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

數學和計算機科學之間的聯系不是單向的；每個領域都豐富了另一個領域。

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

計算復雜性的研究告訴我們，有些問題本質上是困難的，無論我們的算法多么聰明。

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

理論計算機科學是一個領域，其中深刻的數學見解導致了實用的計算工具。

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

理論計算機科學中的挑戰不僅僅是解決問題，而是理解為什么它們難以解決。

"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，我們經常發現最有效的解決方案也是最優雅的。

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

數學和計算機科學之間的相互作用是深刻而美麗結果的豐富源泉。

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

理解計算的極限與理解數學的極限同樣重要。

"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."

計算復雜性的美在于它能夠揭示問題的固有難度，而不管用于解決這些問題的具體算法是什么。

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

在數學中，我們常常追求優雅和簡潔，但在計算機科學中，我們還必須考慮實用性和效率。

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

理論計算機科學不僅僅是關于算法和數據結構；它是關于理解計算的基本限制。