Terence Tao on AI and mathematics

With legalization projects, we’ve noticed that you can work with people who don’t understand all the math of the whole project, but they understand a small part of it. It’s like any modern device. No one can build a computer by themselves, dig up all the metal and refine it, then make the hardware and software. We have all these experts, and we have a huge supply chain, and ultimately we can build a smartphone or anything. At present, with the cooperation of statistics, everyone must know very well all the statistics, and that is a stumbling block, as [Scholze] mentioned. But with this configuration, it is possible to divide and contribute to the project knowing only part of it. I think we should also start legalizing textbooks. If the book is formalized, you can create these highly interactive textbooks, where you can explain the evidence of the result in a very high-level sense, taking in a lot of information. But if there are steps you don’t understand, you can expand them and get into the details—all down to axioms if you want. No one is doing this right now in textbooks because it’s too much work. But if you’re already doing it legitimately, a computer can create these interactive textbooks for you. It will make it easier for mathematicians in one field to start contributing to another because you can fine-tune the sub-tasks of the main task without needing to understand everything.

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