会议手册 CONFERENCE...

CONFERENCEMANUAL

会议手册

INTERNATIONAL FORUM

ON MATHEMATICS AND

HISTORY OF MATHEMATICS

—DEDICATED TO

THE 100TH BIRTHDAY OF

WEN-TSUN WU

2019.05.09-10

TABLE OF CONTENTS

02030303040505

06

06

07

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08141620

Scientific Committee

Keynote Speakers

Plenary Speakers

Masters Forum

Invited Speakers

Local Information

Conference Venue

Accommodation

Shuttle Bus Service

Internet Access

Map

Schedule by Day

Abstracts of Keynote Speeches

Abstracts of Plenary Speeches

Abstracts of Invited Speeches

纪念吴文俊院士诞辰一百周年暨

数学科学与数学史国际学术研讨会

KEYNOTE SPEAKERSIn Alphabetical Order

Xiaoshan GaoAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Banghe LiAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Wenlin LiAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

PLENARY SPEAKERSIn Alphabetical Order

Feimin HuangAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Ruo LiPeking University

Binyong SunAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Tong YangCity University of Hong Kong

Jiayu LiUniversity of Science and Technology of China

Weixiao ShenShanghai Center for Mathematical Sciences, Fudan University

Zhouping XinChinese University of Hong Kong

Xiangdong YeUniversity of Science and Technology of China

Jiping ZhangPeking University

MASTERS FORUMWen-Tsun Wu and Mathematics in China

In memory of SJTU alumnus Wen-Tsun Wu, our distinguished guests of this forum present:Wen-Tsun Wu and his contributions

Mathematics in China: Past, Present and Future

Mathematics at SJTU

03

SCIENTIFIC COMMITTEEIn Alphabetical Order

Members

Chairs

Hanfu ChenAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Shuxing ChenFudan University

Karine ChemlaLaboratoire de Philosophie et Histoire des Sciences , Centre National de la Recherche Scientifique–Université Paris 7

Joseph W. DaubenGraduate Center of the City University of New York

Fuquan FangCapital Normal University

Jiaxing HongFudan University

Boju JiangPeking University

Zhongqin LinShanghai Jiao Tong University

02

INTERNATIONAL FORUM

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2019.05.09-10

纪念吴文俊院士

诞辰一百周年

暨

数学科学与数学史

国际学术研讨会

Jianshu LiHong Kong University of Science and Technology

Daqian LiFudan University

Song JiangInstitute of Applied Physics and Computational Mathematics

Lei GuoAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Zhongci ShiAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Zhiming MaAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Dongming WangBeihang University

Gongqing ZhangPeking University

Nanhua XiAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Zhongqin XuNational Natural Science Foundation of China

Shicheng WangPeking University

Yaxiang YuanAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Jia'an YanAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

Xiaochun SunUniversity of Chinese Academy of Sciences

Shige PengShandong University

Jens HøyrupRoskilde University

Qun LinAcademy of Mathematics and Systems Science, Chinese Academy of Sciences



Xiaoshan GaoAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

INVITED SPEAKERSIn Alphabetical Order

LOCAL INFORMATION

04 05

Andrea BreardUniversité Paris SudFaculté des sciences d'Orsay

Joseph W. DaubenCity University of New York

Jinhai GuoInstitute for the History of Natural Sciences, Chinese Academy of Sciences

Shuchun GuoInstitute for the History of Natural Sciences, Chinese Academy of Sciences

Jens HøyrupRoskilde University

Jiri HudecekCharles University

Young Wook KimDept. of Math. and Korean Society for History of Mathematics, Korea University

Karine ChemlaSPHERE, CNRS & Université Paris Diderot

Kehui DengDonghua University

Shirong GuoInner Mongolia Normal University

Qi HanInstitute for the History of Natural Sciences, Chinese Academy of Sciences

Sung Sa HongSogang University

Zhigang JiShanghai Jiao Tong University

Tatsuhiko KobayashiSeki Takakazu Institute of Mathematics,Japan

CONFERENCE VENUE

Opening Ceremony and Keynote Speeches

09:00-11:30, May 9. 2019

Room 100, Chen Ruiqiu Building, SJTU Minhang Campus

Symposium for Advancement of Mathematics at SJTU

14:00-18:30, May 9, 2019

1F, Lecture Hall, Academic Exchange Center, SJTU Minhang Campus

Talks on History of Mathematics (Session I & Session II)

13:30-17:40, May 9, 2019

2F, Academic Function Room (B), Academic Exchange Center, SJTU Minhang Campus

Forum on Frontiers of Mathematics

08:30-12:10, 14:00-18:05, May 10, 2019


Talks on History of Mathematics (Session III - Session VII)

08:30-11:40, 13:30-18:20, May 10, 2019


May 9. 2019

May 10. 2019

INTERNATIONAL FORUM

ON MATHEMATICS AND


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2019.05.09-10


诞辰一百周年

暨



Shijun LiaoShanghai Jiao Tong University

Chunjing XieShanghai Jiao Tong University

Feng XieShanghai Jiao Tong University

Zhenli XuShanghai Jiao Tong University

Lei ZhangShanghai Jiao Tong University

Miaomiao ZhuShanghai Jiao Tong University

TALKS ON HISTORY OF MATHEMATICS

SYMPOSIUM FOR ADVANCEMENT OF MATHEMATICS AT SJTU

Zhonglai LiBeijing Normal University

Kostas NikolantonakisUniversity of Western Macedonia

Qijin OuShanghai Jiao Tong University

Rina SaShanghai Jiao Tong University

Zelin XuDonghua University

Zhaohua LiTianjin Normal University

Dun LiuInstitute for the History of Natural Sciences, Chinese Academy of Sciences

Tsukane OgawaYokkaichi University

Yonghong Qian

Yusheng Wang China Science and Technology Museum

Dahai ZouInstitute for the History of Natural Sciences, Chinese Academy of Sciences

LOCAL INFORMATION

06 07

ACCOMMODATION

Academic Exchange Center, SJTU Minhang Campus

800 Dongchuan Road, Minhang District, Shanghai

No. 7 Building of Xue Yuan Center of COMAC

100 East Jiangchuan Road, Minhang District, Shanghai

SHUTTLE BUS SERVICE MAP

Date Time Route

INTERNATIONAL FORUM

ON MATHEMATICS AND


—DEDICATED TO


WEN-TSUN WU

2019.05.09-10


诞辰一百周年

暨



08:30

08:40

11:30

20:00

May 9

May 10

Xue Yuan Center of COMAC – Chen Ruiqiu Building

Academic Exchange Center – Chen Ruiqiu Building

Chen Ruiqiu Building – Liu Yuan Restaurant

Academic Exchange Center – Xue Yuan Center of COMAC

08:10

20:00

Xue Yuan Center of COMAC – Academic Exchange Center

Academic Exchange Center – Xue Yuan Center of COMAC

Wi-Fi: SJTUUser Name: wtw_math, wtw_math2Password: math58513

Eduroam is available on campus as well.

INTERNET ACCESS

Si YuanGate

AcademicExchange

Center

Si YuanGate

AcademicExchange

Center

Chen RuiqiuBuilding

Chen RuiqiuBuilding

南洋南路

元

培

路

South Nan Yang Road

Yuan Pei R

oad

SCHEDULE BY DAY

08 09

09:00-10:00 Opening Ceremony

09:00-09:10　Commemoration Video of Wen-Tusn Wu09:10-09:20　Introduction of Guests 09:20-09:30　Welcome Address by Sixian Jiang Secretary of the CPC Committee, SJTU Chairman of the University Council09:30-09:35　Address by Yaxiang Yuan

Vice President of China Association for Science and TechnologyPresident of Chinese Mathematical SocietyMember of Chinese Academy of Sciences

09:35-09:40　Address by Nanhua XiPresident of Academy of Mathematics and Systems Science, Chinese Academy of SciencesMember of Chinese Academy of Sciences

09:40-09:45　Address by Boju JiangSchool of Mathematical Sciences, Peking UniversityMember of Chinese Academy of SciencesCo-chair of Scientific Committee of the Forum

09:45-09:50　Address by Tianjiao Wu Son of Wen-Tsun Wu09:50-10:00　Launch Ceremony of Wu Wen-Tsun Center of Mathematical Sciences, SJTU

10:00-11:30 Keynote Speeches

Chair: Jianshu Li Member of Chinese Academy of Sciences, Chair Professor of Hong Kong University of Science and Technology

Symposium for Advancement of Mathematics at SJTU

14:00-16:00 Masters Forum: Wen-Tsun Wu and Mathematics in China

16:00-16:20 Tea Break

16:20-18:30 Report on Research Progress

18:30 Dinner

14:00-18:30


Afternoon, May 9, 2019

Congming LiShanghai Jiao Tong University

Time Speaker Title

Registration

09:00-20:00

Academic Exchange Center & No. 7 Building of Xue Yuan Center of COMAC

May 8, 2019

09:00-11:30

Room 100, Chen Ruiqiu Building, SJTU Minhang Campus

Zhongqin Lin, SJTU President, Member of Chinese Academy of Engineering

Morning, May 9, 2019

INTERNATIONAL FORUM

ON MATHEMATICS AND


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诞辰一百周年

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16:20-16:30 Introduction to School of Mathematical Sciences, SJTU

Shijun LiaoShanghai Jiao Tong University16:30-16:50 Homotopy Analysis Method and Its Applications

Chunjing XieShanghai Jiao Tong University Stability of Hagen-Poiseuille Flows in a Pipe

Feng XieShanghai Jiao Tong University

Vanishing Viscosity Limit and Boundary Layer Theory in Magneto-Hydrodynamics

Zhenli XuShanghai Jiao Tong University Towards the Fastest Poisson Solver for Particle Simulations

Lei ZhangShanghai Jiao Tong University

Optimal Coarse Graining of Multiscale Problems — from Numerical Homogenization to Coupling

Miaomiao ZhuShanghai Jiao Tong University18:10-18:30

16:50-17:10

17:10-17:30

17:30-17:50

17:50-18:10

Geometric Analysis of a Mixed Elliptic-parabolic Conformally Invariant Boundary Value Problem

10:00-10:30　Banghe Li Member of Chinese Academy of Sciences, Professor of Academy of Mathematics and Systems Science, Chinese Academy of Sciences On Academician Wu Wen-Tsun's Legacy of History of Mathematics10:30-11:00　Xiaoshan Gao Professor of Academy of Mathematics and Systems Science, Chinese Academy of Sciences Wen-Tsun Wu and Mathematics Mechanization11:00-11:30　Wenlin Li Professor of Academy of Mathematics and Systems Science, Chinese Academy of Sciences On Academician Wu Wen-Tsun's Legacy of History of Mathematics

SCHEDULE BY DAY

10 11

13:30-15:30 第一场，主持人：纪志刚Session I, Chair: Zhigang Ji

13:30-14:00 Joseph Dauben（美国） Wu Wen-Tsun and Ancient Chinese Mathematics吴文俊与中国古代数学

