"The connection between mathematics and computer science is not just a one-way street; each field enriches the other."

数学和计算机科学之间的联系不是单向的；每个领域都丰富了另一个领域。

"The study of computational complexity teaches us that some problems are inherently difficult, no matter how clever our algorithms are."

计算复杂性的研究告诉我们，有些问题本质上是困难的，无论我们的算法多么聪明。

"Theoretical computer science is a field where deep mathematical insights lead to practical computational tools."

理论计算机科学是一个领域，其中深刻的数学见解导致了实用的计算工具。

"The challenge in theoretical computer science is not just to solve problems, but to understand why they are hard to solve."

理论计算机科学中的挑战不仅仅是解决问题，而是理解为什么它们难以解决。

"In the study of algorithms, we often find that the most efficient solutions are also the most elegant."

在算法的研究中，我们经常发现最有效的解决方案也是最优雅的。

"The interplay between mathematics and computer science is a rich source of deep and beautiful results."

数学和计算机科学之间的相互作用是深刻而美丽结果的丰富源泉。

"Understanding the limits of computation is as important as understanding the limits of mathematics."

理解计算的极限与理解数学的极限同样重要。

"The beauty of computational complexity lies in its ability to reveal the inherent difficulty of problems, regardless of the specific algorithms used to solve them."

计算复杂性的美在于它能够揭示问题的固有难度，而不管用于解决这些问题的具体算法是什么。

"In mathematics, we often seek elegance and simplicity, but in computer science, we must also consider practicality and efficiency."

在数学中，我们常常追求优雅和简洁，但在计算机科学中，我们还必须考虑实用性和效率。

"Theoretical computer science is not just about algorithms and data structures; it's about understanding the fundamental limits of computation."

理论计算机科学不仅仅是关于算法和数据结构；它是关于理解计算的基本限制。