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22 Dec 2021

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Approach the old and beautiful theory of numbers

The 6th Fudan-Zhongzhi Science Award was granted to two mathematicians


Top scientists and young scholars from all over the world gathered at the 6th Fudan-Zhongzhi Science Award ceremony and the 2021 Fudan Science and Innovation Forum held in Shanghai on December 19 to exchange views on cutting-edge technologies and innovation trends.


This year’s Fudan-Zhongzhi Science Award was jointly awarded to mathematicians Benedict Hyman Gross and Don Bernard Zagier. The Gross-Zagier formula they established connects the height of Heegner points with the central derivatives of the zeta function of the corresponding elliptic curve, and gives important theoretical evidence for the Birch and Swinnerton-Dyer Conjecture. The formula contributed to the solution to many long-standing problems and had a profound influence on the development of number theory in recent decades.



Benedict Hyman Gross: collaboration with Zagier was a mutally-inspring process


As a member of the U.S. National Academy of Sciences, fellow of the American Academy of Arts and Sciences, and Emeritus Professor of Mathematics at Harvard University and the University of California, San Diego, apart from the Gross-Zagier formula, Benedict Hyman Gross did a lot of important work in automorphic forms and other fields, specifically the Gan-Gross-Prasad conjectures, which play critical roles in many recent advances in mathematics.


Gross shared his joy of winning the award via video. He said he was delighted to share the award with his friend Don Zagier, and he also expressed gratitude to mathematicians Jean-Pierre Searle and John Tate. According to Gross, his collaboration with Zagier went back and forth several times, and progress on one side would lead to insight and then progress on the other. Their formulas were very complicated, but all matched up finally. The simplicity of the final identity has pushed others to find more conceptual proofs, but the essential mystery behind it remains the same.


Gross has tried, with his collaborators Wee Teck Gan and Dipendra Prasad, to find a more general setting in which the identity might hold. He also finds that research in this field remains extremely active today and that there were no Chinese mathematicians working in this area of number theory when Don and him began their work some forty years ago, but now the field is led by many mathematicians of Chinese descent, which is an amazing development.


Don Bernard Zagier is the member of the U.S. National Academy of Sciences, foreign member of the Royal Netherlands Academy of Arts and Sciences, and retired scientific member and director of the Max Planck Institute for Mathematics in Germany. Zagier did a lot of important work on modular forms and special functions which resolve questions and problems in diverse areas ranging from topology and moduli spaces to geometry and mathematical physics.


Zagier attended the ceremony in person, and his great passion for mathematics moved all the audience. Showing a piece of note on which he wrote “九章算术(The Nine Chapters on the Mathematical Art)” in Chinese, Zagier introduced the beautiful ancient theory of numbers to the audience at the ceremony.


“Can you find positive integer solutions to A, B and C?” - the question Zagier raised in his speech and joked that it was the “trickiest mathematical question in history” captured the attention of the audience. Actually, no computer in the world can solve this seemingly simple question, he said, however, human brain is the only “computer” that is able to solve this problem, because the key to the solution is the theory of elliptic curves which only the human mind can comprehend.


The discovery of the award-winning Gross-Zagier formula is one of the most exciting moment of Zagier’s career in mathematics.


The hard work of Zagier reveals his keen interest in mathematics, which can be traced back to his adolescence. Zagier graduated from high school at 13, university at 16, and he completed his doctoral thesis at 19, and received his doctorate at 20. But he never thinks he is a genius, and he takes his success as the result of hard work.


“I’m not a genius, and it (pursuit of mathematical excellence) was like a challenge. I did it for fun, and nobody pushes me. I just wanted to see if I can do this, and to prove to myself I can do this,” said Zagier, who continues his passion for mathematics, even at 70.


Exchange views on cutting-edge technologies and stay at the frontier of the world’s innovation trends


Jin Li, president of Fudan University and academician of the Chinese Academy of Sciences, delivered opening remarks. He extended welcome to all the guests, and expressed gratitude to Zhongzhi Enterprise Group and mourned the passing of Xie Zhikun, founder of Zhongzhi Enterprise Group and member of the board of Fudan University, who passed away on December 18.