15:40-17:40 第二场，主持人：韩琦Session II, Chair: Qi Han

15:40-16:10 Jiri Hudecek（捷克）Wu Wen-Tsun’s Work on the Layout of Integrated Circuits and its Place in the Formation of His “Mechanization of Mathematics吴文俊对集成电路布局的研究及其在形成他的“数学机械化”中的地位

16:10-16:40 Andrea Breard（法国）A Handshake away from Wu Wen-Tsun in Paris在巴黎握手告别吴文俊

16:40-17:10 Kostas Nikolantonakis（希腊）Mechanical Solutions of Geometric Problems in the History of Mathematics: Archimedes and Wu Wen-Tsun数学史中几何问题的机械化解法：阿基米德和吴文俊

17:10-17:40 郭世荣Some Aspects of Algorithmic, Mechanization and Constructiveness of Traditional Chinese Mathematics中国传统数学的算法化、机械化与构造性的若干侧面

Dinner晚餐

18:00

14:00-14:30 Karine Chemla（法国）Wu Wen-Tsun’s Talk at the 1986 International Congress of Mathematicians and the Understandingof Qin Jiushao’s Treatment of the “Chinese remainder theorem”吴文俊在1986年国际数学家大会上的演讲及其对秦九韶“中国剩余定理”解法的理解

14:30-15:00 Jens Høyrup（丹麦）On Being First, Being Wrong and Being Right: Knuth, “Knuth”, Wu Wen-Tsun, and Algorithms关于优先、错误和正确：高德纳、“高德纳”、吴文俊，以及算法

15:00-15:30 刘钝

15:30-15:40

The Drawing Boards of Pythagoras and Euclid in Raphael’s School of Athens拉斐尔“雅典学园”中毕达哥拉斯与欧几里得的画板

Tea Break茶歇

Forum on Frontiers of Mathematics

08:30-12:10, 14:00-18:05


May 10, 2019Talks on History of Mathematics (Session I & Session II)

13:30-17:40, May 9, 2019


INTERNATIONAL FORUM

ON MATHEMATICS AND


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2019.05.09-10


诞辰一百周年

暨



Time Speaker Title

08:30-08:40 Opening Ceremony

Xiangdong YeUniversity of Science and Technology of China08:40-09:25 The Structure Theorems and Applications

Zhouping XinChinese University of Hong Kong09:25-10:10 Transonic Shock and Mixed Type Equations

10:10-10:40

Tong YangCity University of Hong Kong10:40-11:25

Some Studies on the Boltzmann Equation without Angular Cutoff

Binyong SunAcademy of Mathematics and Systems Science,Chinese Academy of Sciences

11:25-12:10Arithmetic of Automorphic L-Functions and Cohomological Test Vectors


15:50-16:35The Limit of the Boltzmann Equation to the Euler Equations for Riemann Problems

Jiayu LiUniversity of Science and Technology of China14:00-14:45 Canonical Metrics on Reflexive Sheaves

Jiping ZhangPeking University

17:20-18:05 Block Algebras of Finite Groups


14:45-15:30Some Applications of Thurston’s Algorithm in Complex Dynamics

12:10-14:00

Ruo LiPeking University16:35-17:20

13-Moment System with Global Hyperbolicity for Quantum Gas

Tea Break

Lunch Break

15:30-15:50 Tea Break

SCHEDULE BY DAY

12 13

08:30-10:00 第三场，主持人：徐泽林Session III, Chair: Zhelin Xu

08:30-09:00 小林龍彦（日本） What is Mathematics in Wasan, in Karasan and in Kōmōsan?-From an recognition of strategist Arisawa Munesada和算、唐算、红毛算中的数学是什么？--来自兵法家有沢致貞的认识

09:00-09:30 洪性士（韩国）Western Mathematics in the Joseon Dynasty朝鲜王朝中的西方数学

10:10-11:40 第四场，主持人：邓明立Session IV, Chair: Mingli Deng

10:10-10:40 小川束（日本）Seki Takazu’s Theory on Algebraic Equations in Pre-modern Japan日本前现代时期关孝和关于代数方程的理论

10:40-11:10 金英郁（韩国）Gougushu of Korea and Chinese Mathematics韩国的勾股术和中国数学

11:10-11:40 李兆华Supplementary Proof and Interpreting on Liu yueyun’s Ceyuan Haijing Tongshi

《测圆海镜通释》补证与解读

12:00-13:30 Lunch

午餐

Talks on History of Mathematics (Session III - Session VII)

08:30-11:40, 13:30-18:20


INTERNATIONAL FORUM

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诞辰一百周年

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国际学术研讨会 09:30-10:00 韩琦Li Yan and the Early Stage in the Historiography of Chinese Mathematics李俨与中国数学史研究的初创时期

10:00-10:10 Tea Break

茶歇

13:30-15:30 第五场，主持人：冯立昇Session V, Chair: Lisheng Feng

13:30-13:50 邹大海Wu Wen-Tsun’s“Recovery of Ancient Demonstration” and Qian Baocong’s “Historism”吴文俊的“古证复原”与钱宝琮的“历史主义”

15:40-17:20 第六场，主持人：王青建Session VI, Chair: Qingjian Wang

15:40-16:00 郭书春Endless Memory--Edification and Encouragement (Continuation) 无尽的怀念⸺教诲与鞭策（续）

17:20-18:10 第七场，座谈会，主持人：曲安京Session VII, Discussion, Chair: Anjing Qu

Develop Wu Wen-Tsun’s Legacy of Mathematics, Boost the Study of the History of Chinese Mathematics in the New Era

弘扬吴文俊的数学遗产，推进新时代中国数学史研究

18:10-18:20 闭幕式主持人：郭世荣 Closing Ceremony Host: Shirong Guo

16:00-16:20 王渝生Remebering Wu Wen-Tsun's Inculcation缅怀吴文俊先生的谆谆教诲

16:20-16:40 李仲来Talking about the Cooperation between Professors Shangshu Bai and Wu Wen-Tsun从白尚恕与吴文俊教授的合作谈起

16:40-17:00 钱永红 Wu Wen-Tsun and The history of Chinese Mathematics吴文俊与《中国数学史》

17:00-17:20 郭金海The Whole Story of Wu Wen-Tsun Winning the First Prize in Scientific Award of Chinese Academy of Sciences中国科学院科学奖金评奖吴文俊折桂始末

18:30 Dinner

晚餐

13:50-14:10 徐泽林An Interpretation of Wu Wen-Tsun's historical view of Chinese Traditional Mathematics in Wasan和算成就对吴文俊中算史观的诠释

14:10-14:30 萨日娜A Study of the Role of the Maritime Silk Road in the Spread of the Traditional Chinese Mathematics in Japan海上丝绸之路与中国传统数学在域外的传播研究

14:30-14:50 邓可卉Ancient Chinese Mathematics under the Field Vision of Wu Wen-Tsun吴文俊眼中的中国古代数学

14:50-15:10 纪志刚Wu Wen-Tsun's “Silk Road Spirit” and its Significance to the Study of Mathematical Communication between China and Foreign Countries吴文俊“丝路精神”及其对中外数学交流的意义

15:10-15:30 欧七斤The Starting Point of Mathematical Life：Wu Wen-Tsun 's Four-year Study in Chiao-tung University（1936-1940）步入数学王国：吴文俊在交通大学（1936-1940）

15:30-15:40 Tea Break

茶歇

15

ABSTRACTS OF KEYNOTE SPEECHES

Wen-Tsun Wu and Mathematics Mechanization

Xiao-Shan GaoAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

In this talk, we first introduce the Program of Mathematics Mechanization proposed by Wu, and then give a

brief summary of Wu's work on automated theorem proving, the Ritt-Wu characteristic set method for

symbolic polynomial system solving, and applications in various fields. Finally, we list some research results

influenced by Wu's work on mathematics mechanization.

Great Contributions of Wen-Tsun Wu to Topology


The talk includes:

1. Epoke-making contributions to characteristic classes

2. Originally creating classes of embedding, immersion and isotopy

3. I*-measure

On Academician Wu Wen-Tsun's Legacy of History of Mathematics


Wu Wen-Tsun initiated his impacting research on the history of ancient Chinese mathematics since middle of

the seventeenth of the last century, which constitutes a valuable heritage of history of mathematics. This talk

discusses Wu’s major contributions in the field of history of mathematics.

1.Wu’s theory of mechanization of mathematics offers an excellent example of using history in one’s research

in mathematics

2.Wu’s original view of main-lines of historical development of mathematics opens a new epoch in studies of

history of ancient Chinese mathematics.

3. Wu Wen-Tsun’s Silk Road Foundation of Mathematics and Astronomy is a scientific programme of

far-reaching significance which encourages young scholars to study in mathematical and astronomical

exchanges between China and other countries in history and to explore the multi-cultural origins of modern

mathematics.

At the ending part Wu Wen-Tsun’s contribution to the history of ancient Chinese mathematics is further

appraised by debating certain different comments upon Wu’s work.

17

The Limit of the Boltzmann Equation to the Euler Equations for Riemann Problems


The convergence of the Boltzmann equation to the compressible Euler equations when the Knudsen number

tends to zero has been a long standing open problem in the kinetic theory. In the setting of Riemann solution

that contains the generic superposition of shock, rarefaction wave and contact discontinuity to the Euler

equations, we succeed in justifying this limit by introducing hyperbolic waves with different solution

backgrounds to capture the extra masses carried by the hyperbolic approximation of the rarefaction wave and

the diffusion approximation of contact discontinuity.

13-Moment System with Global Hyperbolicity for Quantum Gas

Ruo Li School of Mathematical Sciences, Peking University

We point out that the quantum Grad's 13-moment system given by Yano is lack of global hyperbolicity, and even

worse, the thermodynamic equilibrium is not an interior point of the hyperbolicity region of the system. To

remedy this problem, we split Grad's expansion into the equilibrium part and the non-equilibrium part, and

propose a regularization for the system. This provides us a new model which is hyperbolic for all admissible

thermodynamic states, and meanwhile preserves the approximate accuracy of the original system. We note

that this procedure is not a trivial application of the theory we developed in the last years.

Canonical Metrics on Reflexive Sheaves

Jiayu LiSchool of Mathematical Sciences, University of Science and Technology of China

We will first recall the stability of vector bundles and Donaldson-Uhlenbeck-Yau theorem. Then we will talk

about Bando-Siu’s generalization of the DUY theorem to reflexive sheaves, i.e. the existence of canonical

metrics on reflexive sheaves. Finally we prove the Bando-Siu conjecture which are joint work with Xi Zhang and

Chuanjing Zhang.

ABSTRACTS OFPLENARY SPEECHES

ABSTRACTS OF PLENARY SPEECHES

1918

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Some Studies on the Boltzmann Equation without Angular Cutoff

Tong YangDepartment of Mathematics, City University of Hong Kong

After reviewing the progress on the Boltzmann equation without angular cutoff in recent years both on spatially

homogeneous and inhomogeneous Boltzmann equation, I will present two results. One is about the

regularizing effect of the homogeneous Boltzmann equation with Debye-Yukawa potential for measure valued

solutions.

