Exponential Equations | Topics

After cracking the "sum of cubes" puzzle for 42, researchers discover a new solution for 3

After solving the sum of cubes puzzle for 42, researchers found a new solution for 3 using an optimized algorithm that utilized mathematical 'sieving' techniques. The discovery suggests there may be infinitely many more solutions for other values of k, with the next solution involving gigantic 21-digit numbers.

SourceMassachusetts Institute of Technology·JournalProceedings of the National Academy of Sciences·DateMar 11, 2021

Taming complexity

Giuseppe Carleo and Matthias Troyer have found a way to overcome the mathematical complexity of many-particle systems using an artificial neural network. The researchers used reinforcement learning to identify important parameters in chaotic systems, enabling calculations with simplified equations for larger systems.

SourceETH Zurich·JournalScience·DateFeb 10, 2017

New method edges closer to holy grail of modern chemistry

University of Chicago chemist David Mazziotti has developed a new method for determining electron behavior in atoms and molecules, achieving accuracy rates of 95-100%. This breakthrough could have wide applications in various chemical phenomena, including fuel efficiency, ozone depletion, and medicine design.

SourceUniversity of Chicago·JournalPhysical Review Letters·DateOct 12, 2006