The Illustrious Journey of Chinese Mathematics: From Ancient Wonders to Modern Achievements

中国古代数学与现代数学的辉煌之路

I. Ancient Chinese Mathematics

一、古代中国数学

1. Early Mathematical Texts

1、早期数学文献

• The Chou Pei Suan Ching, considered the oldest extant mathematical text from China, is dated between 1200 BC and 100 BC, showcasing a unique mathematical development.

• 周髀算经被认为是中国现存的最古老数学文献，可追溯到公元前1200至100年之间，展示了独特的数学发展。

• The Tsinghua Bamboo Slips, dating back to around 305 BC, contain the earliest known decimal multiplication table, emphasizing China’s early mathematical prowess.

• 清华简《乘法口诀》可追溯至公元前305年左右，包含已知最早的十进制乘法表，突显了中国早期数学的才华。

2. Decimal Positional Notation Rod Numerals

2、十进制位表示法-算筹数字

• Chinese mathematics introduced the “rod numerals,” a decimal positional notation system using distinct ciphers for numbers 1-10 and additional ciphers for powers of ten.

• 中国数学引入了“算筹数字”，一种十进制位表示法，其中对1到10之间的数字使用不同的密码，对十的幂使用额外的密码。

• This advanced system, predating the Indian numeral system, facilitated representation of large numbers and computations on the suan pan (Chinese abacus).

• 这种先进的系统在公元前公元前几个世纪就已经使用，并且早于印度数字系统的发展。算筹数字允许表示任意大的数字，并允许在算盘上进行计算。算盘的发明日期不确定，但最早的书面提及可以追溯到公元190年，出现在《算数》中。

3. Geometry in Ancient China

3、中国古代几何学

• The Mohist canon (c. 330 BC) compiled by Mozi’s followers provided insights into geometry and physical science, marking an early contribution to mathematical theorems.

• 《墨经》是公元前330年左右墨子的追随者编纂的哲学文献，描述了与物理科学相关的许多领域，并提供了一些几何定理。

4. Book Burning of 212 BC

4、公元前212年的焚书坑儒

• In 212 BC, Emperor Qin Shi Huang ordered the burning of non-official books, limiting knowledge of ancient Chinese mathematics before this date.

• 公元前212年，秦始皇下令焚烧秦国境内除官方认可之外的所有书籍，这一命令并未普遍遵守，但由于这一命令，我们对公元前212年之前的中国古代数学了解甚少。

5. Han Dynasty Contributions The Nine Chapters

5、汉代的贡献-《九章算术》

• The Han dynasty (202 BC–220 AD) produced significant mathematical works, with The Nine Chapters on the Mathematical Art emerging as a cornerstone.

• 汉代（公元前202年–220年）创作了重要的数学著作，《九章算术》成为其中的支柱。

• The Nine Chapters covered diverse topics, including word problems, geometry for engineering, and introduced mathematical proof for the Pythagorean theorem and Gaussian elimination.

• 《九章》涵盖了农业、商业、几何用于测量高度和中国塔楼的尺寸比例、工程学、测量等246个问题，并包括关于直角三角形和π值的数学证明。它为毕达哥拉斯定理提供了数学证明，以及高斯消元法的数学公式。

6. Zu Chongzhi and π Calculation

6、祖沖之与π的计算

• In the 5th century AD, Zu Chongzhi calculated π to seven decimal places, maintaining its accuracy for nearly a millennium.

• 在公元5世纪，祖沖之计算了π的前七位小数，这一值几乎在接下来的近1000年里一直是最准确的π值。

• Zu Chongzhi’s contributions extended to establishing a method akin to Cavalieri’s principle for finding the volume of a sphere.

• 他还建立了一种后来被称为骑士原理的方法来计算球体的体积。

7. Golden Era of Chinese Algebra (13th Century)

7、中国代数的黄金时代（13世纪）

• The 13th century, particularly the latter part of the Song period, witnessed the high-water mark of Chinese mathematics with the development of Chinese algebra.

• 中国数学的巅峰出现在13世纪，尤其是宋朝后期，伴随着中国代数的发展。

• Chu Shih-chieh’s “Precious Mirror of the Four Elements” (fl. 1280–1303) played a pivotal role in solving simultaneous higher order algebraic equations.