Another one is about the well-posedness of perturbative solution to the inhomogeneous Boltzmann equation

when the initial perturbation has only algebraic decay in the velocity variable.

Some Applications of Thurston’s Algorithm in Complex Dynamics


Thurston introduced an algorithm in his study of dynamics of a branched covering of S^2. The algorithm

produces a sequence of rational maps which converge under suitable conditions. In the talk, I will discuss

applications of this algorithm to transversality problems and also to the study of renormalization for

multicritical polynomials.

Arithmetic of Automorphic L-Functions and Cohomological Test Vectors

Binyong SunAcademy of Mathematics and Systems Science, Chinese Academy of Sciences

It was known to Euler that $\zeta(2k)$ is a rational multiple of $\pi^{2k}$, where $\zeta$ is the Euler-Riemann

zeta function, and $k$ is a positive integer. Deligne conjectured that similar results holds for motives over

number fields, and automorphic analogue of Deligne's conjecture was also expected. I will explain the

automorhic conjecture, as well as some recent progresses on it. The Archimedean theory of cohomological

representations and cohomological test vectors will also be explained, as they play a key role in the proof.

The Structure Theorems and Applications

Xiangdong YeSchool of Mathematical Sciences, University of Science and Technology of China

In this talk (1) we discuss Furstengberg's structure theorem of an ergodic system and its application to

multiple ergodic recurrence. (2) we discuss Host-Kra's finer structure theorem of an ergodic system and its

application to the L^2 convergence of the multiple ergodic averages (3) we discuss Shao-Ye's structure

theorem of a minimal system and its application to the pointwise convergence of the multiple ergodic averages

(for distal systems).

Block Algebras of Finite Groups

Jiping ZhangSchool of Mathematical Sciences, Peking University

The main problem of modular representation theory of finite Groups is the investigation of block algebras in

terms of defect groups. Recently some inductive conditions have been developed to verify the long-standing

open problems. We will report some new progress on Alperin weight conjecture and Robinson conjecture.

Transonic Shock and Mixed Type Equations

Zhouping XinInstitute of Mathematical Sciences, Chinese University of Hong Kong

In this talk, I will discuss some progress on multi-dimensional steady compressible flows which are governed

by the well-known compressible Euler system. We will survey briefly studies on steady transonic flows in some

realistic situations. We will focus on flows with transonic shocks in nozzles with physical boundary conditions.

In particular, I will present some recent results on the Courant-Friedrich\'s transonic shock problem, which is

a nonlinear free boundary value problem with nonlinear boundary conditions for a system of mixed-type partial

differential equations. 2-dimensional well-posedness will be discussed in terms of the geometry and the given

exit pressure. First, we will present the nonlinear structural stability of the Courant-Friedrich\'s shock solution

under generic perturbations of the shape of the nozzle, the incoming flow, and the exiting pressure. Then we

will discuss how to determine the location of the transonic shock if the nozzle is a perturbation of a flat pipe

where the background shock is not unique. Some key ideas of the analysis will be presented and open

problems will also be discussed.

ABSTRACTS OF INVITED SPEECHES

21

Wu Wen-Tsun and Ancient Chinese Mathematics

Joseph W. DaubenCity University of New York

Wu Wen-Tsun was not only one of the world’s greatest mathematicians, he was also an erudite scholar with a

sincere interest in the history of mathematics, and of the history of ancient Chinese mathematics in particular.

One of his most influential essays in this regard was a paper he wrote in 1977 and translated into English as

“The out-in complementary principle” in 1983,whereby it served to revolutionize subsequent understanding of

traditional Chinese mathematics. Until then, even the most noted historians of Chinese mathematics had made

the anachronistic mistake of approaching their analysis of ancient texts in terms of contemporary, modern

understanding of the mathematics in question. Examples will be drawn from the works of various historians of

mathematics in interpreting such classic works as the Zhoubi suanjing, Jiuzhang suanshu, and the Haidao

suanjing, and their commentaries over more than a millennium of different editions, collations, and critical

commentaries.

吴文俊和中国古代数学

道本·周美国纽约市立大学

吴文俊不仅是世界上最伟大的数学家之一，而且是一位对数学史，特别是中国古代数学史有浓厚兴趣的博

学多识的学者。他在这方面最具影响力的论文之一写于1977年，该文在1983年被翻译为英文，名为《出入

相补原理》(The out-in complementary principle)，这篇论文彻底改变了后来人们对中国传统数学的理

解。在此之前，即使是最著名的中国数学史家也犯了年代误植的错误：即用现、当代人对于数学的理解来

解释古代文本。我们会从不同数学史家阐释《周髀算经》《九章算术》《海岛算经》等经典文献的著作之

中、以及从他们对于一千多年来不同的版本、校勘乃至批判性注释的评论之中选取若干例证。


2322

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Wu Wen-Tsun’s Talk at the 1986 International Congress of Mathematicians and the Understanding of Qin Jiushao’s Treatment of the “Chinese remainder theorem”

Karine ChemlaREHSEIS-CNRS Paris

In 1986, Wu Wen-Tsun gave an invited talk at the International Congress of Mathematicians that took place in

Berkeley. In the context of that talk, he treated various aspects of mathematics in China under different

rubriques such as “Theoretical studies involving integers” and “algebra”. Wu Wen-Tsun gave a highly

interesting presentation of Qin Jiushao’s 秦九韶 procedure to solve fundamental types of congruence

problems, which I will discuss in my presentation. In particular, Wu Wen-Tsun took Qin Jiushao’s layout for his

main algorithm into account. I will further suggest that even more features of Qin Jiushao’s layout can be

taken into account, and that doing so yields striking results. It shows that in Song-Yuan mathematics,

“Theoretical studies involving integers” and work in “algebra” were not as separate as we might think.

Moreover, this invites us to return to the discussion of the meaning of the Chinese character “origin yuan 元.”

On Being First, Being Wrong and Being Right: Knuth, “Knuth”, Wu Wen-Tsun, and Algorithms

Jens HøyrupRoskilde University, Denmark

In 1972, Donald Knuth, in order to give cultural standing to computer science, analyzed some Babylonian

mathematical texts under the aspect of “algorithms”, suggesting in the eyes of readers that this was meant to

apply broadly to pre-modern calculating cultures. Around the same time, Wen-tsun, in line with his interest in

mechanical proof, suggested a reading of ancient Chinese mathematics along similar lines, speaking of its

“mechanical” nature (later shifting to the “algorithm” language). Wu’s suggestion has been claimed to be

narrower and even slightly plagiarizing.

The intervention takes a closer look at what Knuth actually says, and at the extent to which this is justified as

an analysis of Babylonian mathematics. It then compares it to ancient Chinese mathematics and concludes

that Wu had a much better case than Knuth precisely because he deals with the ancient Chinese mathematical

culture narrowly.

吴文俊在1986年国际数学家大会上的演讲及其对秦九韶“中国剩余定理”解法的理解

林力娜法国国家科研中心-巴黎七大科学史研究所

1986年，吴文俊应邀在伯克利市（美国加利福尼亚州）举行的国际数学家大会上发表演讲。该演讲中，他

分作不同小节论述了中国古代数学的多个方面，如“数论”和“代数”。吴文俊用秦九韶算法解同余问题

的基本类型做了一次非常有趣的展示，我将在报告中对此加以讨论。特别是吴文俊考虑将秦九韶的“布

算”作为他的主要算法。我将进一步表明，我们甚至可以考虑更多的秦九韶“布算”的特点，这样做产生

了惊人的结果。这表明，在宋元数学中，“数论”和“代数”的工作并不像我们想象的那样独立。此外，

这将促使我们重新讨论汉字“天元”的意义。

关于优先、错误和正确：高德纳、“高德纳”、吴文俊，以及算法

延斯·霍伊鲁普丹麦罗斯基尔德大学

1972年，高德纳为了给计算机科学以文化地位，在“算法”方面分析了一些巴比伦数学文本。在高德纳的

读者看来，其分析旨在将有关结论广泛地应用于前现代计算文化。大约与此同时，吴文俊对机械证明兴趣

正浓，并由类似思路提出了对中国古代数学的一种解读，即谈到了中国古代数学的“机械化”本质（后改

称“算法”）。有人认为吴文俊提出的这一观点比高德纳的说法更为狭隘，甚至是略微“参考”了后者。

本文更加仔细地观察了高德纳实际上说了什么，以及如果把他的说法视作对巴比伦数学的分析的话，其合

理程度如何。本文随后将高德纳的说法与中国古代数学进行比较，并得出以下结论：吴文俊的观点比高德

纳的好得多，原因恰恰是高德纳狭隘地对待了中国古代数学文化。


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国际学术研讨会The Drawing Boards of Pythagoras and Euclid in Raphael’ s School of Athens

LIU DunInstitute for the History of Natural Sciences, Chinese Academy of Sciences

It is well-known that two mathematical figures appearing remarkably in Rapharl’s masterpiece School of

Athens. In accordance with G. P. Bellori’s refactoring, this talk focuses on the graphics of the two drawing

boards in front of Pythagoras and Euclid respectively, analyses the connotation of the pictures by means of

iconography, and reveals the impact of ancient Greek civilization on the Renaissance arts throughout the angle

of inheritance of that so-called Quadrivium, namely arithmetic, geometry, astronomy, and music.

Wu Wen-Tsun’s Work on the Layout of Integrated Circuits and its Place in the Formation of his “Mechanization of Mathematics”

Jiri HudecekCharles University

During the Cultural Revolution, Prof. Wu studied a method of Fisher and Wing of “extraction of planar graphs

from the incidence matrix”, which he found applicable in the design of integrated circuits, and created an

alternative method based on his theory of imbedding of polytopes in Euclidean spaces. He published his

findings in 1973 and, in an expanded and revised form, in the 1978 Chinese language edition of his older book A

Theory of Imbedding, Immersion and Isotopy of Polytopes in Euclidean Space. Wu’s work on the design of

integrated circuits has received relatively little attention, but I argue that it shows some crucial elements of

Wu’s approach to “mechanization of mathematics” as it developed after 1977. In particular, it marked a

transition to a more “constructive”, algorithmic style of presentation, using a detailed exposition of the steps of

calculations, and also experimented with forms inspired by traditional Chinese mathematics (e.g. structuring

of the argument into procedures shu instead of theorems). Furthermore, it was Wu’s first contact with

computer mathematics and as such was often invoked by him in later recollections of the formation of his

“mechanization of mathematics”. A closer look at the 1973 publication of his results and its 1978 revision

reveals the gradual formation of Wu’s vision of the kind of mathematics he wanted to produce, and of its

integration with current social needs and technological development.

