Re:What do we mean by "the foundations of mathematics"?
by jimwhite42 on Thursday November 02, 2023 @09:51AM
(#38113502)
I think a little hesitance on the overall success of these sorts of projects is prudent, given the history of axiomatic and formal expections and reality.
But let's say they make huge amounts of progress - they might improve the ergonomics enough that the formal foundations of mathematics will be brought into mathematics departments as a standard, legitimate and popular subject. But I still can't see how this would affect most mathematics.
Re:What do we mean by "the foundations of mathematics"?
by BoiledCabbage on Thursday November 02, 2023 @01:46PM
(#38117380)
> But I still can't see how this would affect most mathematics.
It won't, in the same way that introducing physics didn't affect philosophers. They were still free to do philosophy. But most new innovation and innovators came up doing physics instead - and that's been where all the growth had been for centuries.
In the end ungrounded theory is better than nothing. But grounded theory beats out ungrounded theory hands down.
Which is happening right now — and the younger mathematicians who are supporting those efforts (and more broadly, things like Lean libraries) are gaining the experience while making the ergonomic changes.
That is, the person you’re replying to isn’t unaware of the historic problems: they’re pointing out that migration is starting now with early adopters like Tao and Scholze.