristic of Griffithss work is that, while it often has a specific problem in view, it has served in multiple instances to open up an entire area to research.
  • Early on, he made connections between deformation theory and Hodge theory through infinitesimal methods, which led to his discovery of what are now known as the Griffiths infinitesimal period relations. These methods provided the motivation for the Griffiths intermediate Jacobian, which solved the problem of showing algebraic equivalence and homological equivalence of algebraic cycles are distinct. His work with C.H. Clemens on the non-rationality of the cubic threefold became a model for many further applications of transcendental methods to the study of algebraic varieties.
  • His wide-ranging investigations brought many new techniques to bear on these problems and led to insights and progress in many other areas of geometry that, at first glance, seem far removed from complex geometry. His related investigations into overdetermined systems of differential equations led a revitalization of this subject in the 1980s in the form of exterior differential systems, and he applied this to deep problems in modern differential geometry: Rigidity of isometric embeddings in the overdetermined case and local existence of smooth solutions in the determined case in dimension \(3\), drawing on deep results in hyperbolic PDEs(in collaborations with Berger, Bryant and Yang), as well as geometric formulations of integrability in the calculus of variations and in the geometry of Lax pairs and treatises on the geometry of conservation laws and variational problems in elliptic, hyperbolic and parabolic PDEs and exterior differential systems.
  • All of these areas, and many others in algebraic geometry, including web geometry, integrable systems, and
  • Riemann surfaces, are currently seeing important developments that were stimulated by his work.
  • His teaching career and research leadership has inspired an astounding number of mathematicians who have gone on to stellar careers, both in mathematics and other disciplines. He has been generous with his time, writing many classic expository papers and books, such as “Principles of Algebraic Geometry”, with Joseph Harris, that have inspired students of the subject since the 1960s.
  • Griffiths has also extensively supported mathematics at the level of research and education through service on and chairmanship of numerous national and international committees and boards committees and boards. In addition to his research career, he served 8 years as Duke’s Provost and 12 years as the Director of the Institute for Advanced Study, and he currently chairs the Science Initiative Group, which assists the development of mathematical training centers in the developing world.
  • His legacy of research and service to both the mathematics community and the wider scientific world continues to be an inspiration to mathematicians world-wide, enriching our subject and advancing the discipline in manifold ways.
Aug 122014
 

明天上午(韩国时间, 东九区时间)九点, ICM 2014 会准时在韩国首尔(Coex , Seoul , Korea)开幕. 依惯例, 开幕式上会为引人注目的 Fields Medal 获得者颁发奖章. 坊间流传的一个(如若发生)会载入历史的传奇是:

本届 ICM 会有一个女性数学家获得 Fields Medal!

这真是一个令人振奋的消息! 全世界的数学工作者屏住呼吸兴奋的等待着亲眼目睹见证这个激动人心的时刻!

Maryam Mirzakhani(born May 1977) is an Iranian mathematician, Professor of Mathematics (since September 1, 2008) at Stanford University.

Maryam Mirzakhani 是今年非常有力的竞争者, 和任何候选人站在一起都是那样出众引人注目. 她还是 IMO 满分.

1995 年, 今年中国领队姚一隽去加拿大参加 IMO 的时候, 这一年也是张筑生第一次做领队, 一共有 14 个满分, 其中有两个女生: 咱们中国的朱晨畅, 现在在德国 Gottingen University; 来自伊朗的 Maryam Mirzakhani, 8 月 16 日上午作 ICM 一小时报告.

很多人看好法国的 Sophie Morel. Sophie Morel 专长数论. 不过, 恐怕 Sophie Morel 今年拿不到奖章, 但她四年后还有一次机会.

此外, Laure Saint-Raymond 和 Marianna Csörnyei 也是相当给力的人选.

一个不好的消息是: 国际数学家大会召开在即, 韩劝阻埃博拉(Ebola virus)疫区数学家不要与会.

Aug 052014
 

ICM 2014 Program
这届国际数学界大会(International Congress of Mathematicians, ICM)的安排, 已经明确无误的说明:

 4 个数学家将获得本届大会的 Fields Medal.

张大师将于 8 月 21 日作 ICM 闭幕式之前的压轴报告, 这是只有今年的 Fields Medalist, Gauss Prize, Chern Medal 得主才有的殊荣

张益唐 7 月1 日在北大本科生毕业典礼有一个讲话

这个暑假, 张大师在中国科学院晨兴数学中心和他的母校北京大学做了好几次讲座.

