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Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao A scrupulous writer, in every sentence that he writes, will ask himself at least four questions, thus: (George Orwell, “Politics and the English Language“, 1946) A paper should not just be a sequence of formulae or logical steps. It should also be organized and motivated in such a way that the reader is always aware what the near-term and long-term objectives of any portion of the paper are, how the current arguments are advancing towards these goals, how crucial they are to those goals, and why the claimed results at each step are at least plausible (or if they are surprising, to indicate exactly why and how they are surprising). Informal, heuristic, or motivational reasoning is therefore very welcome, but should be clearly indicated as such to distinguish it from formal, rigorous reasoning (for instance, these portions of the paper can be placed in remarks or foot

Motivate the paper | What's new What's new Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao Home About Career advice On writing Books Mastodon+ Applets Subscribe to feed Motivate the paper A scrupulous writer, in every sentence that he writes, will ask himself at least four questions, thus: What am I trying to say? What words will express it? What image or idiom will make it clearer? Is this image fresh enough to have an effect? ( George Orwell , “ Politics and the English Language “, 1946) A paper s

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