吴文俊对集成电路布线问题的研究及其在形成他的“数学机械化”中的地位

胡吉瑞捷克布拉格查理大学

文革期间，吴教授研究了Fisher和Wing提出的“从关联矩阵中提取平面图”的方法，发现它适用于集成电

路的设计，并在欧几里得空间中嵌入多面体的理论基础上，创造了一种新的方法。他在1973年发表了他的

研究成果，并在1978年出版的旧作《可剖形在欧式空间中的实现问题》的中文版中对其进行了扩充和修

订。吴在集成电路设计方面的工作相对较少受到关注，但我认为，它展示了吴在1977年后发展起来的“数

学机械化”方法中的一些关键元素。特别是，它标志着一种更具“构造性”的、算法式的表达方式的转

变，使用了对计算步骤的详细阐述，并尝试了受中国传统数学启发的形式（例如，将论证结构化为步骤

“术”，而不是定理)。此外，这是吴第一次接触计算机数学，因此，后来在回忆“数学机械化”的形成

时，他经常提起这一点。仔细看看1973年出版的研究成果和1978年的修订版，就会发现吴对于他想要创造

的那种数学，以及它与当前社会需求和技术发展的融合的愿景，正在逐步形成。

拉斐尔“雅典学园”中毕达哥拉斯与欧几里得的画板

刘钝中国科学院自然科学史研究所

拉斐尔名画《雅典学园》中的两个人物，身前各有一块画板。通过图像辨识与分析，可以断定它们分别代

表毕达哥拉斯和欧几里得的工作，由此可知文艺复兴时代的大画家如拉斐尔，对古代希腊文化有一定的认

识，对几何、算术与和声也有所了解，或有高人指点或自己具备初步的拉丁文与希腊文知识。


A Handshake away from Wu Wen-Tsun in Paris

Andrea BréardUniversité Paris-Sud, Faculté des Sciences d’Orsay

Shortly after the Second World War, and the occupation of the Université de Strasbourg by the German

National Socialists, Wu Wen-Tsun came to France in 1947 to work in Strasbourg on his PhD under Charles

Ehresmann (1905—1979) where he became acquainted with a group of young topologists. After graduation, Wu

actively participated in Henri Cartan’s (1904—2008) seminar at the Ecole Normale Supérieure in Paris, which

then played a key role in the development of research related to fiber bundles and their homotopy-related

properties. Wu returned to China, on a shaky ocean liner, in 1951, came back briefly to France in 1958, in

particular to Strasbourg where he attended the PhD defense of André Haefliger (1929—), and, after a long

break, returned for the first time again to Paris, or more precisely to Orsay and the Institut des Hautes Etudes

Scientifiques in Bures-sur-Yvette, in 1975, at a time when his research had taken new directions.

In this talk I will present some archival evidence of Wu Wen-Tsun’s connections to the mathematical

community in France. I will focus in particular on his early relations to the topologist René Thom (1923—2002)

around 1950, and on the role of Nicolaas H. Kuiper (1920—1994) in the revival of Wu Wen-Tsun’s relations with

French mathematics after 1973. This will not only shed new light on Wu Wen-Tsun’s proximity to foreign

mathematicians, but, more generally, my analysis of archival records will allow to approach historically in

more detail the new era of Chinese-French academic exchanges following the Cultural Revolution.

在巴黎握手告别吴文俊

白安雅巴黎第十一大学奥赛科学学院

二战以及德国纳粹占领斯特拉斯堡大学结束之后不久，吴文俊于 1 9 4 7 年来到法国，在夏尔 · 埃雷斯曼(Charles Ehresmann，1905-1979)的指导下攻读博士学位，在那里他结识了一群年轻的拓扑学者。毕业后，吴文俊积极参加昂利·嘉当(Henri Cartan，1904-2008)在巴黎高等师范学院开设的研究班，这一研究班当时在纤维丛及其同伦相关性质的研究进展中发挥了关键作用。1951年，吴文俊乘坐一艘摇晃的远洋客轮回到中国，并在1958年回到法国作短期停留，特地去斯特拉斯堡参加安德烈·海富里热(André Haefliger，1929 -)的博士论文答辩。1975年，在长期联系中断之后，吴文俊首次重返巴黎，更准确地说，他回到位于伊韦特河畔比尔市（Bures-sur-Yvette）的奥赛和高等科学研究所，当时他已开始新的研究方向。

在这次演讲中，我将提供一些档案证据，证明吴文俊与法国数学界的联系。我将特别关注他与拓扑学者勒内·托姆(René Thom，1923-2002)在1950年左右的早期关系，以及尼古拉斯H.魁培尔(Nicolaas H. Kuiper，1920-1994)在1973年后吴文俊与法国数学界关系的复苏中所扮演的角色。这不仅会使我们对吴文俊与外国数学家的亲近关系有新的认识，而且，从更广泛的意义上讲，我对档案记录的分析使我们能够更详细地从历史角度探讨文革后中法学术交流的新时代。

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Mechanical Solutions of Geometric Problems in the History of Mathematics: Archimedes and Wu Wen-Tsun

Kostas NikolantonakisUniversity of Western Macedonia

The Method of Mechanical Theorems(Περ� µηχανικ�ν θεωρηµάτων πρ�ς �ρατοσθένη �φοδος), is considered one

of the major surviving works of Archimedes. The Method takes the form of a letter from Archimedes to

Eratosthenes and contains the first attested explicit use of a kind of indivisibles. The palimpsest includes

Archimedes’ account of the “mechanical method”, so-called because it relied on the law of the lever, which

had been first demonstrated by Archimedes, and of the center of mass which he had found for many special

shapes.

Archimedes did not admit the method of indivisibles as part of rigorous mathematics, therefore he did not

publish his method in the formal treatises that contain the results. In these treatises, he proved the same

theorems by exhaustion, finding rigorous upper and lower bounds which both converge to the answer required.

Nevertheless, the mechanical method was what he used to discover the relations for which he later gave

rigorous proofs.

In an analogous way, in the 20th century Professor Wu explained that he was initially struck by the power of the

computer. He was also devoted to the study of Chinese ancient mathematics and began to understand what

Chinese ancient mathematics really was. He was greatly struck by the depth and powerfulness of its thought

and its methods. It was under such influence that he investigated the possibility of proving geometry theorems

in a mechanical way.

With his new ideas Wu could take a problem in elementary geometry and transform it into an algebraic

question about polynomials. Computers could answer questions about polynomials, so Wu had a powerful

method of proving geometric theorems on a computer. He wrote the important book Mechanical Theorem

Proving in Geometries (1984) in Chinese which was translated into English and published ten years later.

The book has six chapters:

1.Desarguesian geometry and the Desarguesian number system.

2.Orthogonal geometry, metric geometry and ordinary geometry.

3.Mechanization of theorem proving in geometry and Hilbert’s mechanization theorem.

4.The mechanization theorem of (ordinary) unordered geometry.

5.Mechanization theorems of (ordinary) ordered geometries.

6.Mechanization theorems of various geometries.

It is in Chapter 4 that Wu explained how to translate geometrical problems into polynomial equations. In 2000

Wu published Mathematics Mechanization: Mechanical Geometry Theorem-proving, Mechanical Geometry

Problem-solving and Polynomial Equations-solving.

In this presentation we are going to give examples of the use of the mechanical method from the work of

Archimedes and then we will try to make an analogical approach for the work of Professor Wu.


数学史中几何问题的机械化解法：阿基米德和吴文俊

哥斯达斯·尼哥兰多纳基斯希腊西马其顿大学

《（发现）定理的力学方法》被认为是阿基米德现存的主要著作之一。该“方法”采用了阿基米德写给埃拉托色尼的一封信的形式，包含了首次确证的、对某种不可分量的显式使用。重写本包括阿基米德对“力学方法”的描述，之所以叫“力学方法”，是因为它依赖杠杆定律，而杠杆定律最早是由阿基米德证明的。重写本还包括阿基米德发现的许多特殊形状的质心定律。

阿基米德不承认不可分量的方法是严格数学的一部分，因此没有在包含结果的正式论文中发表他的方法。在这些论文中，他用穷竭法证明了同样的定理，找到了严格的上界和下界，它们都收敛于所需的结果。然而，力学方法是他用来发现关系的方法，后来他对这些关系进行了严格的证明。

类似地，在20世纪，吴教授解释说，他最初被计算机的力量所震撼，也致力于研究中国古代数学，开始了解中国古代数学到底是什么。其思想和方法的深度及力量给他留下了深刻的印象。正是在这种影响下，他研究了用机械方法证明几何定理的可能性。

有了新想法，吴可以把初等几何中的一个问题转化成一个关于多项式的代数问题。计算机能够解决多项式的问题，所以，吴有一个强大的方法在计算机上来证明几何定理。他著有《几何定理机器证明的基本原理》(1984)一书，并于10年后被翻译成英文出版。

此书包含六章：Desargues几何与Desargues数系垂直几何、度量几何与常用几何几何定理证明的机械化与Hilbert机械化定理（常用）无序几何的机械化定理（常用）有序几何的机械化定理各种几何的机械化定理

在第四章中，吴解释了如何将几何问题转化为多项式方程。2000年，吴出版了《数学机械化：几何定理的机器证明》、《机械几何问题的求解》和《多项式方程的求解》。

在这次演讲中，我们将从阿基米德的作品中举例说明力学方法的使用，然后我们将尝试对吴教授的著作进行类比。

中国传统数学中机械化与构造性算法体系的若干侧面

郭世荣内蒙古师范大学科学技术史研究院

在总结古代东西方数学的主要特点时，吴文俊院士将中国传统数学的基本特色概括为“在从问题出发以解决问题为主旨的发展过程中建立了以构造性与机械化为其特色的算法体系”，这也是其中国数学史观的核心思想。过去40年，这一思想一直指导着中国数学史家的研究工作。他对中国传统数学的算法体系的论述是纲领性和框架性，有许多问题需要深入研究。

这些问题大致可以分两大类。其一是关于算法的，这方面有一系列问题。比如，在中国传统数学的算法体系中，机械化与构造性的具体表现与实现过程是怎样的？中国古代数学家是如何构造算法的？在构造具体算法时他们关心的主要问题是什么？他们更倾向于什么样的算法？在由机械化程序实现算法的过程中，数学家应用了什么算法设计的手段与内容？诸如此类。其二是对算法的确认。从中国传统数学的特点来看，对算法的正确性和合理性的确认一般来说是隐藏在数学文本背后的，在多数情况下数学家并不把算法的证明写入他们的数学文本中。但这不意识着他们不确认自己算法的正确性。而算法的合理性主要是追求算法思想的简洁性或程序的简化性等特点。这类问题涉及到中国传统数学的推理与论证结构。

这两类问题的研究任务是艰巨的，是大型课题。本文中，我们试图对上述问题的某些侧面进行思考，提出一些看法。

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Some Aspects of the Mechanized and Constructive Characteristics in Chinese Traditional Algorithm System

GUO ShirongInstitute for the History of Science and Technology, Inner Mongolia Normal University

When summarizing the main characteristics of ancient East and West mathematics, Wu Wen-Tsun，An

academician of Chinese Academy of Sciences，summed up the basic characteristics of traditional Chinese

mathematics as “in the development process of starting from problems to solving problems in end, an

algorithm system with the characteristics of constructive and mechanized was established”. This summary

also represents the core idea of his view on the history of mathematics in China. This idea has been guiding the

research work of Chinese mathematical historians over the past 40 years. His analyses, however, of the

algorithm system of Chinese traditional mathematics is only programmatic and framed. There are many

problems need to be studied more deeply.

