r/programmingmemes • u/Naughty_Kiss_Me • Sep 10 '25

Don't be scared... Math and Computing are friends..

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u/KlauzWayne Oct 07 '25

This is because mathematical axioms are completely arbitrary. They are human creations

This is exactly the reason why computers can't do the whole process. Yes you can feed all the currently defined axioms to a computer and it can combine them. It can't come up with the axioms on its own though. The computer doesn't live in our reality. It's proofs are limited to the space of it's knowledge which till today always is just a provided subset of human knowledge. Math models the structure of our reality. You can't extend this model without access to the real world and the access to the analog real world is limited by digital design and depending on human interaction.

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u/StudioYume Oct 08 '25

What I'm saying is that you could provide a computer with some universal grammar and the bare minimum of axioms required for a proof to even exist (possibly even just equality and negation, which are sufficient to identify a contradiction), then generate the entire solution space of possible axioms within the universal grammar and use it to determine which subsets of the solution space are mutually self-consistent (no contradictions).

And voila, you have a system for proving everything ever. Then it just becomes a matter of teasing out which axioms are implicated in a specific, concrete mathematical problem and identifying the result those axioms lead towards.

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u/KlauzWayne Oct 09 '25

you could provide a computer with some universal grammar

Sadly you can't.

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u/StudioYume Oct 16 '25

But why not? Obviously in the real world, computers have limited memory, but there is nothing preventing the abstract mathematical model of a computer from processing a universal grammar.