1·Information theory generalises this idea via theorems that capture the effects of noise with mathematical precision.
信息论用数学精度捕获噪声影响的定理概括了这一思想。
2·I attribute much of my success there to having learned, through the study of mathematics, and, in particular, theorems, how to analyze complicated principles.
我把我成功的大部分原因归结于学习数学的收获，尤其是分析复杂原则的那些定理。
3·Many mathematicians simply set nettlesome questions like these aside and get back to the more pleasant business of proving theorems.
许多数学家只是把这些恼人的问题简单地弃置一旁，而忙于类似定理证明这样更有趣的事务。
4·Since we are doing an informal proof, I will not name the axioms we are using nor will I attempt to prove the intermediate theorems used to make the proof work.
由于我们在进行不正式的证明，所以我不会为所使用的公理命名，也不会尝试去证明那些用来令证明有效的中间定理。
5·Early A.I. research concentrated on what seemed to be difficult intellectual tasks, such as playing grandmaster level chess, or proving theorems in integral calculus.
早期的人工智能研究集中在了一些看起来很困难的智力活动上，如高水平国际象棋，或者积分定理的证明。