Core Insights - The lecture by Professor Efim G. Gemanov at Beijing Jiaotong University emphasized the beauty and intelligence of mathematics, expressing strong confidence in China's potential to produce a Fields Medal winner [1] - The Fields Medal is regarded as the "Nobel Prize of Mathematics," recognizing young scholars under 40 for groundbreaking contributions, which often shape the future of global mathematics [1] Group 1: China's Mathematical Landscape - Gemanov highlighted the importance of overall improvement in a country's mathematical capabilities over individual awards, stressing the need for top universities, high schools, and IT companies [2] - He noted that China's foundational sciences have reached a world-class level, with an increasing number of international scholars choosing to conduct research in China [2] - The Shenzhen International Mathematics Center, where Gemanov works, aims to gain a more significant position in the global mathematics landscape, hosting large international conferences to attract scholars [2] Group 2: Talent Development in Mathematics - Zhang Jiping, a prominent mathematician, acknowledged that while China leads in certain mathematical fields, there is still a need for overall improvement in talent cultivation [2] - Both Gemanov and Zhang emphasized the importance of perseverance and deep thinking in becoming a great mathematician, with Gemanov stating that significant results often take years of contemplation [3] - Zhang pointed out the necessity of fostering independent thinking and problem-solving skills in students, advocating for a balance between academic rigor and life skills [3][4] Group 3: Attitudes Towards Failure - Zhang Jiping remarked on the inevitability of failure in research, suggesting that successful outcomes are often a small fraction of total attempts, and that embracing failure is crucial for growth [4]

Core Viewpoint - The lecture by Professor Efim G. Zhemanov emphasizes the importance of mathematics in modern society and expresses strong confidence in the potential for China to produce a Fields Medal winner in the future [1][2]. Group 1: Mathematics in China - Zhemanov believes that the overall improvement of a country's mathematics level is more important than individual awards, highlighting the need for top universities, high schools, and IT companies in China [2]. - He notes that China's foundational science has reached a world-class level, with an increasing number of international scholars choosing to conduct research in China [2]. - The Shenzhen International Mathematics Center, where Zhemanov works, aims to become a more significant player on the global mathematics stage, hosting large international conferences to attract scholars [2]. Group 2: Talent Development - Zhang Jiping, a prominent mathematician, acknowledges that while China leads in certain mathematical fields, there is still a need for overall improvement in talent cultivation [2][3]. - Both Zhemanov and Zhang emphasize the importance of perseverance and deep thinking in developing great mathematicians, suggesting that true understanding comes from exploring the origins and derivations of mathematical concepts [3]. - Zhang stresses the necessity for students to learn independent thinking and problem-solving skills, advocating for a balance between academic rigor and life skills [3][4]. Group 3: Research and Failure - The process of research is inherently fraught with challenges, and both Zhemanov and Zhang highlight the importance of resilience in the face of failure, with Zhang noting that successful researchers may only achieve a small fraction of their attempts [4].

Group 1 - The article highlights the achievements of young female mathematician Wang Hong, who won the 2025 Salem Prize, regarded as a precursor to the Fields Medal, the highest award in mathematics [1] - Wang Hong also received the ICCM Mathematics Award the day before, which is known as the "Fields Medal for Chinese mathematicians" [1] - Born in 1991 in Guilin, Guangxi, Wang graduated from Peking University and obtained her master's degree from École Polytechnique and Paris-South University, followed by a PhD from MIT in 2019 [1] Group 2 - In February of this year, Wang and her colleagues published a 127-page paper proving the long-standing mathematical problem known as the "Hanging Garden Conjecture," which created a significant impact in the mathematics community [1] - In June, Wang gave a lecture at Peking University that attracted a full audience, including notable attendees such as researcher Wei Dongyi [1]

Core Points - Chinese mathematician Wang Hong has recently won two prestigious mathematics awards: the 2025 Salem Prize and the ICCM Mathematics Prize [1][3] - The Salem Prize is awarded for significant contributions in Fourier analysis and related fields, typically to mathematicians under 40 years old [9][12] - Wang Hong's achievements in harmonic analysis and geometric measure theory have positioned her as a leading candidate for the Fields Medal, often regarded as the "Nobel Prize of Mathematics" [7][14] Group 1 - Wang Hong received the 2025 Salem Prize for her outstanding contributions to unresolved problems in harmonic analysis and geometric measure theory [1] - The ICCM Mathematics Prize, which Wang also won, is considered the "Fields Medal" of the Chinese mathematics community [3] - The likelihood of winning the Fields Medal is notably high for those who have previously won the Salem Prize, with ten past recipients achieving this honor [12] Group 2 - Wang Hong's recent research breakthroughs include solving the three-dimensional Kakeya conjecture, a significant problem in the field [31][34] - Her academic journey includes degrees from prestigious institutions such as École Polytechnique and MIT, culminating in a postdoctoral position at the Institute for Advanced Study [22][24] - Wang's work has been published in top mathematics journals, further solidifying her reputation in the mathematical community [31]

Core Viewpoint - The article highlights the significant achievements of mathematician Wang Hong, who received two prestigious awards: the 2025 Salem Prize and the ICCM Mathematics Award, marking a remarkable year for Chinese mathematicians [2][5][56]. Group 1: Awards and Recognition - Wang Hong was awarded the 2025 Salem Prize for her contributions to solving major open problems in harmonic analysis and geometric measure theory [17][29]. - The ICCM Mathematics Award was also given to Wang Hong, along with fellow Peking University alumni Deng Yu and Yuan Xinyi, recognizing their exceptional work in mathematics [5][30]. - The Salem Prize is considered a precursor to the Fields Medal, with a notable history of past winners going on to receive the Fields Medal [2]. Group 2: Wang Hong's Academic Journey - Wang Hong transitioned from studying Earth and Space Sciences at Peking University to pursuing mathematics, showcasing her passion for the field [10]. - She graduated from Peking University in 2011, furthered her studies at École Polytechnique and Paris 11 University, and completed her PhD at MIT in 2019 under renowned mathematician Larry Guth [11][13]. - Wang is currently an assistant professor at UCLA and a tenured professor at the Institut des Hautes Études Scientifiques (IHES), where she is the first female tenured professor in its history [15]. Group 3: Contributions to Mathematics - Wang Hong made significant advancements in several century-old mathematical problems, including the Kakeya set conjecture, which she proved in collaboration with Professor Joshua Zahl [20][28]. - She has also contributed to the Fourier restriction conjecture and the Falconer distance set conjecture, publishing two papers in top mathematical journals this year alone [23]. - Her groundbreaking work has positioned her as a leading candidate for the Fields Medal, especially following her recent accolades [29]. Group 4: Fellow Awardees - Deng Yu, another ICCM awardee, is a professor at the University of Chicago and has received numerous accolades, including the Putnam Fellow award and the IMO gold medal [32]. - Yuan Xinyi, also an ICCM awardee, is known for his work in Arakelov geometry and algebraic dynamics, having made significant contributions to various mathematical fields [45]. - All three awardees share a common background as alumni of Peking University's mathematics department, highlighting the institution's role in nurturing top mathematical talent [55].