1·Only when each logical step has been checked by other mathematicians will the proof be accepted.
只有在每个逻辑步骤都由其他数学家验证之后，该证明才会被接受。
—— 《柯林斯英汉双解大词典》
2·Some present the lives of colorful mathematicians.
其中一些展示了丰富多彩的数学家的生活。
3·In their groundbreaking work regarding complexity and the limitations of formal systems, mathematicians Gregory Chaitin and A.N. Kolmogorov force us to consider this last claim more closely.
数学家 Gregory Chaitin 和 A.N.Kolmogorov 在他们关于复杂性和形式系统的局限性的开创性工作中，迫使我们更仔细地考虑最后一个说法。
4·Mathematicians, by contrast, tend historically towards solitude.
相比之下，数学家在历史上倾向于独处。
5·Mathematicians describe his results as elegant and beautiful but they are much too complex to be appreciated by laymen.
数学家描述他的结果是优雅而美丽的，但是这些结果太复杂了，外行人无法欣赏。