MATHSIANS

  Mathematical Proof That Rocked Number Theory Will Be Published But some experts say author Shinichi Mochizuki failed to fix a fatal flaw in the solution of a major arithmetic problem By Anikesh Banerjee The papers released on the Internet in August 2012 by Japanese mathematician Shinichi Mochizuki of Kyoto University, claiming to provide proof for the abc conjecture in number theory, said to be the most important unresolved problem in modern mathematics. Credit:  Getty Images After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation. His 600-page proof of the abc conjecture, one of the biggest open problems in number theory, has been accepted for publication. Acceptance of the work in  Publications of the Research Institute for Mathematical Sciences  (RIMS)—a journal of which Mochizuki is chief editor, published by the institute where he works at Kyoto University—is the latest development in a...

MEXICAN MATHEMATICIAN SOLVES DECADES OLD MATHEMATICAL PROBLEM THAT COULD REVOLUTIONIZE LENS DESIGN By Anikesh Banerjee A lens works by making light rays converge on a point, called the focus. Properly converged light rays result in a sharp image, which is what every camera tries to achieve when it’s hunting for focus. This is also how our eyes and even telescopes work. The problem, one that’s apparently been  baffling mathematicians for almost 2,000 years , is that lenses do not perfectly focus light rays. Light rays in the centre of a lens converge properly, but rays nearer the edges do not. This results in what photographers see as distortion and colour fringing at the edges. Lens design will never be the same again. There are ways to  reduce spherical aberration  using more lenses, but this is still not a perfect solution and increasing the number of lenses increases the overall cost and complexity of a lens and camera system. The image on top shows how light rays...