Core Viewpoint - The article discusses the recent proof of the Kakeya conjecture in three-dimensional space by Chinese mathematician Wang Hong and Columbia University professor Joshua Zahl, which has generated significant interest and could position Wang as a strong candidate for the Fields Medal in 2026 [1][5][6]. Group 1: Kakeya Conjecture Overview - The Kakeya conjecture, proposed by Japanese mathematician Sōichi Kakeya in 1917, involves determining the minimum area that a needle can sweep when rotated in a confined space [8][9]. - The conjecture states that a Kakeya set in three-dimensional space must have both Minkowski and Hausdorff dimensions equal to three, indicating that these sets geometrically fill the space despite appearing sparse [10][11][12]. Group 2: Proof Details - Wang Hong and Joshua Zahl published a 127-page paper proving the three-dimensional Kakeya conjecture, employing complex strategies including non-concentration conditions and multi-scale analysis [3][20]. - Their proof involves defining a situation K(d) and demonstrating a relationship that allows for the induction of dimension parameters towards three [21][23]. - The authors utilized multi-scale analysis to study the organization of pipe-like structures, leading to insights about the density and overlap of these structures [24][25][28]. Group 3: Background on Wang Hong - Wang Hong, born in 1991, is a notable mathematician who could become the first Chinese woman to win the Fields Medal if awarded [7][34]. - She has an impressive academic background, having studied at prestigious institutions and focusing on Fourier transform-related problems [36][38].