陶哲轩博客写数学问题时，通常先把对象定义清楚，再给直觉、反例和证明轮廓。把「Garth Gaudry」改写成可阅读的中文笔记，重点是：问题在问什么、已知到哪一步、下一步最容易走偏在哪。原站广告、分享条和导航已去掉。

问题在问什么

Garth Gaudry, who made many contributions to harmonic analysis and to Australian mathematics, and was also both my undergradaute and masters advisor as well as the head of school during one of my first academic jobs, died yesterday after a long battle with cancer, aged 71.

Garth worked on the interface between real-variable harmonic analysis and abstract harmonic analysis (which, despite their names, are actually two distinct fields, though certainly related to each other). He was one of the first to realise the central importance of Littlewood-Paley theory as a general foundation for both abstract and real-variable harmonic analysis, writing an influential text with Robert Edwards on the topic. He also made contributions to Clifford analysis ,

已知结果和反例

But, amongst Australian mathematicians at least, Garth will be remembered for his tireless service to the field, most notably for his pivotal role in founding the Australian Mathematical Sciences Institute (AMSI) and then serving as AMSI’s first director, and then in directing the International Centre of Excellence for Education in Mathematics (ICE-EM), the educational arm of AMSI which, among other things, developed a full suite of maths textbooks and related educational mat

I knew Garth ever since I was an undergraduate at Flinders University . He was head of school then (a position roughly equivalent to department chair in the US), but still was able to spare an hour a week to meet with me to discuss real analysis, as I worked my way through Rudin’s “Real and complex analysis” and then Stein’s “Singular integrals”, and then eventually completed a masters thesis under his supervision on Clifford-valued singular integrals. When Princeton accepted

证明或构造的主线

先写出对象、假设和失败的例子，再进入证明。没有反例的直觉，很容易把局部技巧当成一般定理。

阅读时建议盯住的点

先写出对象、假设和失败的例子，再进入证明。没有反例的直觉，很容易把局部技巧当成一般定理。

阅读和落地时建议先做的 5 件事

1. 用自己的语言重写定义和结论，不看原文能不能说清对象是什么。
2. 找一个最小反例或边界情形，确认假设少一条会怎样。
3. 把证明拆成可独立检验的引理，每步只保留一个新想法。
4. 若涉及计算或形式化，先写可复现的小例子，再谈一般情形。
5. 记下尚未解决的缺口：缺估计、缺构造，还是缺正确的范畴。

和智能体、形式化工具怎么接

龙虾PRO做 OpenClaw 落地时，数学笔记最有用的部分往往是「可检验的步骤」：定义、反例、引理边界。智能体适合帮忙展开计算和检索，不适合代替你决定哪条假设能扔。

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