Automorphic forms and geometric group theory

牛顿力学为许多日常现象提供了非常准确的描述。尽管如此，物理学家们相信，量子力学中有一个更基本的描述。因此，对量子效应很小的系统的量子力学描述应该表现得像经典描述一样。在许多情况下，存在定义明确的经典和量子描述的数学模型。刚才提到的物理学导致了对这些模型的数学预测，这些预测可以被严格地证明或反驳。

Newtonian mechanics provides a very accurate description of many everyday phenomena. Nevertheless, physicists believe that a more fundamental description is available in quantum mechanics. It follows that the quantum-mechanical description of a system in which quantum effects are small should behave like the classical description. In many cases, well-defined mathematical models of the classical and quantum descriptions exist. The physics just mentioned leads to mathematical predictions about these models, predictions which can be proven or disproven rigorously.