以表彰他們在洛倫茲幾何與黎曼幾何中的非線性偏微分方程方面的高度創新工作，及對廣義相對論和拓撲學的應用。
黎曼 (Riemann) 發明一種幾何學，以描述高維彎曲空間；其後愛因斯坦用之以描述重力場。自此，相關的非線性偏微分方程理論已成為一個核心研究方向。這些方程雖然優雅，但不易求解，難度眾所周知。一個關鍵之點是其解是否演生出奇點。
德梅特里奧斯・克里斯托多羅 (Demetrios Christodoulou) 對於數學物理，尤其是廣義相對論，有非常重要的貢獻。他最近關於真空愛因斯坦方程中，捕獲曲面是否存在，取得了令人驚訝的動力學證明，指出黑洞可以通過引力波的相互作用而產生。在這個工作之前，他還深入研究了有對稱性的較簡單情形，並證明裸奇點同樣可以產生，但是它並不穩定。他還同塞爾秀•克萊納爾 (Sergiu Klainerman) 一起證明了的閔可夫斯基空間 (Minkowski spacetime) 的非線性穩定性。借助非凡的數學技術，克里斯托多羅的工作顯示出他對方程式背後的物理的深入瞭解。
After Newton’s introduction of calculus and in particular differential equations to describe the motion of the planets, classical physics and geometry developed with more complex phenomena naturally being formulated in terms of partial differential equations. The Einstein equations in general relativity and the Ricci Flow equation in Riemannian geometry are two celebrated geometric partial differential equations. The first describes the geometry of four dimensional spacetime and it relates gravitation to curvature. The second gives an evolution of Riemannian geometries in which the flow at a given time is dictated by the curvature of the space at that time. Both of these equations are very elegant in their formulation. They are nonlinear partial differential equations in several unknown quantities which in turn depend on several variables. While they are of quite different characteristics in terms of the classification of such equations, they share the feature that they are notoriously difficult to study rigorously (even on a computer). Central to the understanding of the solutions, is whether they form singularities or not, and if so what is their nature. In the spacetime setting, examples of singularities are black holes and more generally gravitational collapse. In the Ricci Flow, should singularities arise in the course of the evolution, then for certain applications they need to be resolved. Christodoulou, in the case of Einstein’s equations, and Hamilton in the case of the Ricci Flow, have made many of the fundamental breakthroughs in the theory of these geometric equations and especially in understanding their singularities. Their works have spectacular applications both to mathematics and to physics.
