The Kepler Conjecture, proposed by German astronomer and mathematician Johannes Kepler in 1611, states that there is no more efficient way to stack spheres than in a pyramid shape. This arrangement maximizes the density of the structure while maintaining stability. For over 400 years, mathematicians have attempted to prove this theory, and in 1998, Thomas Hale, a professor at the University of Pittsburgh, finally succeeded.
Hale’s proof was the result of a case study that began in 1996 and involved over 150 variables and 100,000 linear optimizations. The work was presented in an unusual format, consisting of over 250 pages and three gigabytes of computer data. A panel of 12 experts reviewed the submission and concluded that Hale’s formal proof was 99% correct, with the caveat that the correctness of the computer-generated data could not be verified.
Despite this limitation, Hale was promised a “mathematical theorem” for his achievement. In January 2003, a joint project was launched to provide the missing pieces of the proof, and in August 2014, Hale was finally able to confirm the correctness of the computer-generated results through further calculations.
The Kepler Conjecture has significant implications for fields such as physics and engineering, as it provides a mathematical basis for understanding the optimal arrangement of spheres in various structures. Hale’s proof represents a significant milestone in the history of mathematics, demonstrating the power of computer-assisted proofs and the persistence of mathematicians in solving long-standing problems.