1. A Transition Formula for Mean Values of Dirichlet Polynomials
2014,6.23./6.25. 9:30-11:30
晨兴 110
主持人: 王元

2. 关于 Siegel 零点
2014.7.2.9:30-11:30
晨兴 110

3. Distribution of Prime Numbers and the Riemann Zeta Function
July 8, 10, 2014 16:00-17:00, 镜春园82号甲乙丙楼的中心报告厅
July 15, 16:30-17:30 镜春园 78 号院的 77201 室.
主持人: 刘若川

4. 关于 Siegel 零点(2)
014.7.16./7.30./8.4./8.6. 9:30-11:30
N820

Jul 242014
 

Conjecture

There exist elliptic curve groups \(E(\Bbb Q)\) of arbitrarily large rank.

用 \(r\) 表示 \(\Bbb Q\) 上的椭圆曲线 \(E\) 的秩—the rank of the Mordell–Weil group \(E(\Bbb Q)\).

一个悬而未决的著名难题是: \(r\) 是否可以任意大?

Martin-McMillen 2000 年有一个 \(r\geq24\) 的例子:

\begin{equation*}\begin{split}y^2+xy+y&=x^3-120039822036992245303534619191166796374x\\&+ 504224992484910670010801799168082726759443756222911415116\end{split}\end{equation*}

Hasse-Weil \(L\)-function \(L(s, E)\) 在 \(s=1\) 处的零点的阶数 \(r_a\) 称为 \(E\) 的 analytic rank(解析秩).

Manjul Bhargava, Christopher Skinner, Wei Zhang(张伟) 7 月 7 日在 arXiv 上传的论文 “A majority of elliptic curves over \(Q\) satisfy the Birch and Swinnerton-Dyer conjecture“, 宣布了取得的进展:

  1. \(\Bbb Q\) 上的椭圆曲线, when ordered by height(同构类以高排序), 至少有 \(66.48\%\) 满足 BSD conjecture;
  2. \(\Bbb Q\) 上的椭圆曲线, when ordered by height, 至少有 \(66.48\%\) 有有限 Tate–Shafarevich group;
  3. \(\Bbb Q\) 上的椭圆曲线, when ordered by height, 至少有 \(16.50\%\) 满足 \(r=r_a=0\), 至少有 \(20.68\%\) 满足 \(r=r_a=1\).

谁将在 8 月 13 日的 ICM 2014 开幕式上获得 Fields medal?坊间向来不缺传闻. 数论大牛 Manjul Bhargava 无疑是最耀眼的明星.

Jul 112014
 

张益唐暑假在北京.

7 月他在母校北京大学的北京国际数学研究中心 (BICMR) 有一个系列的学术报告: Distribution of Prime Numbers and the Riemann Zeta Function I, II, III. 这个报告分三场, 原定时间是 July 8, 10, 15,  2014 16:00-17:00, 地点是镜春园 78 号院的 77201 室.

BICMR 官网上这个报告的 Abstract 是这么写的:

The distribution of prime numbers is one of the most important subjects in number theory.

There are many interesting problems in this field. It may not be difficult to understand the problems themselves, but the solutions are extremely difficult.

In this series of talks we will describe the application of certain analytic tools to the distribution of prime numbers. In particular, the role played by the Riemann zeta function will be discussed. We will also describe some early and current researches on the Riemann Hypothesis.

These talks are open to everyone in the major of mathematics, including undergraduate students.

Yitang Zhang at BICMR Distribution of Prime Numbers and the Riemann Zeta Function

Yitang Zhang at BICMR :Distribution of Prime Numbers and the Riemann Zeta Function

8 日下午 4 点, 田刚现身. 因为人比较多, 改为在镜春园82号甲乙丙楼的中心报告厅进行. 主持人刘若川是 1999 年的 IMO 金牌(他本来也是 1998 年中国国家队的队员).

报告从复分析开始, 解析开拓,  zeta 函数的定义, 留数定理, 伯努利数, 然后

\[\zeta(2k)=\sum_{n=1}^\infty\frac1{n^{2k}}=(-1)^{k+1}\frac{(2\pi)^{2k}B_{2k}}{2(2k)!}\]

的两个证明:一个是欧拉给的, 一个来自 Riemann.

张大师说: 欧拉的算功无双, 本来可以证明 \(\zeta(3)\) 是无理数的, 他错过了这个证明.

听报告的人, 会知道张大师非常强调复变函数的极端重要性! 复变不行的人, 没法玩解析数论.

10 日下午 4 点的第二场, 依旧在镜春园82号甲乙丙楼的中心报告厅. 不过, 15 日的一场会在镜春园 78 号院的 77201 室, 16:30 开始.

