Mathematician has solved the Kakeya conjecture
10 months ago
- #Kakeya Conjecture
- #Mathematics
- #Harmonic Analysis
- The Kakeya conjecture, posed by Soichi Kakeya in 1917, asks for the smallest surface area needed to rotate a needle to point in the opposite direction.
- Hong Wang and Joshua Zahl solved the Kakeya conjecture in three dimensions, a major mathematical achievement of the 21st century.
- The solution involves complex calculations and spans 127 pages, with only the authors fully understanding the intricate reasoning.
- Wang's work connects the Kakeya conjecture to the restriction conjecture in harmonic analysis, which has applications in medical imaging and digital file compression.
- The restriction conjecture deals with the behavior of the Fourier transform on curved surfaces like spheres.
- Wang's approach uses wave packets and overlapping parallelepipeds, described as 'baroque suprematism' by mathematician Antonio Córdoba.
- Luis Vega, a Spanish mathematician, indirectly inspired Wang's focus on the restriction conjecture.
- Wang is a humble figure, avoiding speculation about winning the Fields Medal, despite her groundbreaking work.