Opportunities and challenges in experimental mathematics

“Experimental mathematics” has emerged in the past 25 years or so to become a competing paradigm for research in the mathematical sciences. An exciting workshop entitled Challenges in 21st Century Experimental Mathematical Computation was held at the Institute for Computational and Experimental Research in Mathematics (ICERM), July 21-25, 2014, which explored emerging challenges of experimental mathematics in the rapidly changing era of modern computer technology. This report summarizes the workshop findings (without mentioning any of the research presentations).

While several more precise definitions have been offered for “experimental mathematics,” we used the informal one given in the book The Computer

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Formal proof completed for Kepler’s conjecture on sphere packing

Introduction

On 10 August 2014, a team led by Thomas Hales of the University of Pittsburgh, USA, announced that their decade-long effort to construct a computer-verified formal proof of the Kepler conjecture was now complete. The project was known as Flyspeck, a rough acronym for “Formal Proof of Kepler.”

The Kepler conjecture is the assertion that the simple scheme of stacking oranges typically seen in a supermarket has the highest possible average density, namely pi/(3 sqrt(2)) = 0.740480489…, for any possible arrangement, regular or irregular. It is named after 17th-century astronomer Johannes Kepler, who first proposed that planets orbited in

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2014 Fields Medals announced

On 13 August 2014, at the quadrennial meeting of the International Congress of Mathematicians, this year held in Seoul, Korea, the four winners of the 2014 Fields Medals were announced by the International Mathematics Union, which administers the awards.

This year’s awardees are:

Artur Avila, a Brazilian mathematician (the first Brazilian mathematician to win the prize) has done notable research in the study of chaos theory and dynamical systems. These areas seek to understand the behavior of systems that evolve over time in which very small changes in the initial conditions can lead to wildly varying outcomes. One well-known example

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