Core Viewpoint - The article discusses the resolution of Hilbert's sixth problem, a significant mathematical challenge posed by David Hilbert in 1900, which has been solved by a team of Chinese researchers after 125 years [1][11]. Group 1: Authors and Their Backgrounds - The research was conducted by three authors: Deng Yu, a professor at the University of Chicago; Zaher Hani, an assistant professor at the University of Michigan; and Ma Xiao, also an assistant professor at the University of Michigan [2][27]. - Deng Yu graduated from Peking University and MIT, and completed his PhD at Princeton [28]. - Zaher Hani completed his undergraduate studies at the American University of Beirut and his master's and PhD at UCLA, studying under renowned mathematician Terence Tao [31][34]. - Ma Xiao graduated from the Young Scholars Program at the University of Science and Technology of China and completed his PhD at Princeton in 2023 [35]. Group 2: Significance of the Research - The resolution of Hilbert's sixth problem is not only a theoretical milestone but also provides new mathematical tools for the study of fluid mechanics [5][6]. - The achievement has been celebrated within the mathematical community, with some referring to it as a "miracle year for Chinese mathematics" [6][8]. Group 3: Methodology and Findings - The authors approached the problem by deriving fluid dynamics equations from microscopic Newtonian mechanics using Boltzmann kinetic theory [4][25]. - They introduced a cumulative quantity analysis method to track the complete history of particle collisions, leading to the proof of the long-term validity of the Boltzmann equation [18][20]. - The research culminated in the derivation of the Euler equations for compressible fluids and the Navier-Stokes-Fourier equations under incompressible conditions [21][25].