以表彰他在數學分析方面的工作與其在多項學科上的應用：偏微分方程、數學物理、組合學、數論、遍歷理論與理論計算機科學。
數學分析論述極限過程，例如圓圈可以用內接正多邊形近似，隨邊數增加而任意逼近（阿基米德使用的方法），又或動力學中瞬時速度的概念等，牛頓和萊布尼茨的微積分便提供了一個數學分析工具，成功地應用於行星軌道，航空飛行和海嘯波浪等問題上。
為這些極限過程確證的多是各種組合數學的不等式。如要精確地立出和證明這些不等式，需要高度的洞察力和心智創造力。分析學的工具和語言是眾多數學領域的基礎，從概率論、統計物理以至偏微分方程、動力系統、組合數學和數論。
Mathematical analysis is concerned with the study of infinite processes, and the differential calculus of Newton and Leibniz lies at its heart. It provided the foundation and the language for Newtonian mechanics and the whole of mathematical physics. Over the past three centuries it has permeated much of mathematics and science.
Associated with the limiting process there are many technically difficult “estimates” or inequalities, of a combinatorial or algebraic nature, which prepare the ground and justify passing to the limit. Such estimates are often extremely hard since they address some subtle and important aspect of the problem at hand. Establishing this becomes a key step, opening the door to a wide variety of applications.