These problems can be roughly divided into two categories. One is about the algorithms themselves, including

a series of problems. For example, in the algorithm system of Chinese traditional mathematics, what are the

concrete representation and implementation processes of mechanization and constructivity and how did

ancient Chinese mathematicians construct algorithms? What are their main concerns in constructing specific

algorithms? What algorithms do they prefer? In the process of implementing algorithm by mechanized

program, what method and content of algorithm design have been applied? And some other problems like

these.

The other category is how to confirm the correctness of algorithms. The confirmation of the correctness and

rationality of algorithms is generally hidden behind the mathematical texts. In most cases, mathematicians did

not write their demonstrations of algorithms into their mathematical texts. But this does not mean that they

did not ensure the correctness of their algorithms. The rationality of the algorithm is mainly to pursue the

simplicity of the idea of the algorithm or the simplification of the program. All these involve the reasoning and

argumentation structure of Chinese traditional mathematics.

The research tasks of the problems of the two categories are arduous and large-scale. We try to discuss some

aspects of the above problems in this presentation.

What is Mathematics in Wasan, in Karasan and in Kōmōsan?--From a Recognition of Strategist Arisawa Munesada

Tatsuhiko Kobayashi Seki Takakazu Institute of Mathematics, Japan

Arisawa Munesada(有沢致貞,1689~1752) is a strategist who served the Kaga feudal clan(加賀藩,

present-day Ishikawa [石川] prefecture) in the Edo period. Although the competent of M. Arisawa was

to study how to win in the war, on the other hand the research on the mathematics, the astronomy,

and the calendar was not neglected in his young age.

In 1725 for Kyohō tenth years [享保10年], M. Arisawa wrote a mathematics book entitled the Chū

san-shiki [籌算式]. Chū san [籌算] means Napier’s Bones is a manually–operated calculating device

created by the Scotch mathematician John Napier (1550~1617). Shiki [式] means calculation here.　

Because M. Arisawa recognized the importance of practical mathematics, the calculation by using

Napier’s bones was very satisfactory for him. About such his recognition is described in the preface of

his book, the Chū san-shiki, and there he classifies mathematics into three, and as follows:

(1) Pre-modern Japanese mathematics : Wasan (和算), calculation by using Soroban (珠算)

(2) Chinese mathematics : Kara san or Tō san (唐算), calculation by using counting rods (算木).

(3) Western mathematics : Kōmōsan (紅毛算), calculation by using Napier’s bones(籌算).

Then, are there what kind of differences in those three mathematics? Moreover, what was the Chinese

book that M. Arisawa had learned Chū san? We will discuss these things in this symposium.

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Western Mathematics in the Joseon Dynasty

Sung Sa HongSogang University Korea

Until the Qing dynasty adopted the new calendar system, Shixianli (時憲曆) in 1645, the Joseon

mathematicians and astronomers could not pay any attention to the mathematical development in

China influenced by the western mathematics and astronomy, which were brought by the Jesuits. The

calendar system was brought into Joseon in the same year and hence it became really urgent to study

the western sources, namely Xiyang Xinfalishu (西洋新法曆書, 1645) by Adam Schall von Bell (湯若望,

1591-1666). It was originated from Chongzen Lishu (崇禎曆書) initiated by Xu Guangqi (徐光啓, 1562-1633).

In 1646, an envoy to Qing could bring back Xiyang Xinfalishu, later called Xinfa Suanshu (新法算書). As

is well known, the mathematics books in Xinfa Suanshu were written by taking Euclid’s Elements and

others compiled by Clavius (1538-1612) as reference books. Tianxue Cuhan (天學初函, 1629) compiled

by Li Zhizao (李之藻, 1565-1630), contains the first six chapters of the Elements translated by Ricci (利瑪竇, 1552-1610) and Xu Guangqi, and more by them. It was brought into Joseon in the last decade of

the 17th century.

Until then, the mathematics books of Xinfa Suanshu could not be understood by any Joseon mathematicians.

Joseon mathematicians in the second half of the 17th century to the first half of the 18th century,

were mostly busy to revive the tianyuanshu (天元術) in Suanxue Qimeng (算學啓蒙, 1299). In the

meantime, Shuli Jingyun (數理精蘊, 1723) was compiled in China and it was brought into Joseon in 1730.

We discuss the history of the study of western mathematics in Joseon and its consequences to the

development of the Joseon mathematics.

和算、唐算、红毛算中的数学是什么？⸺来自兵法家有沢致貞的认识

小林龙彦日本关孝和数学研究所

有沢致貞是江户时期侍奉于加賀藩的兵法家。尽管有沢致貞致力于研究如何在战争中获胜，但另一方面，在青年时期他也未忽视对数学、天文学和历法的研究。

1725年，即享保10年，有沢致貞写了《籌算式》一书。筹算是指由苏格兰数学家约翰·纳皮尔发明的一种用手操作纳皮尔骨筹来计算的工具。“式”在此指计算。

因为有沢致貞认识到实用数学的重要性，用纳皮尔骨筹的计算令他十分满意。关于他的这些认识在其《籌算式》的序言中已进行描述，在那里他还将数学分成三个种类：前近代的日本数学：“和算”，用珠算计算中国数学：“唐算”，用算筹计算西方数学：“红毛算”，用纳皮尔骨筹计算

那么，这三种数学的不同之处有哪些？此外，有沢致貞学过的中国算书会是什么？我们将在此研讨会中讨论这些问题。

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Seki Takazu’s Theory on Algebraic Equations in Pre-modern Japan

OGAWA Tsukane Yokkaichi University

Seki Takakazu is one of the founders of Pre-modern Japanese mathematics in 17th century. He was the first

mathematician who researched algebraic equations themselves. I will introduce his lifework and in particular

view his work “Byoudai Meichi” (病題明致). “Byoudai” means a problem which has more than one solution. He

states several methods modifying a Byoudai to get only one solution. Considering the discriminant or

coefficients of an equation obtained for a problem, he added conditions or altered the values of it. His “Byoudai

Meichi” is difficult for us to understand because he had few mathematics language to state his ideas clearly.

Li Yan and the Early Stage in the Historiography of Chinese Mathematics

HAN QiInstitute for the History of Natural Sciences, Chinese Academy of Sciences

Li Yan (1892-1963) was the most influential historian of Chinese mathematics in the twentieth century. Based

on his writings and the letters written to him, I will discuss and analyse his academic career in his early stages

in the 1910s and 1930s within a broader network of scholars.

朝鲜王朝中的西方数学

洪性士韩国西江大学

直到清朝在1645年开始使用新的历法体系《时宪历》，朝鲜数学家和天文学家还未能对受西方数学和天文学影响的中国的数学发展予以关注，西方数学和天文学由耶稣会士引入中国。《时宪历》历法体系在1645年传入朝鲜，因此迫切需要对西方文献进行研究，即研究由汤若望(Schall von Bell，1591-1666)编制的《西洋新法历书》，此书源于由徐光启(1562-1633)发起编制的《崇祯历书》。

1646年，一名出使清朝的使节可能将后来叫做《新法算书》的《西洋新法历书》带回了朝鲜。众所周知，《新法算书》中的数学著作是参考克拉维乌斯(Clavius，1538-1612)汇编的欧几里得《几何原本》和他所编撰的其它数学著作编译而成。李之藻(1565-1630)所编《天学初函》(1629)中包含利玛窦(1552-1610)和徐光启翻译的《几何原本》的前六卷及和他们合译的其它著作。《天学初函》在17世纪的最后十年传入朝鲜。

在此之前，朝鲜数学家无人懂得《新法算书》中的数学。17世纪后期和18世纪前期的朝鲜数学家忙于复原《算学启蒙》(1299)中的天元术。同时，中国在1723年编纂了《数理精蕴》，该书于1730年传入朝鲜。

我们将讨论朝鲜的西方数学研究史及其对朝鲜数学发展的影响。

李俨与中国数学史研究的初创时期

韩琦中国科学院自然科学史研究所

李俨先生（1892-1963）是20世纪最为丰产和最有影响力的中国数学史家，根据他的著述和往来书信，本文将探讨其早期的学术生涯和学术交流网络。

前近代日本时期关孝和关于代数方程的理论

小川束日本四日市大学

17世纪的关孝和是前近代日本数学的奠基者之一。他是亲身研究代数方程的第一人。这里将介绍他的生平事迹尤其是审视他的著作《病題明致》。“病題”意味着一题多解。他叙述了修正病題以得到唯一解的几种方法。考虑到针对一个问题所列方程的判别式和系数，他增加条件或改变了问题的数值。《病題明致》很难理解，因为关孝和几乎未用数学语言清晰地阐释他的思想。


Gougushu of Korea and Chinese Mathematics

Young Wook KimKorea University, Dept. of Math. and Korean Society for History of Mathematics

The theory of right triangles (gougushu) has always been one of the central themes in the oriental mathematics. In

the history of Korean mathematics, gougushu or gugosul appears in the earliest texts available (17th c.) and we

believe that it has been also the main theme in Korean mathematics. In 18th century western mathematics had

been introduced to Korea via Shuli Jingyun (in 1730) and other books. We have been studying the influence of

these books in Korean gougushu.

Due to the late introduction Korean gougushu of 17th and early 18th century did not have western influence at

all, for example the gougushu of the middle class mathematicians like Hong Jeong-ha and Yu Su-seog. We

compared gougushu of Shuli Jingyun and Hong and Yu and found almost no intersections in their methods. By

the end of the 18th century the book seems to be more popular and when Jeong Yakyong or Jeong Yag-yong

wrote Gugo Sulyo, a dictionary of gougushu formulae, he seemed to have a glance at Shuli Jingyun. In fact

Gugo Sulyo’s title of the first chapter is identical to one of Shuli Jingyun or similar to them. But a closer

comparison of the two books and also with those by Hong Jeong-ha and Yu Su-seog reveals more differences

than similarities. Later in the 19th century Korean mathematicians like Nam Byeong-gil and Lee Sang-hyeog

studied Shuli Jingyun properly and this is reflected in Lee’s book Chageunbang Mong-gu.

In this talk we compare the formulae from the Korean gougushu and study from both viewpoints, namely

computational technics in tianyuanshu and the formulae used. This reveals the western influence in gougushu

and theory of equations in the 18th and 19th century. We found that the Korean mathematicians’ development

of theories were unique and all different from each other probably from their needs or viewpoints. This also will

tell us how the western mathematics were evaluated and accepted in the history with the introduction in Korea

of the western astronomy and calendrical computations.