• 汤时节（fl. 1280–1303）的《四元玉鉴》是这一时期最重要的著作，解决了同时具有更高阶代数方程的方法，类似于霍纳法。《四元玉鉴》还包含了帕斯卡三角形的图表，其中包含了到第八次幂的二项式展开的系数，尽管这两者在中国的作品中早在1100年就出现过。中国还利用了被称为魔方和魔圈的复杂组合图，这在古代被描述并由杨辉（公元1238–1298年）完善。

8. Cross-Cultural Exchange Jesuit Missionaries

8、跨文化交流-耶稣会传教士

• During the Renaissance, European and Chinese mathematics remained separate traditions.

• 在文艺复兴时期，欧洲和中国的数学仍然是独立的传统。

• Jesuit missionaries, notably Matteo Ricci (16th–18th centuries), facilitated the exchange of mathematical ideas between the two cultures.

• 耶稣会传教士，尤其是马太·里奇（16至18世纪），促进了两种文化之间数学思想的交流，尽管此时进入中国的数学思想要远多于输出。

9. Legacy and Decline

9、遗产与衰落

• Despite earlier prominence, Chinese mathematical output declined from the 13th century onwards.

• 尽管在早期占有突出地位，但中国数学的产出从13世纪开始逐渐减少。

• Mathematical ideas flowed more from Europe to China during the Jesuit missions, marking a shift in the direction of influence.

• 在耶稣会传教士时期，数学思想更多地从欧洲流入中国，标志着影响方向的变化。

Ancient Chinese mathematics boasts a rich history, evident in texts like the Chou Pei Suan Ching and Tsinghua Bamboo Slips dating back to 1200 BC. The decimal positional notation using “rod numerals” predates Indian numerals, aiding computations on the suan pan. The Han dynasty’s “Nine Chapters on the Mathematical Art” covers diverse topics. Zu Chongzhi’s 5th-century π calculation and the 13th-century Chinese algebraic peak illustrate mathematical prowess. Jesuit missionaries facilitated cross-cultural exchanges. Despite early eminence, Chinese math declined post-13th century, influenced more by European ideas. Modern Chinese mathematics, marked by Fields Medal laureates, thrives globally with collaborative research and educational initiatives.

古代中国数学拥有丰富的历史，如《周髀算经》和可追溯到公元前1200年的《清华简》。采用“算筹数字”的十进制位表示法早于印度数字系统，有助于在算盘上进行计算。汉代的《九章算术》涵盖了多领域。祖沖之在5世纪的π计算和13世纪的中国代数巅峰展示了数学的卓越。耶稣会传教士促进了跨文化交流。尽管早期卓越，但中国数学在13世纪后逐渐衰落，更受欧洲思想的影响。现代中国数学以菲尔兹奖得主为标志，在全球范围内通过合作研究和教育倡议蓬勃发展。

II. Modern Chinese Mathematics

二、现代中国数学

In addition to its rich ancient mathematical heritage, China has made significant strides in modern mathematics. The development of modern Chinese mathematics can be traced through various stages, reflecting the nation’s commitment to scientific advancement and education.

除了其丰富的古代数学遗产外，中国在现代数学方面取得了显著的进展。现代中国数学的发展可以通过不同阶段的历史来追溯，反映了该国在科学进步和教育方面的承诺。

1. 20th Century Contributions

1、20世纪初的贡献

• In the early 20th century, China witnessed a mathematical renaissance driven by renowned mathematicians such as Hua Luogeng and Wu Wenjun. Hua Luogeng, often hailed as the “Father of Chinese Mathematics,” made substantial contributions to number theory, algebraic geometry, and mathematical analysis. Wu Wenjun, a pioneer in optimization theory, played a pivotal role in advancing mathematical research.

• 在20世纪初，中国经历了一场由华罗庚和吴文俊等著名数学家主导的数学复兴。华罗庚，常被誉为“中国数学之父”，在数论、代数几何和数学分析方面做出了重要贡献。吴文俊是优化理论的先驱，对数学研究产生了深远的影响。

2. Integration of Western and Chinese Traditions

2、西方与中国传统的整合

• Following the establishment of the People’s Republic of China in 1949, there was a deliberate effort to integrate Western mathematical theories with traditional Chinese mathematical thought. This integration led to a diverse and comprehensive approach to mathematical research, fostering collaborations between Chinese mathematicians and their global counterparts.

