以表彰他们对於3维与4维几何学的卓越贡献
从牛顿和莱布尼茨开始，微积分学就和力学结缘，自此几何与物理成为紧密相关的学问，一枝两叶。在19世纪，几何学发展迅速，使人们充分了解了2维曲面的各种几何变化，包括代数曲线的结构与物理学中流体力学的多种性质。
3维空间与4维时空是20世纪与21世纪物理学与几何学研究的重点。3维空间与4维时空有多种奇妙的特性。西蒙・唐纳森(Simon K Donaldson) 和 克利福・陶布斯(Clifford H Taubes) 引导出全新的观念与技巧，做出了突出的贡献。这些全新的观念与技巧很多是从理论物理，包括量子场论，发展出来的。
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.
