Still, the non-mathematical reader can go far in understanding mathematical reasoning.

不过，非数学专业的读者在理解数学推理方面还是可以走得很远的。

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The more we can discover about the mathematical properties of generic swarm processing, the better our understanding will be of both artificial complexity and biological complexity.

我们能够发现的通用群处理过程的数学属性越多，我们对仿生复杂性与生物复杂性的理解就越好。

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And that is a rather deep purely mathematical consequence of understanding gravitation in this way.

以这种方式理解万有引力，是纯数学的一个十分深刻推论。

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Pupils should instead be given time to gain a secure understanding of mathematical concepts, it adds.

BBC: Primary maths plan threatens 'too much too soon'

He says all pupils must be helped to build a secure basis of mathematical understanding early on.

BBC: Primary maths plan threatens 'too much too soon'

At no point does proceeding from one step to the next require understanding, let alone mathematical intuition.

ECONOMIST: Just what does it mean to prove something?