大量的使用复变, 满黑板的解析数论公式. 今天的主要任务是质数定理的证明, 以及黎曼假设在质数分布的作用.

15 日下午 4:30 的最后一场, 要深入一点. 田刚坐在教室最后一排, 刘若川, 许晨阳坐在教室左边的走廊.张大师谈到有 Goldston, Pintz and Yildirim 的工作, 说他自己最大的贡献是把 \(c\) 改进为 \(\dfrac14+\dfrac1{1168}\). 

Jul 012014
 
Yitang Zhang speaks at 2014 Undergraduate graduation ceremony of Peking University

Yitang Zhang speaks at 2014 Undergraduate graduation ceremony of Peking University

7月1日, 北京大学2014年本科生毕业典礼暨学位授予仪式在邱德拔体育馆举行. 张益唐作为校友代表发言.

他首先向毕业生们分享了自己多年来的经历与感悟, 并告诫同学们金钱不是唯一的选择标准, 北大人要有志于做学问, 不要轻易放弃理想, 要敢做大学问, 攻克大问题. 张益唐希望北大人要谦虚, 即使在获得荣誉与成就之后也要踏踏实实. 演讲过程中, 同学们的掌声不断, 大家都被这个一心做大学问的数学家所鼓舞.

校党委书记朱善璐, 校长王恩哥, 学校原党委书记闵维方等出席了典礼. 信息科学技术学院杨芙清院士, 中文系袁行霈教授, 数学科学学院姜伯驹院士等学者代表, 教师代表, 历史系钱乘旦教授, 校友代表, 美国新罕布什尔大学张益唐教授等参加毕业典礼. 全国百余所重点中学的校领导及毕业30年, 50年的北大校友代表应邀来到现场, 共同见证新一届北大毕业生的重要时刻. 毕业典礼由副校长高松主持.

张大师的演讲全文

同学们好!(掌声)

我先讲一下我这个人不大善于在这样的场合做公开讲话,所以我能讲到哪儿是哪儿~(掌声,叫好)

Yitang Zhang speaks at 2014 Undergraduate graduation ceremony of Peking University

Yitang Zhang speaks at 2014 Undergraduate graduation ceremony of Peking University

今天能够回到母校,和众多的学弟学妹见面,我的心情是非常高兴、而且非常激动的。离开母校那么多年,我经常是在怀念这个母校,母校给我打下的扎实的学术基础,还有周围那个师长曾经教过我的。今天在一起,尽管我们年龄差可能差很大,但我们说一句话:我们都是北大人。(掌声,张招牌推手,笑声)

好,我回想起在母校求学的时候的有很多很多事情,今天我想讲一个事情。我在这里读本科的时候,年龄已经比你们现在要大几岁,也就是那时候我已经即将要告别青春了。(轻微笑声)有一次呢我读了一篇中国科学,呃不是中国科学,中国青年上的文章,叫《我们还年轻》。我不想就复述这整个的这篇文章的内容,我只想引用一句话。这里头提到有一位前辈——我也不知道他的名字——这位前辈对年轻人说:如果我是你们中间的一个,哪怕是最倒霉的一个,我仍然觉得十分的荣幸。因为你们年轻,你们有未来。(掌声,张摊手)

现在想起来这已经三十多年过去了,时间过得是真快啊。闲云潭影日悠悠,物换星移几度秋。(掌声,张做表情,胡乱摆手,众大笑。)今天我又回到母校我站在这里当我回想这篇文章的时候,我应该把它改一个字,叫:你们还年轻,你们有未来,你们的前程将是繁华似锦。(正常掌声。)

今年二月在 Princeton 大学的中国学生春节晚会上,我说过一句话,这里我把这句话再重复一遍。我说什么呢?我很xuan(羡?)慕你们,xuan慕我的学弟学妹,你们现在各方面的条件你们的机会你们、很多地方都比我们那时候要好得多。比方说你们现在的物质条件跟几十年前我们,同样也是在北大同样这一片地方求学的时候,那是,不是一个数量级的。

我很xuàn慕你们。那么,在xuàn慕你们的同时,是不是我也应该鼓励你们呢?但我想今天在这里,我觉得我不是来教导你们的。我只是想谈一下我自己,就说人生经历过来有些体会,跟大家、跟大家交流一下。

第一呢,你们现在毕业了,就要告别校园。一部分,你们可能要进那个研究生院,继续深造;一部分要走上社会要选择不同的职业。我们知道现在这个社会是很多元化的,人生选择是很多的。从我自己来讲,我也不能说是哪一种选择就一定是好,你选择这个职业就一定是好,选择那个就一定不好。这个你们都可以、都可以去选择。但我想提一点我自己的建议:我不相信金钱是,就现在我们选唯一的选择标准。也许,我们可以挣很多钱,但赚钱赚多了并不一定就等于说你的,呒,你的人生就确实有意义。这个这方面是,我我是这么坚信的。所以,如果我们是有志于做学问的话,我建议你不要轻易放弃你的理想。我们是北大人,所以我们把做学问是看得很高的。而且,我们北大人应该有这样一种气魄:我们敢做大的学问!我们敢攻克大的难题!(掌声,张全身抖动一次)对不起啊!