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韩国的勾股术与中国数学

金英郁韩国高丽大学数学系，韩国数学史学会

勾股术一直是东方数学中的中心主题之一。勾股术在韩国现存最早的数学著作(17世纪)就已出现，我们也认为它是韩国数学中的主题。18世纪，通过《数理精蕴》及其他书籍，西方数学被介绍到韩国。我们一直在研究这些书对韩国勾股术的影响。

由于西方数学传入朝鲜较晚，17世纪晚期和18世纪初期的韩国勾股术完全没有西方的影响，例如像中人数学家洪正夏和刘寿锡的勾股术。我们比较《数理精蕴》和洪正夏及刘寿锡的勾股术发现他们的方法几乎没有交集。到18世纪末期，《数理精蕴》似乎更流行了，丁若镛撰写其勾股术公式汇编《勾股述要》一书时他似乎浏览过《数理精蕴》。实际上，《勾股述要》一书第一章中的小标题与《数理精蕴》相应部分的标题相同或相似。但是，通过对两部著作的细致比较，并与洪正夏和刘寿锡的著作进行比较，表明不同点比相似点更多。19世纪晚期，韩国数学家南秉吉和李尚爀全面地研究了《数理精蕴》，这在李尚爀的《借根方蒙求》一书中有所体现。

在本报告中，我们比较韩国勾股术中的公式并从两种视角进行研究，即天元术中的计算技巧和所使用的公式。这揭示了勾股术和18及19世纪方程理论中的西方影响。我们发现韩国数学家对理论的发展是独特的，而相互间的所有差异都可能是因为他们的需求和视角不同引起的。这也将告诉我们，随着西方天文学和历法计算方法在韩国的引入，西方数学在历史上是如何被评价和接受的。

《测圆海镜通释》补证与解读

李兆华天津师范大学

《测圆海镜》（1248年）记载的勾股测圆术是中国古代数学的一项重要成果。晚清数学家又将这一成果予以发展和完善。其中，刘岳云（1849—1917）《测圆海镜通释》(1896年)具有独到的见解。因传本缺少必要的解说，兼有文字脱误，故准确的理解该书的内容存在困难。本文在校正原文的基础上，依据计算结果，就其难点予以分析，试图阐明其理论与方法。从而说明，在晚清勾股测圆术的研究中，刘岳云的理论建树。

Supplementary Proof and Interpreting on Liu Yueyun’s Ceyuan Haijing Tongshi

LI ZhaohuaSchool of Mathematics, Tianjin Normal University

Gougu Ceyuanshu (Method for Finding Diameter of a circle in contact with Nine Right Triangles) recorded in Ceyuan

Haijing (Sea Mirror of Circle Measurements ,1248) is one of the most important results of mathematics in China.

Furthermore, the result had been improved and systematized by mathematicians in the late Qing Dynasty. Among

them was Liu Yueyun (1849-1917)who gained better understanding of Ceyuan Haijing and completed his book

Ceyuan Haijing Tongshi ( A Concise Explanation on Ceyuan Haijing，1896) .However ，because of the lack of

necessary interpreting and some mistakes appearing on text，his book is difficult to be understood. Based on

collating and calculating, this paper analyzes knotty points of knowledge，explaines both Liu’s theory and method.

The paper considers that devoted to development of theory on Gougu Ceyuan Shu, Liu’s book is of typical significant

in researches during the late Qing dynasty.

Wu Wen-Tsun’s “Recovery of Ancient Demonstration” and Qian Baocong’s “Historism”

ZOU DahaiInstitute for the History of Natural Sciences, Chinese Academy of Sciences

Professor Wu Wen-Tsun is a master of modern mathematics in China, as well as an outstanding historian of

mathematics. He began to study the history of mathematics in the mid-1970s, and published many papers on the

history of mathematics, which immediately caused great repercussions. In particular, his principle for “recovery of

ancient demonstration”, and his approach to summarize and describe characteristics of two mainstreams of

mathematics in the world history by the features of constructibility, mechanization and the features of deductive

methods, axiomatization, have played an important leading role in the study of mathematics history in China. This

paper focuses on Wu’s principle for the “recovery of ancient demonstration” which has the significance of scientific

methodology. We believe that in order to understand Wu’s principle, it should be combined with the academic

situation and existing research ideas, methods and practices in that period. In order to study how Wu promoted this

principle, this paper mainly referred to Professor Qian Baocong’s ideology that a scholar was “necessary to

establish the viewpoint of historism” and his practices based on the ideology. This paper analyzes the important

significances and inadequacies of Qian’s study, and then clarifies the ideological environment in which “Wu’s

Principles” was generated, and then the paper analyzes the breakthrough and uniqueness of the “Wu’s Principles”.

In view of the strong practicality of the study of history of science, the practice of research on a concrete subject is

usually a kind of work which is related to but different from the ideas, principles and methodology. For different

situations, there are big or small differences between the practices of research and the idealized ideas, principles

and methodology. This paper will present some views on the research methods of history of science from the

operational aspects.

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吴文俊的“古证复原”与钱宝琮的“历史主义”

邹大海中国科学院自然科学史研究所

吴文俊先生是我国现代数学的大师，也是杰出的数学史家，他在20世纪70年代中期开始介入数学史的研究，发表了多篇数学史论文，立即引起巨大反响，特别是他的“古证复原”原则和以构造性、机械化特征与演绎、公理化特征总结和刻画两种数学主流的思想，对我国数学史研究产生了重要的引领作用。本文重点关注吴先生具有科学方法论意义的“古证复原”原则。我们认为，要理解吴先生“古证复原”原则的提出，应该结合当时学术界的状况和既有研究思想、方法和实践。本文主要以钱宝琮先生关于“必须树立历史主义观点”的思想和实践为参照，指出其积极意义和不足之处，进而阐明“吴原则”产生的思想环境，“吴原则”的突破和独特意义。鉴于科学史研究具有很强的实践性，有关研究的思想、原则和研究工作的实践属于两个有关但不同的层面，针对不同的情况两者存在或大或小的距离，本文亦将从操作方面对科学史研究的方法提出自己的若干浅陋之见，供同仁们参考。


An Interpretation of Wu Wen-Tsun's Historical View of Chinese Traditional Mathematics in Wasan

XU ZelinSchool of Humanities, Donghua University

Wu Wen-Tsun believes that is characterized by structuring and mechanization, and geometry is algebraic geometry

centering on solving equations. Because of its perfect real number system and the spirit of infinitesimal algorithm,

compared with ancient Greek axiomatic mathematics, Chinese traditional mathematics is more effective to promote

the modern mathematics. This paper examines Wu Wen-Tsun 's academic viewpoint from the overall perspective of

the Chinese character culture circle, and discusses the modern mathematics as an alternative gesture——Wasan’s

achievements in the aspect of algebra algebraic geometry and calculus can be compared with modern western

mathematics. This paper analyzes the relationship between these achievements and the tradition of ancient Chinese

mathematics (especially the mathematics in Song and Yuan Dynasties), and further illustrates the constructive and

algorithmic characteristics of Oriental mathematics through the procedural "art"(术) in Wasan. This paper believes

that the development of Wasan based on the mathematics of the Song and Yuan Dynasties can fully and effectively

interpret Wu Wen-Tsun's understanding of traditional Chinese mathematics. As for whether traditional Chinese

mathematics in history has truly influenced the development of modern Western mathematics, it is an another

historical issue that requires empirical evidence. Compared with the "Needham Puzzle", Wu Wen-Tsun 's historical

view of Chinese traditional mathematics is more instructive for studying the history of Chinese science.

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和算成就对吴文俊中算史观的诠释

徐泽林东华大学人文学院

吴文俊认为中算的特点是构造性、机械化，几何是以解方程为中心的代数化几何，因拥有完善的实数系和优越的无穷小算法思想，与古希腊公理化数学相比，对于促进近代数学的发展更能发挥作用。文章以汉字文化圈整体视域审视吴文俊的学术观点，论述作为另类形态的近代数学⸻和算，在代数学、代数化几何和微积分方面所取得的与西方近代数学相媲美的成就，分析这些成就与中算（特别是宋元数学）传统的关系，并通过和算中一些程序性较强的“术”来进一步说明东方数学的构造性与算法化。文章认为，在宋元数学基础上发展起来的和算，充分、有力地诠释了吴文俊对中算的认识，至于历史上中算是否真实地影响到西方近代数学的发展，则是需要实证的历史问题，较“李约瑟难题”而言，吴文俊的中算史观对于研究中国科学史更具有指导意义。

海上丝路与中国传统数学在日本的传播研究

萨日娜上海交通大学科学史与科学文化研究院

2001年吴文俊院士从他荣获的国家最高科学技术奖奖金中先后拨出100万元人民币建立了“数学与天文丝路基金”（以下简称“丝路基金”），鼓励学者们深入开展中国古代数学与天文学沿丝绸之路在域外传播的研究，努力探讨东方数学与天文遗产在近代科学发展历程中的推动作用和历史地位。2016年一部历史巨著《丝绸之路—一部全新的世界史》中英国著名历史学家，牛津大学伍斯特学院高级研究员彼得・弗兰科潘写道“历史总是提醒我们在过去发生的变化，并帮助我们理解为什么今天也会发生着变化。丝绸之路一直很重要。今天也不例外，丝绸之路又重新崛起，......”，其中以全球性的视野指出丝绸之路的历史是一部浓缩的世界人类通史。作为海上丝路东海线的一个亚洲国家，日本在其历史上的各个时期均受到了中国古代科技文明的影响。经过海上丝路有大量汉文数学典籍传入日本，为日本传统数学的发展奠定了基础，对其学术体系的建构也起到了非常重要的推动作用。文中系统梳理了经海上丝路传入日本的中国古代传统数学典籍，分类整理每个不同历史时期传日的传统数学相关信息记录，为进一步深入细致的研究作铺垫。比较中日文献中记载的传统数学内容，找出证明中国传统数学流传日本的相关文字记录，阐明中国古代数学在日本的传播和吸收过程。又考察日本不同历史时期传统数学的发展情况，确认海上丝路文明对日本传统数学的形成与发展中产生的深远影响。


A Study of the Role of the Maritime Silk Road in the Spread of the Traditional Chinese Mathematics in Japan

SA RinaSchool of History and Culture of Science, Shanghai Jiao Tong University

In 2001, Wu Wen-Tsun, the academician and the winner of the Nation’s Highest Science and Technology Prize,

sponsored the "Mathematics and Astronomy Silk Road fund" (hereinafter referred to as the "Silk Road Fund") with

his rewarded bonus so as to encourage the scholars to carry out an in-depth research into the communication and

the spread between the medieval China and other Asian countries in the area of the mathematics and the astronomy

along the silk road in the ancient time, as well as to make efforts to discuss the objective functions and historical

status of the legacy left over from the eastern mathematics and astronomy in the mainstream development of the

modern science. In 2016, in his historic book The Silk Roads: A New History of the World , Peter Frankopan, as a

famous British historian and a senior researcher in the Worcester college in Oxford, wrote, “History reminds us how

changes have a occurred in the past and help us to understand why change is taking place today. The silk roads

have always been important. And today is no different; the silk roads are rising again......”He held the idea from a

global perspective that the history of the silk road reflected the essence of the general worldwide human history in

brief. Japan, as an Asian country located to the east sea line along the maritime silk road, has been influenced by

the ancient Chinese science and technology civilization in its various historical periods. A lot of Chinese mathematical

works were spread to Japan, which laid the foundation for the development of Japanese traditional mathematics,

and played a very important role in constructing Japanese academic system. The ancient Chinese classics on

traditional mathematics introduced through the maritime silk road to Japan were systematically sorted out, and the

relevant information records of the traditional mathematics spread to Japan in various historical periods were

classified to pave the way for further deep and detailed research. This paper compares the contents of the traditional

mathematics recorded in the Chinese and Japanese literatures, aiming to find out the relevant written records as a

proof of the spread of the traditional Chinese mathematics to Japan, and to elaborate the process of the spread and

the adoption of the ancient Chinese mathematics in Japan. It is a comprehensive study of the development of the

traditional mathematics in different historical periods in Japan which confirms the profound influence of the

maritime silk road civilization on the formation and the development of the traditional mathematics in Japan.

