The Abel Prize /ˈɑːbəl/ (Norwegian: Abelprisen) is a Norwegian prize awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes. It comes with a monetary award of 7.5 million Norwegian Kroner (NOK).

The Abel Prize’s history dates back to 1899, when its establishment was proposed by the Norwegian mathematician Sophus Lie when he learned that Alfred Nobel‘s plans for annual prizes would not include a prize in mathematics. In 1902, King Oscar II of Sweden and Norway indicated his willingness to finance a mathematics prize to complement the Nobel Prizes, but the establishment of the prize was prevented by the dissolution of the union between Norway and Sweden in 1905. It took almost a century before the prize was finally established by the Government of Norway in 2001, and it was specifically intended “to give the mathematicians their own equivalent of a Nobel Prize.” The laureates are selected by the Abel Committee, the members of which are appointed by the Norwegian Academy of Science and Letters.

The award ceremony takes place in the Aula of the University of Oslo, where the Nobel Peace Prize was awarded between 1947 and 1989. The Abel Prize board has also established an Abel symposium, administered by the Norwegian Mathematical Society.

Source: Abel Prize – Wikipedia

The modularity theorem (formerly called the Taniyama–Shimura conjecture) states that elliptic curves over the field of rational numbers are related to modular forms. Andrew Wiles proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat’s last theorem. Later, Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor extended Wiles’ techniques to prove the full modularity theorem in 2001.

Source: Modularity theorem – Wikipedia