以表彰他們對於3維與4維幾何學的卓越貢獻
從牛頓和萊布尼茨開始，微積分學就和力學結緣，自此幾何與物理成為緊密相關的學問，一枝兩葉。在19世紀，幾何學發展迅速，使人們充分了解了2維曲面的各種幾何變化，包括代數曲線的結構與物理學中流體力學的多種性質。
3維空間與4維時空是20世紀與21世紀物理學與幾何學研究的重點。3維空間與4維時空有多種奇妙的特性。西蒙・唐納森(Simon K Donaldson) 和 克利福・陶布斯(Clifford H Taubes) 引導出全新的觀念與技巧，做出了突出的貢獻。這些全新的觀念與技巧很多是從理論物理，包括量子場論，發展出來的。
Over the past 30 years, geometry in 3 and 4 dimensions has been totally revolutionized by new ideas emerging from theoretical physics. Old problems have been solved but, more importantly, new vistas have been opened up which will keep mathematicians busy for decades to come.
While the initial spark has come from physics (where it was extensively pursued by Edward Witten), the detailed mathematical development has required the full armoury of non-linear analysis, where deep technical arguments have to be carefully guided by geometric insight and topological considerations.