Ancient Chinese Mathematics Under the Field Vision of Wu Wen-Tsun

DENG KehuiSchool of Humanities, Donghua University

Prof. Wu Wen-Tsun Wrote a series of articles on ancient mathematics in China in the 1980s of last century. His

knowing on the theories and methods to the history of mathematics was profound. For example, he point out 3

principles of Recruit Old Proof（“古证复原”）, and then corrected 2 ones. His discoveries affect profoundly. He

suggested that the ancient mathematics in China had a clear line and was different from the ancient Western.

secondly, he thought the geometry and algebra were interpenetrated and had the characteristic of algebraization of

geometry. At last, he thought ancient mathematics in China had the characteristic of proceeding of concrete issues

and raising concise theories and general methods. The paper illustrated Wu's above viewpoints.

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吴文俊眼中的中国古代数学

邓可卉东华大学人文学院

吴文俊先生对中国古代数学的研究集中体现在80年代的一系列论文中。他对中国数学史研究的理论和方法具有高屋建瓴的认识，例如他提出了“古证复原”的三项原则，后来又修正为二项。他的这些工作影响深远。吴文俊提出的中国古代数学有自身发展的清晰主线，其发展过程、思考方法和表达风格迥异于西方数学；他还指出，中国古代的几何总是与代数互相渗透，具有几何代数化的特点；最后，他认为中国古代数学具有从具体问题入手到最终提出简明原理和一般化方法的特点。报告举例论述了吴文俊的以上观点。

吴文俊“丝路精神”及其对中外数学交流研究的意义

纪志刚上海交通大学科学史与科学文化研究院

本文以东西方数学交流的研究历史为切入视角，着重阐述吴文俊“数学与天文丝路基金”的创立与影响，指出吴文俊 “ 丝路精神 ” 理论精髓在于 “ 知识交流与文化融合 ” ，实践途径则是 “ 原典分析与语言学习”。基于对梵语、阿拉伯语和拉丁语等古代数学经典文献的深入解读，古代中国、印度、阿拉伯和中世纪欧洲数学知识相互交流与传播的研究获得了新进展，这是吴文俊“丝路精神”指导下中外数学交流史研究的新成果，进而揭示正是不同文明之间数学知识的“交流与互鉴”推进东西方数学文化的不断进步。


The Starting Point of Mathematical Life：Wu Wen-Tsun's Four-year Study in Chiao-tung University（1936-1940）

OU QijinInstitute of SJTU History Study

In 1936, 17-year-old Wu Wen-Tsun was admitted to the Department of Mathematics, School of Science, National

Chiao-tung University. Four years later, in 1940, he successfully completed his studies and received a Bachelor of

Science degree. During his college years, Chiao-tong University gathered well-known teachers with strict teaching,

rigorous academic atmosphere and complete disciplines. In his department of mathematics, it has a reasonable

curriculum, laying equal stress on Mathematics and physics, and many famous teachers. Under the careful

cultivation of Dean Qiu Weiyu, Director Hu Dunfu and Professor Zhu Gongjin, etc. Wu Wen-Tsun dedicated to

learning, diligent and diligent, had developed a solid mathematics basics and a strong interest in mathematics, and

set up his ambition to follow the academic road gradually to his kingdom of Mathematics.

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步入数学王国：吴文俊在交通大学（1936-1940）

欧七斤上海交通大学党史校史研究室

1936年9月，17岁的吴文俊在其父吴福同（交大早期毕业生）、中学兼职教员赵贻镜（交大物理系讲师）等人熏陶之下，考入国立交通大学科学学院数学系就读。通过上海交通大学档案馆馆藏的吴文俊学业档案文献、2003年8月上海交大校史研究室专访吴文俊的口述史料，并结合交大校史、吴文俊传记等著述资料，可以大体梳理清楚青年吴文俊在交大四年读书经历和求学所得，并评析交大对他开启数学人生的重要影响。大学一年级，他住读徐家汇交大校内，享受了较好的学习与生活条件；大二开学前夕，抗日战争爆发，他被迫随交大师生迁至法租界租借校舍⸺中华学艺社、震旦大学继续求学，在三年艰难岁月中完成学业，于1940年7月顺利毕业，获得理学士学位。吴文俊在校期间，交大名师荟萃，教学严谨，学风淳朴，学科齐备；所读数学系课程设置合理，数理兼学，名家众多。在科学学院院长裘维裕、数学系主任胡敦复、教授朱公谨、武崇林、陈怀书等人的悉心培育和严格要求下，吴文俊在校期间一心向学，勤奋用功，打下了比较扎实的数学专业基础知识，对数学产生了浓厚兴趣，并树立了走数学之路的志向。吴文俊的数学人生由交大起航，走向他的数学王国。

无尽的怀念⸺教诲与鞭策（续）

郭书春中国科学院自然科学史研究所

本文是笔者2009年发表的《无尽的怀念⸺教诲与鞭策》的续篇，继续追忆吴文俊先生对我和K. Chemla（林力娜）完成中法对照《九章算术》的工作十分关心，在该书出版后发起并主持法国大使馆和中国科学院召开的发布会，高度评价李俨、钱宝琮、严敦杰先生对中国数学史研究的重大贡献，赞颂“几经濒临夭折的中国传统数学，赖王（王锡阐）、梅（梅文鼎）、李（李俨）、钱（钱宝琮）等先辈的努力而绝处逢生并重现光辉”，多次表示“严敦杰先生是我向来最崇敬的学者之一”，在2000年10月出任纪念祖冲之逝世1500周年国际学术研讨会主席并作了热情洋溢的讲话，给与会者极大的鼓舞，后来积极支持祖冲之科技园和祖冲之研究会的工作，关心国务院批准的重大文化出版工程、国家文化发展规划纲要的重点出版工程项目《中华大典·数学典》的编纂，并出任名誉主编，关心中国科学院自然科学史研究所的工作，题写了“所史陈列馆”的馆名和“前史后鉴，古为今用”八个大字，反对数学史研究中崇洋媚外、反对杜撰历史资料等6个方面的教诲。追忆吴先生对自己和中国数学史研究事业的关心，温习吴先生的教诲，鞭策自己，继续做好中国数学史研究，是对吴先生诞辰100周年最好的纪念。

Wu Wen-Tsun's “Silk Road Spirit” and Its Significance to the Study of Mathematical Communication between China and Foreign Countries

JI ZhigangSchool of History and Culture of Science, Shanghai Jiao Tong University

From the perspective of the history of mathematical communication between east and west, this paper focuses

on the establishment and influence of Wu Wen-Tsun's ‘Silk Road Fund for Mathematics and Astronomy’, and

points out that the theoretical essence of Wu Wen-Tsun's “Silk Road Spirit” lies in ‘knowledge exchange and

cultural integration’, while the practical approach is ‘classical analysis and language learning’. Based on the

in-depth interpretation of Sanskrit, Arabic, Latin and other ancient mathematical classics, new progress has

been made in the study of the mutual exchange and dissemination of mathematical knowledge between

ancient China, India, Arab and medieval Europe. This is a new achievement in the history of mathematical

exchange between China and foreign countries under the guidance of Wu Wen-Tsun's “Silk Road Spirit”. Then

it is revealed that it is the ‘exchange and mutual learning’ of mathematical knowledge between different

civilizations that promotes the continuous progress of eastern and western mathematical cultures.


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缅怀吴文俊先生的谆谆教诲

王渝生中国科技馆

本文回顾了前后40年间，我在中国科学院研究生院学习期间，在中国科学院自然科学史研究所工作和后来担任副所长期间，在中国科技史学会和全国数学史学会担任秘书长期间，在中国科技馆担任馆长期间，同吴文俊先生接触和交往中受到他的谆谆教诲，和他同我的导师严敦杰之间的学术交往往事，探讨吴文俊对中国数学史的独到见解及对数学机械化思想形成的贡献。例如以下几个重要节点：

1978年，吴文俊在中国科学院研究生院为首届研究生开设了《几何定理的机器证明》选修课程，我有幸选修了这门课程。吴文俊在第一堂课就明确提出中国传统数学算法化、程序化、机械化的特征，《九章算术》以算为主、以术为法、寓理于算、不证自明，同古希腊《几何原本》和公理化体系及逻辑演绎证明异其旨趣。

1981年，吴文俊在大连召开的全国第一次数学史讨论会上作了《古今数学思想》与《古证探原》的报告，提出了“古证复原三原则”。

从1986年《吴文俊文集》到1996年《吴文俊论数学机械化》的10年进展。

1999年，吴文俊用他获得的国家科技奖设立了“丝路天文数学基金”，用以探讨古代东西方的数学天文学交流与传播，从而促进了国内数学天文学史研究新的生长点。

2002年，在北京举办的第24届国际数学家大会上，吴文俊到中国科技馆做了《中国古算与实数系统》的报告，阐述我国古代数学家对实数的全面认识体系比西方早很多年，并归纳了中国古代传统数学的优秀基因和突出亮点。

Endless Memory--Edification and Encouragement (Continuation)

GUO Shuchun Institute for the History of Natural Sciences, Chinese Academy of Sciences

This paper is the continuation of Edification and Encouragement published by me in 2009, continuing to recall

Mr. Wu Wen-Tsun's great concern for me and K. Chemla (Lin Lina) in finishing the Chinese and FrenchVersion

of the Nine Chapters on the Mathematical Procedures. Professor Wu launched and hosted the press conference

organized by both the French Embassy and the Chinese Academy of Sciences after the publication of the book.