Science and innovation are not only the primary driving force behind human civilization, but also the most solid and important foundation for mankind to help each other, overcome difficulties and achieve common prosperity, said Jin. Fudan University has been committed to promoting the development of science and innovation, facilitating the communication of the latest scientific achievements, and accelerating the pace of high-tech industrialization. With the integrated social resources and the united social forces, it provides more opportunities and a larger platform for the transdisciplinary cooperation and the integration of innovation elements, which is also the original intention of Fudan Science and Innovation Forum and Fudan-Zhongzhi Science Award.


Jin said today’s world is undergoing profound changes unseen in a century, and the globe has become a closely intertwined community of shared future. “Cooperation” is an unavoidable path to human development, therefore, the integration and cooperation of science will undoubtedly be the core force to promote the building of a community of shared future for mankind. He was very pleased to see that the Fudan-Zhongzhi Science Award Committee has decided to present this year's Award to two experts in number theory—the queen of mathematics in Gauss’s eyes.


At present, world-class universities have become the most forward-looking and vital force of scientific and technological innovation. Universities are the breeding ground of top talents, the gathering place of leading disciplines and the source of science and innovation. Fudan University has seized the opportunity of the global innovation development strategy and Shanghai Global Science and Technology Innovation Center, and it will continue to be committed to the innovation of fundamental disciplines and strive to achieve a breakthrough from "Zero" to "One" in fundamental research.



Liu Fuhua, chief compliance officer of Zhongzhi Enterprise Group, gave a congratulatory speech and presented the certificate of honor and trophy to the winners. He said Zhongzhi  Enterprise Group would support China’s science and technology as always, and continue to support Fudan-Zhongzhi Science Award to commemorate Xie, who has been devoted to China’s development in sci-tech education.


Samuel Chao Chung Ting, chair of the Award Committee and laureate of Nobel Prize in Physics, announced the winners and award citation at the forum.


Zhang Renhe, vice president of Fudan University, hosted the ceremony.


Liu Ming, academician of the Chinese Academy of Sciences and dean of Frontier Institute of Chip and System, Fudan University, made a speech entitled “Prospects for Integrated Circuit Technology Innovation-Challenges and Opportunities”, which was followed by the report “Mathematics: Science or Art?” given by Efim Zelmanov, the U.S. National Academy of Sciences and laureate of Fields Medal.


Xu Ningsheng, chair of Fudan-Zhongzhi Science Award Executive Council and academician of the Chinese Academy of Sciences also attended the Forum.


Forging a platform for pioneers in science and innovation to share ideas


Fudan Science and Innovation Forum is hosted by Fudan University, organized by Fudan Institute for Advanced Study, and sponsored by Zhongzhi Enterprise Group. In addition to the main forum, the two-day event also incorporates three sub-forums respectively centering on biomedicine and artificial intelligence, data science & artificial intelligence and integral psychology.


The sub-forums brought together more than forty experts and scholars who delivered keynote speeches on the applications and prospects of artificial intelligence, pattern analysis and bioinformatics, data science, big data & machine intelligence, applications of 3D technology, the unity of minds between humans and the environment, psychology & art, etc.


Fudan Science and Innovation Forum has been held since 2015. The forum aims to forge a platform for pioneers in science and innovation to share ideas on a global scale and to stay at the frontier of the trend of cutting-edge innovation worldwide. In addition, the forum strives to inspire the general public, especially the youth, to innovate and continuously improve the innovation capability of Shanghai, contributing wisdom to transforming Shanghai into a science and technology innovation center with world influence.


The Fudan-Zhongzhi Science Award was jointly founded by Fudan University and Zhongzhi Enterprise Group in 2015 to give recognition to the scientists who have made original and distinguished achievements in the fields of biomedicine, physics and mathematics. The award is announced every year in these three fields on rotation. It’s the second time the Award has been granted to the distinguished scientists in mathematics. Since the first award in 2016, 12 scientists of different nationalities have been commended, and 5 of them have become Nobel Prize winners after receiving the Fudan-Zhongzhi Science Award.


Presented by Fudan University Media Center

Source: Fudan Institute for Advanced Study

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