以表彰他们在洛伦兹几何与黎曼几何中的非线性偏微分方程方面的高度创新工作，及对广义相对论和拓扑学的应用。
黎曼 (Riemann) 发明一种几何学，以描述高维弯曲空间；其后爱因斯坦用之以描述重力场。自此，相关的非线性偏微分方程理论已成为一个核心研究方向。这些方程虽然优雅，但不易求解，难度众所周知。一个关键之点是其解是否演生出奇点。
德梅特里奥斯・克里斯托多罗 (Demetrios Christodoulou) 对於数学物理，尤其是广义相对论，有非常重要的贡献。他最近关於真空爱因斯坦方程中，捕获曲面是否存在，取得了令人惊讶的动力学证明，指出黑洞可以通过引力波的相互作用而产生。在这个工作之前，他还深入研究了有对称性的较简单情形，并证明裸奇点同样可以产生，但是它并不稳定。他还同塞尔秀•克莱纳尔 (Sergiu Klainerman) 一起证明了的闵可夫斯基空间 (Minkowski spacetime) 的非线性稳定性。借助非凡的数学技术，克里斯托多罗的工作显示出他对方程式背后的物理的深入了解。
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.
