ECONOMY

Terence Tao on AI and mathematics


With formalization projects, what we’ve noticed is that you can collaborate with people who don’t understand the entire mathematics of the entire project, but they understand one tiny little piece. It’s like any modern device. No single person can build a computer on their own, mine all the metals and refine them, and then create the hardware and the software. We have all these specialists, and we have a big logistics supply chain, and eventually we can create a smartphone or whatever. Right now, in a mathematical collaboration, everyone has to know pretty much all the mathematics, and that is a stumbling block, as [Scholze] mentioned. But with these formalizations, it is possible to compartmentalize and contribute to a project only knowing a piece of it. I think also we should start formalizing textbooks. If a textbook is formalized, you can create these very interactive textbooks, where you could describe the proof of a result in a very high-level sense, assuming lots of knowledge. But if there are steps that you don’t understand, you can expand them and go into details—all the way down the axioms if you want to. No one does this right now for textbooks because it’s too much work. But if you’re already formalizing it, the computer can create these interactive textbooks for you. It will make it easier for a mathematician in one field to start contributing to another because you can precisely specify subtasks of a big task that don’t require understanding everything.

The entire interview is worth reading.  As Adam Smith once said…




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