Core Points - Wang Hong, a 34-year-old Chinese mathematician, has been awarded the 2025 Salem Prize, which is considered a precursor to the Fields Medal, the highest honor in mathematics [1] - Wang also received the Gold Medal at the 10th International Congress of Chinese Mathematicians (ICCM), which is often referred to as the "Chinese Fields Medal" [1] - The Salem Prize committee recognized Wang for her groundbreaking research in harmonic analysis and geometric measure theory [1] Achievements - Wang gained significant recognition for her work on the Kakeya conjecture, particularly for a 127-page paper published this year in collaboration with Columbia University professor Joshua Zahl, proving the Kakeya set conjecture in three-dimensional space [1] - In addition to her work on the Kakeya conjecture, she has made important contributions to the Fourier restriction conjecture and the Falconer distance conjecture [1] - In 2023 alone, Wang published two articles in four top mathematics journals [1] Historical Context - Among the 56 Salem Prize winners from 1968 to 2024, 10 have gone on to win the Fields Medal [1] - The Fields Medal is awarded every four years to 2-4 mathematicians for outstanding contributions, with a total of 65 mathematicians having received it as of 2022, including two of Chinese descent: Shing-Tung Yau in 1982 and Terence Tao in 2006 [1] Industry Perspective - Industry insiders believe that Wang's rapid succession of world-class achievements demonstrates her extraordinary mathematical talent and research potential, positioning her as one of the most promising candidates for the Fields Medal among Chinese mathematicians [2]

Core Points - The 2025 Salem Prize was awarded to Wang Hong and Vesselin Dimitrov, recognized as indicators of future Fields Medal winners [2] - The ICCM Mathematics Prize was awarded to Wang Hong, Deng Yu, and Yuan Xinyi, all alumni of Peking University, and is often referred to as the "Chinese Fields Medal" [5][41] Group 1: Awards and Recognition - Wang Hong's achievements include the Salem Prize for her contributions to harmonic analysis and geometric measure theory, particularly for proving the Kakeya set conjecture [14][21] - The ICCM Mathematics Prize recognizes young mathematicians under 45, with Wang Hong, Deng Yu, and Yuan Xinyi being notable recipients this year [5][41] Group 2: Wang Hong's Academic Journey - Wang Hong transitioned from Earth and Space Sciences to Mathematics, earning her degrees from prestigious institutions including Peking University and Paris XI University [8][12] - She is a tenured professor at the Institute of Advanced Scientific Studies in France, being the first female tenured professor in its history [11] Group 3: Contributions to Mathematics - Wang Hong has made significant contributions to various mathematical problems, including the Fourier restriction conjecture and Falconer distance set conjecture, with multiple publications in top journals [17][14] - Her collaboration with Joshua Zahl led to a groundbreaking 127-page paper on the Kakeya set conjecture, a long-standing problem in mathematics [14] Group 4: Other Awardees - Deng Yu, another ICCM awardee, is a professor at the University of Chicago and has made significant contributions in nonlinear dispersive equations and fluid dynamics [24][26] - Yuan Xinyi, also an ICCM awardee, is known for his work in Arakelov geometry and has received multiple prestigious awards, including the Clay Research Fellowship [31][39]

Core Viewpoint - A 17-year-old girl, Hannah Keiro, has successfully disproven the Mizohata-Takeuchi conjecture, a significant mathematical theory that has implications for Fourier analysis and partial differential equations (PDE) [4][5][3]. Group 1: Mizohata-Takeuchi Conjecture - The Mizohata-Takeuchi conjecture, established in the 1980s, serves as a crucial link between harmonic analysis, PDEs, and geometric analysis, suggesting that if the weight accumulation in all line directions is not too large, Fourier propagation will not be overly concentrated [2][11]. - Disproving this conjecture necessitates a reevaluation of decades of thought regarding core issues in Fourier restriction and the well-posedness of PDEs, including the Stein conjecture [3][2]. Group 2: Hannah Keiro's Achievement - Hannah Keiro, while completing a homework assignment assigned by her mentor, found a counterexample to the Mizohata-Takeuchi conjecture, which took considerable time to convince her mentor, Ruixiang Zhang, of its validity [5][6][24]. - Keiro's background includes participation in a mathematics summer camp at UC Berkeley, where she expressed her interest in advanced mathematics to professors, leading to her engagement with the conjecture [23][24]. Group 3: Implications of the Disproof - The disproof indicates that for certain functions and weights, the lower bound of integrals exceeds the upper bound proposed by the conjecture, suggesting that the conjecture does not hold in general [19][20]. - The paper also introduces a local version of the Mizohata-Takeuchi conjecture, questioning whether a slight loss in the inequality could still allow it to hold [21]. Group 4: Background of Ruixiang Zhang - Ruixiang Zhang, Keiro's mentor, has a distinguished academic background, including being a gold medalist at the International Mathematical Olympiad and receiving the SASTRA Ramanujan Award in 2023 for his contributions to number theory and related fields [30][36][37].

Core Viewpoint - A 17-year-old girl, Hannah Kairo, has overturned the Mizohata-Takeuchi conjecture, a significant mathematical theory that has implications for Fourier analysis and partial differential equations (PDEs) [4][5][3]. Group 1: Mizohata-Takeuchi Conjecture - The Mizohata-Takeuchi conjecture, established in the 1980s, connects harmonic analysis, PDEs, and geometric analysis, suggesting that if the weight accumulation in all line directions is not too large, Fourier propagation will not be overly concentrated [2][11]. - If this conjecture is disproven, it necessitates a reevaluation of decades of thought regarding core issues in Fourier restriction and the well-posedness of PDEs, including the Stein conjecture [3][2]. Group 2: Hannah Kairo's Achievement - Hannah Kairo, at just 17 years old, initially set out to complete a homework assignment from her mentor, but ended up discovering a counterexample to the Mizohata-Takeuchi conjecture [5][4]. - Her mentor, Ruixiang Zhang, is a notable scholar in modern harmonic analysis and PDEs, and she successfully convinced him of her findings after considerable effort [6][25]. Group 3: Implications of the Discovery - The discovery indicates that for certain functions and weights, the lower bound of the integral exceeds the upper bound proposed by the conjecture, introducing a logarithmic factor that invalidates the conjecture [19][20]. - The paper also proposes a local version of the Mizohata-Takeuchi conjecture, questioning whether a slight loss in the inequality could still hold true [22][21]. Group 4: Background of Hannah Kairo - Hannah Kairo was born in the Bahamas and developed an interest in mathematics from a young age, later participating in a mathematics summer camp at UC Berkeley [24]. - She has already begun presenting her work at international academic conferences, demonstrating confidence and enjoyment in sharing her knowledge [27][28].