这位非科班出身的数学家对数字特别痴迷。

This untutored mathematician had an obsession with numbers

对于数学家来说，不可交换的对象与可交换的对象是一样真实的。

Noncommuting objects are as real to the mathematician as commuting objects.

多年来，日晷一直吸引着科学家和数学家们。

For many years sundials have cast their spell over scientists and mathematicians

由于风险过高，银行便聘请数学家来解决这些问题。

The risks can be so complex that banks hire mathematicians to puzzle them out.

就数学家们来说，用学者的眼光来看问题不无裨益。

As far as mathematicians are concerned, there's a certain virtue in wearing intellectual blinkers

只有每一逻辑步骤都被其他数学家验证之后，证明才能成立。

Only when each logical step has been checked by other mathematicians will the proof be accepted.

数学家们转而去挑选周期解。

The mathematicians turned to culling periodic solutions.

虽然人类数学成就的复杂性持续再创新高，但我们当中许多本身并非数学家(或者职业并非工程师）的人，可能很难记住我们最后一次使用微积分是什么时候了。

While human achievements in mathematics continue to reach new levels of complexity, many of us who aren't mathematicians at heart ( or engineers by trade) may struggle to remember the last time we used calculus.

例如，谈论数学天才或多或少生来就这样，这种方法会使学生形成固定思维，但描述一位爱上数学并成长为具有惊人技能的伟大数学家，则会形成成长型思维模式。

For instance, talking about mathematical geniuses who were more or less born that way puts students in a fixed mind-set, but descriptions of great mathematicians who fell in love with math and developed amazing skills produce a growth mind-set.