He spoke highly of the significant contributions of Mr. Li Yan, Mr. Qian Baocong and Mr. Yan Dunjie to the study

of the history of mathematics in China, said, “thanks to the efforts of Wang Xichan,Mei Wending, Li Yan, Qian

Baocong and other predecessors, Chinese traditional mathematics that was several times on the verge of

collapse have survived and regained splendor” with full of praise, and he also mentioned that “Mr. Yan Dunjie is

one of the scholars for whom I have always been showing the very respect” for many times. He served as the

chairman of the International Symposium of the 1500 Anniversary Commemoration of the Death of Zu Chongzhi

in October 2000 and delivered a speech with great enthusiasm that greatly encouraged the attendees. After

then, he actively supported the work of Zu Chongzhi Science and Technology Park and Zu Chongzhi Research

Association. Furthermore, he cared about the compilation of Shuxuedian of the Zhonghuadadian（《中华大典·

数学典》，Mathematical Canon of Chinese Grand Canons）,a key publishing project of Outline of the National

Cultural Development Plan as well as a major cultural publishing project approved by the State Council, taking

the honorary editor-in-chief. He also showed concerns about the work of the Institute for the History of Natural

Sciences in Chinese Academy of Sciences, for which he wrote scroll “qianshihoujian, guweijinyong”（前史后

鉴，古为今用,the previous history is lesson to later generations, and the past serves the present）’’. He

criticizes the idea of unconditional worship of foreign in the study of the history of mathematics and fabrication

of historical data, etc.

To recall Mr. Wu’s concern for me as well as the study of the history of mathematics in China, review what he

had told us, urge myself, and continue to make contribution to the study of the history of mathematics in China

are the best commemoration of the 100th anniversary of Mr. Wu's birthday.


Talking about the Cooperation between Professors Shangshu Bai and Wu Wen-Tsun

LI Zhonglai School of Mathematics Sciences, Beijing Normal University

Brief introduction to Professors Wu Wen-Tsun and Shangshu Bai cooperation. Series on Studies the History of

Chinese Mathematics and the Series of History of Chinese Mathematics were issued under his general editorship.

The establishment of doctoral programs in Beijing Normal University and Northwest University (Chinese) were

supported By W.Wu. And S.Bai application for the Science Foundation of the Chinese Academy of Sciences and the

National Natural Science Foundation were supported also too. And attended two international conferences

organized by S.Bai. Professor W.Wu writes the preface of Collected Papers of S.Bai: History of Chinese Mathematics,

was invited, etc.

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从白尚恕与吴文俊教授的合作谈起

李仲来北京师范大学数学科学学院

简介吴文俊和白尚恕先生的合作的几件事: 吴文俊主编《中国数学史研究丛书》和《中国数学史大系》,吴文俊支持在北京师范大学和西北大学建立博士点,吴文俊支持白尚恕主持申请的中国科学院科学基金和国家自然科学基金项目,吴文俊参加白尚恕组织的两次国际会议. 邀请吴文俊先生写《白尚恕文集:中国数学史》的序言的过程等。

Remebering Wu Wen-Tsun's Inculcation

WANG YushengChina Science and Technology Museum

This article reviewed the before and after 40 years, during my studying in graduate school, Chinese Academy of

Sciences, working in the institute for the History of Natural Science, Chinese Academy of Sciences and later

served as deputy director ,being a secretary-general in Chinese Society for the History of Science and Technology

and in the National Society for the History of Mathematics and a director in the China Science and Technology

Museum, my contacts with Mr. Wu Wen-Tsun and the inculcations from him and his academic exchanges with

my tutor Yan Dunjie. In the meantime, the article aimed to discuss Wu Wen-Tsun’s unique opinion on Chinese

history of mathematics and his contribution to the thought of mathematical mechanization. Some important

points are as follows:

In 1978,Wu Wen-Tsun opened an elective course called "Machine proof of geometric theorems" for the first

graduate students in graduate school, Chinese Academy of Sciences. I was lucky enough to take the course. In

the first class, Wu Wen-Tsun clearly put forward the characteristics of algorithmic, programmatic and mechanized

Chinese traditional mathematics. 《九章算术》focuses on calculation, takes technique as the method,

combines theory with calculation, and proves itself without evidence, which is different from the 《几何原本》

of ancient Greece, axiomatic system and logical deduction.

In 1981, Wu Wen-Tsun made a report on "ancient and modern mathematical thoughts" and "exploration of

ancient evidence" at the first national mathematical history discussion meeting held in Dalian, and put forward

the "three principles of restoration of ancient evidence".

The development of ten years from 《吴文俊文集》in 1986 to 《吴文俊论数学机械化》in 1996.

In 1999, Wu Wen-Tsun used his national science and technology award to set up the "silk road astronomy and

mathematics fund", which was used to discuss the exchanges and dissemination of mathematical astronomy

between the east and the west in ancient times, thus promoting a new growth point in the study of the history

of Chinese mathematics and astronomy.

In 2002, at the 24th International Congress of Mathematicians held in Beijing, Wu Wen-Tsun made a report on

"Chinese Ancient Arithmetic and Real Number System" in China Science and Technology Museum, expatiated

that Chinese ancient mathematicians had a comprehensive understanding of the real number system many

years earlier than western countries, and summarized the excellent genes and highlights of Chinese ancient

traditional mathematics.


Wu Wen-Tsun and The History of Chinese Mathematics

QIAN Yonghong

In 1975, After perusal of The History of Chinese Mathematics, edited by Mr. Qian Bao-cong and lots of other

books on Chinese and Western history of Mathematics, Prof. Wu Wen-Tsun published his paper On the Great

Contribution of Ancient Chinese Mathematics to World Culture in ACTA MATHEMATICA SINICA(Vol.18,No.1). At

the end of his essay, Wu cited the below conclusion of Qian Bao-cong’s Address Great Achievements in

Ancient Chinese Mathematics(CHINESE SCIENCE BULLETIN Vol.2 No.10) which was made as early as in 1951

at mathematics group of Natural Science Teaching and Research Association of secondary schools in Hangzhou.

After the 5th century, most of Indian Mathematics were Chinese style. After the 9th century, most of Arabian

Mathematics were Greek style. Till 10th century, these two styles had merged together and spread to Europe

by the Muslims in the northern of Africa and Spain. Consequently, the Europeans had restored the lost Greek

mathematics on one hand, and absorbed the powerful force of Chinese mathematics on the other. Modern

mathematics thus began to develop dialectically

According to Qian Baocong's conclusion, Wu Wen-Tsun Drew the following sketch in his paper:

And resolutely put forward his viewpoint as follows:

The reason why modern mathematics can develop till today is mainly based on Chinese mathematics, not

Greek mathematics. The main course determining the history of mathematics is Chinese (Mathematics) rather

than Greek.

This article will also briefly comment on both Wu Wen-Tsun and Qian Baocong’s researching methods and

achievements in the history of mathematics in China.

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吴文俊与《中国数学史》

钱永红

1975年，吴文俊先生在研读钱宝琮先生主编的《中国数学史》及大量的中外数学史专著之后，在《数学学报》上发表了《中国古代数学对世界文化的伟大贡献》论文，结尾引用了钱宝琮1951年在杭州市中等学校自然科学教学研究会数学组的讲演稿《中国古代数学的伟大成就》（《科学通报》第2卷第10期）的结论：

第五世纪以后，大部分印度数学是中国式的，第九世纪以后，大部分亚刺伯（阿拉伯）数学是希腊式的，到第十世纪中这两派数学合流，通过非洲北部与西班牙的回教徒，传到欧洲各地。于是欧洲人一方面恢复已经失去的希腊数学，一方面吸收有生力量的中国数学。近代数学才得开始辩证的发展。

吴文俊依据钱宝琮的结论，绘制出以下简图：

并毅然提出：近代数学之所以能够发展到今天，主要是靠中国（式）的数学，而非希腊（式）的数学，决定数学历史发展进程的主要是中国（式）的数学，而非希腊（式）的数学。

本文将简要回顾吴文俊和钱宝琮二位数学史大家的中国数学史研究方法与研究成果。

中国5c

10c9c

欧洲希腊

印度

阿拉伯

中国CHINA

希腊GREECE

INDIA

ARABIA

5c

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印度 EUROPE欧洲

阿拉伯


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中国科学院科学奖金评奖吴文俊折桂始末

郭金海中国科学院自然科学史研究所

吴文俊早年专攻拓扑学，其关于示性类与示嵌类的研究达到国际水平。中国科学院主要由于中央高层推动的学习苏联的热潮与苏联学术奖励制度和培养科学干部经验的影响，于1955年建立学术奖励制度，决定颁发第一次科学奖金。吴文俊以1952—1955年发表于《数学学报》的关于示性类与示嵌类研究的9篇论文，由中国科学院数学研究所推荐参加了评奖，最终与华罗庚、钱学森一并获得1956年度中国科学院科学奖金一等奖。本文以近年发掘的档案资料为基础，详尽地还原了吴文俊在这次科学奖金评奖中折桂的始末经过。吴文俊在这次科学奖金评奖中折桂，奠定了他在当代中国数学史上的重要地位。其折桂的关键在于他在拓扑学领域关于示性类和示嵌类的杰出研究成果，但也与江泽涵、廖山涛、施祥林对其参评论文的高度或良好评价，中国科学院数学物理学化学部数学组对其参评论文的一致肯定密切相关。

The Whole Story of Wu Wen-Tsun Winning the First Prize in Scientific Award of Chinese Academy of Sciences

GUO JinhaiInstitute for the History of Natural Sciences, Chinese Academy of Sciences

Wu Wen-Tsun specialized topology in his early years. His research on the characteristic class and imbedding

class reached the international level. The Chinese Academy of Sciences established the academic award

system and decided to award the first scientific award in 1955. The main reasons are the upsurge for learning

from the Soviet Union promoted by the high-ranking officials of the Central Committee of the Communist Party

of China, the influence of the Soviet Union’s academic award system and experience of cultivating scientific

cadres. Wu Wen-Tsun recommended by the Institute of Mathematics, Chinese Academy of Sciences, participated in

the awards evaluation with 9 papers about the research on characteristic class and imbedding class published

in Acta Mathematica Sinica from 1952 to 1955. Finally, he won the first prize with Loo-Keng Hua（华罗庚）and

Hsue-Shen Tsien（钱学森）in the scientific award of 1956, Chinese Academy of Sciences. Based on the

archives excavated in recent years, this paper restores the whole story of Wu Wen-Tsun winning the first prize

in the scientific award in detail. It points out that Wu Wen-Tsun won the first prize laid his important status in

the history of mathematics of contemporary China. The key to his success in the awards evaluation not only

lies his outstanding research results on characteristic class and imbedding class, but also closely relates with

the high or good appraisal of his papers for the award by Kiang Tsai-Han（江泽涵）, Liao Shantao（廖山涛）and Shi Xianglin（施祥林），the unanimous approval of mathematical group in the Academic Division of

Mathematics, Physics, and Chemistry, Chinese Academy of Sciences, to his papers for the award as well.


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