当然这里我说一下做大的问题,我也不是建议说你去做大问题不做小问题,因为这在现实生活中可能这是很难做到的,这我们都知道。但我希望至少我们有这么一种气魄,我们至少,我们一直在关注着大的问题的。这是可以的。

那好刚才我说到是气魄,我们要有大的气魄。但我们要具体做学问,其实我想不光[管?]是做学问,做任何一种事情可能都是这样的。我要提另外一个词:谦虚。我们来做,气魄大,我们敢做。但做的时候,谦虚,我相信这一点。做学问,我也许我想做别的可能也一样,这是一个实实在在的事情,不要把,事先啊,把自己设定得太高。我为什么说不要把自己设定太高呢?可能会有一点:我觉得我这人聪明得不得了,我过来我做什么我都能做成,我攻无不克战无不胜。如果那样的话,可能在现实中间,你的失落感将来到时候会更强。真正做学问的,就是一个实实在在的问题。如果一开始你并没有把自己就设定得太高,我们就实实在在来做。我就想讲一下我自己的例子。我做什么孪生素数啊,就是说,现在也算是出名了。但我想我那时候怎么做的呢?我没有觉得啊呀我这个人怎么聪明我、我真没有这个感觉。在具体做的过程中,我经常觉得自己的程度很差,这是真的。但程度差我我并不失落,我就实实在在地这么去做。这个中间有很多挫折,但是每一次我都能坚持下去。如果别人说你有什么成功的秘诀,我只能说,说大实话,我就实实在在这么去做学问,而且坚持着做。我过去是这样的,将来也会这样的。正因为你对自(掌声。大屏幕上播出一男生模仿张推手。众大笑,张回头看屏幕,似未看到这一幕)怎么啦?

正因为你对自己你你你抱有着很谦虚的一种心态,那么就我这个一年多来也算是出了名了。但出了名以后不管这个媒体啊什么啊怎么说我啊别人怎么想啊,我觉得有一点我很满意,我没有趾高气扬,我没有得意忘形,我没有狂妄自大。这三句成语都不是好话,(轻微笑声)但我确实我没有。为什么我没有呢?因为很简单,我心里很清楚,我不认为自己有那么了不起。我过去是实实在在的,很谦虚我们就很低调做过来,将来我还会这样的。

在这里呢,我就顺便提一下,我想也许我们的学弟学妹有人有这样的经历。你们都是高分进入北大的,在进入北大之前,会不会有一种感觉,呒,周围没有一个人像我这么聪明的。(轻微笑声)但进来以后呢,哎周围怎么有很多人跟我一样聪明,甚至有人比我更聪明呢?这样也许会有一种失落感,这是正常的。但你真正在做学问的时候,不要把这种东西看得太重。有失落感可能是正常的,但是不要搞弄的过分了,可能会自暴自弃,这并不是一件好事情。

另外呢,我就是希望我们的学弟学妹,以后不管是在做学问,还是在其他领域里不管做什么工作,有一样我们说不要怕困难。不要怕困难。当然不要怕困难我也可以说豪言壮语,(张握拳头)我这人什么困难我都不怕,我一定……其实那个不一样,有时候对待现实中间的挫折,特别像我这个经验。你们不要说好像我现在是出名了,其实我犯过很多很多愚蠢的错误,也遇到过很多失败很多挫折。这个时候我的建议是不妨你内心就淡定一点,你失败一次就是一个新的起点和开头。这样,就,我们有这样的心态,我相信,我还是说一下,我们是北大人,我们将来能应该能够为我们的民族,为整或甚至为整个世界人类做出很大的贡献。

最后,我愿意向在座的学弟学妹表示衷心的祝福,祝福你们的未来。你们还年轻!(张手舞足蹈一番。掌声)

注释
  1. 本文节选自北京大学新闻网 7 月 2 日新闻 “北大举行2014年本科生毕业典礼暨学位授予仪式”.
  2. 7 月 23 日补充的张的演讲全文, 最早可能出现在人人网, 也可能是豆瓣. 这里根据视频对错处做了一些修正.