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  • Maryam Mirzakhani is being honoured for her "rare combination of superb technical ability, bold ambition, far-reaching vision, and deep curiosity".

  • Martin Hairer's is being honoured for a major breakthrough that gives a way of attacking problems that had previously been impenetrable.

  • Artur Avila is being honoured for "formidable technical power, the ingenuity and tenacity of a master problem-solver, and an unerring sense for deep and
    significant questions."

  • Manjul Bhargava is being honoured as a number theorist of "extraordinary creativity," with "a taste for simple problems of timeless beauty."