[t_mann]

I may have actually given him a bit too much credit initially (I'll admit, I didn't read the full article). Even if I acknowledge that Wolfram probably knows a lot more graduate-level math than me, sentences like these raise some eyebrows:

"There are regions of 'metamathematical space' (the slices of proof space) that might have higher 'densities of proofs' corresponding to more interconnected fields of mathematics - or more 'metamathematical energy'. And as part of the generic behavior of multicomputational systems we can expect an analog of Einstein’s equations, and we can expect that 'proof geodesics' will be 'gravitationally attracted' to regions of higher 'metamathematical energy'. (...) In the presence of large amounts of 'metamathematical energy' there’ll effectively be a metamathematical black hole formed. And where there’s a 'singularity in metamathematical space' there’ll be a whole collection of proof paths that just end—effectively corresponding to a decidable area of mathematics."

Is this for real? Is this a legit mathematical theory that leads to new mathematical discoveries? Are these conjectures that he expects to be rigorously provable? Or are these just ramblings of someone who left the game a long time ago and who thinks that he still 'has it'?

[FrozenVoid]

It seems to make sense, if you view that as current math theories treated as "windows" into a space of possible mathematics, like e.g. quantum string theory possibility space(10^500) vs "accepted string theories" https://www.dummies.com/article/academics-the-arts/science/p...

[tinco]

Not to give any credence to Wolfram's theories, I'm wholly unqualified, but why not? Mathematics extends all the way into algorithms and complexity. We have already established that for example machine learning could lead to new mathematical discoveries, and machine learning is easily described by math.

Of course whether such a space is in any way practically computable or of a scale that could even reasonably comprehendable to a human being or even to some machine is an unanswered question.

[t_mann]

Sure, in principle it's interesting, and I can fathom that statements like these could in principle be provable. This 'graphical' perspective could lead to interesting insights eg in proof theory (I actually wouldn't be surprised if things like that had already been done).

My point was rather: making any statement in modern mathematics is hard. I was wondering how serious he is about formally establishing any insights about his ideas, eg a connection between proof spaces and Einstein's equations (presumably general relativity).

[eximius]

Theorising about a structure behind proofs made of an alphabet isnt new - its part of theorems like Godels Incompleteness, etc.

Actually exploring or evaluating objects in this space has always (and continues to be) intractable due to the high complexity and computational power required.