Re:Terence Tao: Math 2.0 [pdf]
by mrlongroots on Sunday October 11, 2026 @04:14PM
(#50047353)
> This is an empirical question, right? We could have three teams of researchers, team A focusing purely on understanding, team B focusing purely on solving problems, and team C focusing on a combination of understanding and solving problems. See which one makes the most progress.
This is not me being snarky, but all meaningful questions can be settled empirically---e.g., "what happens to my body if I jump off the cliff". But empirical trials have a cost (time, money, irreversibility etc.) and we model and predict because it's cheaper than the trial.
My point is that pushing for human understanding as the primary goal assumes an answer to an empirical question that we don't yet have evidence for. How do we know that human understanding is the right instrumental goal, as opposed to solving open problems as fast as possible? Even if we think human understanding has intrinsic value, how do we know which approach will maximize human understanding in the long run?
The idea that all meaningful questions can be answered empirically is known as "verificationism" and is philosophically quite dubious.
> all meaningful questions can be settled empirically
This is a logical positivist view, that not everyone agrees with.
Re:Terence Tao: Math 2.0 [pdf]
by mrlongroots on Wednesday October 14, 2026 @02:36AM
(#50083303)
My point was much simpler, and in the context of the parent comment. With a gun to the head, I have no opinion on whether there exists a question that can not be settled empirically or how big that set is, just that I find it a convenient belief to operate off on a daily basis.
I respect Tao and I belive he's trying to think deeply about the issues, but a lot of his thinking seems to revolve around preserving the current roles and prestige of mathematicians, and also makes a lot of assumptions about the capabilities of AI years or decades into the future.