• 在1949年中华人民共和国成立后，有意识地努力将西方数学理论与传统中国数学思想相结合。这种整合导致了多元化和全面的数学研究方法，促进了中国数学家与全球同行之间的合作。

3. Contemporary Achievements

3、当代成就

• In recent decades, Chinese mathematicians have gained international recognition for their achievements in various mathematical disciplines. Fields such as algebraic geometry, number theory, and applied mathematics have seen notable contributions from Chinese mathematicians, who have actively participated in global research endeavors.

• 在近几十年里，中国数学家以在代数几何、数论和应用数学等各种数学学科中取得的显著贡献而赢得国际认可。中国数学家积极参与全球性的研究工作。

4. Mathematics Education and Research Centers

4、数学教育与研究中心

• China has established world-class mathematics education and research centers, contributing to the training of a new generation of mathematicians. These centers serve as hubs for cutting-edge research and provide a platform for collaboration between mathematicians from different parts of the world.

• 中国建立了世界一流的数学教育和研究中心，为新一代数学家的培养做出了贡献。这些中心是尖端研究的枢纽，为来自世界各地的数学家提供了合作平台。

5. International Collaboration

5、国际合作

• Chinese mathematicians actively engage in international mathematical conferences, workshops, and collaborations, contributing to the global mathematical community. The exchange of ideas and research findings between Chinese mathematicians and their international counterparts has enriched the landscape of modern mathematics.

• 中国数学家积极参与国际数学会议、研讨会和合作，为全球数学社区做出贡献。中国数学家与国际同行之间的思想和研究成果的交流丰富了现代数学的格局。

6. Fields Medal Recognition

6、菲尔兹奖的认可

• China’s prowess in mathematics is underscored by the fact that several Chinese mathematicians have received the prestigious Fields Medal, the highest honor in the field. These individuals have made groundbreaking contributions to areas such as algebraic geometry and number theory.

• 中国在数学方面的卓越表现得以证明，事实上有多位中国数学家获得了菲尔兹奖，这是该领域的最高荣誉。这些人在代数几何和数论等领域取得了突破性的贡献。

• Shing-Tung Yau: Shing-Tung Yau is a mathematician who has made outstanding contributions to the fields of mathematics and geometry. He was awarded the Fields Medal in 1982, primarily for his work in differential geometry and topology.

• 陈省身：陈省身是一位在数学和几何学领域做出杰出贡献的数学家。他于1982年获得了菲尔兹奖，主要是因为他在微分几何和拓扑学方面的工作。

• Wu Wenjun: Wu Wenjun is one of the founding figures of Chinese mathematics, earning high acclaim in the mathematical community for his research in probability theory and mathematical logic. He was honored with the Fields Medal in 1990.

• 吴文俊：吴文俊是中国数学的奠基人之一，他在概率论和数学逻辑方面的研究为他赢得了数学界的高度赞誉。他在1990年获得了菲尔兹奖。

• Hua Luogeng: Hua Luogeng is an eminent mathematician and regarded as one of the founding figures of modern Chinese mathematics. His work in number theory and algebraic geometry led to him receiving the Fields Medal in 1982.

• 华罗庚：华罗庚是一位杰出的数学家，被誉为中国现代数学的奠基人之一。他在数论和代数几何方面的工作使他于1982年获得了菲尔兹奖。

• Shing-Tung Qiu: Shing-Tung Qiu is a mathematician who has made remarkable contributions to the fields of topology and mathematical physics. He was awarded the Fields Medal in 1982.

• 丘成桐：丘成桐是一位在拓扑学和数学物理方面有卓越贡献的数学家。他在1982年获得了菲尔兹奖。

In summary, modern Chinese mathematics stands as a dynamic and influential force in the global mathematical landscape. The nation’s mathematicians continue to shape the future of mathematics through groundbreaking research, international collaboration, and a commitment to mathematical education.

总体而言，现代中国数学在全球数学领域中是一个充满活力且有影响力的力量。该国的数学家通过开创性的研究、国际合作和对数学教育的承诺，不断塑造着数学的未来。