Japanese mathematician Masaki Kashiwara was awarded this year’s Abel Prize. First awarded in 2003, the Abel prize is often considered to be an equivalent of the Nobel prize, which does not have a category for mathematics. It has been modelled as such. The prize includes a monetary award of 7.5 million kroner (roughly $720,000) and a glass plaque designed by Norwegian artist Henrik Haugan. What is the Abel Prize? The Abel Prize “recognises pioneering scientific achievements in mathematics”. It is named after Norwegian mathematician Niels Henrik Abel (1802-29), who in his short life made pioneering contributions to multiple fields. The prize was established by the Norwegian Parliament in 2002, on Abel’s 200th anniversary. That said, it was first proposed as early as 1899 by Norwegian mathematician Sophus Lie, who had learnt that Nobel’s annual prizes would not include one in the field of mathematics. This plan never materialised. The Abel Prize is awarded and administered by the Norwegian Academy of Science and Letters on behalf of the Norwegian government. The recipients are chosen by an expert committee appointed by the Academy under the advice of the International Mathematical Union (IMU) and the European Mathematical Society (EMS). Genius of Abel Abel’s most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, one that had been unresolved for more than 250 years. He was also an innovator in the field of elliptic functions, a discoverer of what would later be known as Abelian functions. He made all his discoveries while living in crippling poverty. He died of tuberculosis at the age of 26. Commenting on the richness of Abel’s work in his short lifespan, French mathematician Charles Hermite once said, “ Abel has left mathematicians enough to keep them busy for five hundred years.” Kashiwara’s contributions Kashiwara, 78, was awarded “for his fundamental contributions to algebraic analysis and representation theory, in particular the development of the theory of D-modules and the discovery of crystal bases,” according to the Abel citation. His work has not only helped solve some hard problems that have been around for a long time but also opened new avenues for research by connecting areas that were not known to be connected before. For instance, Kashiwara discovered crystal bases which allowed mathematicians to replace complex calculations with much simpler graphs of vertices connected by lines. Over the years, Kashiwara has “reshaped and deeply enriched the fields of representation theory, in its numerous incarnations, and algebraic analysis,” the citation said.
