1. The risks can be so complex that banks hire mathematicians to assess them. 这类风险可以是如此复杂以至于银行雇佣数学家们去评估它们。
2. 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。
3. 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。
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. To mathematicians, a chair is equivalent to an apple; a mug—at least, one with a handle—is like a doughnut. 对于数学家而言，一把椅子相当于一个苹果；一个杯子——至少是有把手的——就像一个油炸圈饼。
