内容 科学与方法 · 30
Science and Method · Mathematical Definitions and Teaching
A definition teaches only when it preserves the reason for the concept.
定义只有保留概念出现的理由时，才真正能教人。
Teaching mathematics is not the same as reciting finished formalism.
数学教学不等于背诵完成后的形式主义。
命题
Mathematical Definitions and Teaching turns method into a visible object of mathematical reflection.
卷三 6 · 定义和教学 把方法本身变成可以被数学反思的对象。
读法检查 worked example
题
What is a bad definition in this sense?
按这个标准，坏定义是什么？
解
One that is logically compact but hides the problem it was made to solve.
逻辑上很短，却藏起它原本要解决的问题。
互链 context
与哈代数学审美 hardy-apology/overview、非欧几何原作 non-euclidean-originals/lobachevsky-overview、分析严密化史 math-meta/topic-calculus-and-analysis-rigor 和拓扑学起源 math-meta/topic-topology-origins 对读。
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