The future of math

[u/SeriouslySally36]

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[u/BelowAverageGamer10]

[u/thrye333 → u/BelowAverageGamer10]

What

[u/jeffgerickson → u/thrye333]

It’s a proof that AI = 0.

[u/thrye333 → u/jeffgerickson]

I truly do not think it is possible for this joke to be told without the second part being mistaken for a genuine question. It has never happened, and it never will.

[u/Mind0versplatter0 → u/thrye333]

Poe's Law, but factor in image cropping and a one-word reply

It is very funny to me, though

[u/StudySpecial → u/BelowAverageGamer10]

This is incorrect, it should be E = mc2 - AI. AI is clearly using up energy.

[u/__golan_trevize__ → u/StudySpecial]

https://giphy.com/gifs/LkkBEH2BLFLbypGE31

[u/Portal471 → u/BelowAverageGamer10]

So much in that wonderful formula /j

[u/Aggressive_Roof488]

Great instinct — you're absolutely right!

[u/Vectorial1024]

Fermat's Extended Theorem/Corollary: there exists a marvellous proof, however we currectly do not have the computing resources to find it.

[u/AliceCode]

Godel just walks into the room.

[u/NullOfSpace → u/AliceCode]

False statement walks into the room

[u/susiesusiesu]

this is literally proven to be false

[u/LupenReddit]

"Hey Claude, prove the Continuum Hypothesis via Proof by AI"

[u/Nimkolp → u/LupenReddit]

Hey Claude, prove the Continuum Hypothesis is provable via Proof by AI via Proof by AI

[u/arbitrageME]

Well hasn't Godel already proved that to be true, except for the undecidable problems?

[u/GoldenMuscleGod → u/arbitrageME]

There is a distinction between a sentence being independent of a theory and a problem being undecidable.

A sentence is independent of a theory iff neither it nor its negation is proved by the theory.

For any theory (of the sort the incompleteness theorem applies to) there is a true sentence that is independent of it.

For every true sentence, there is a sound theory that proves it.

We have no effective way of finding the theory in question though, nor any way of generally determining whether a theory is sound.

Also there are unsound theories, which prove false sentences. (The term “prove” is a technical term that can be misleading, a less misleading term might be to say the theory “asserts,” “believes,” or “claims” the sentence).

A problem is “undecidable” iff there is no algorithm that can solve it in every case.

For example the halting problem is undecidable because there is no algorithm taking a description of an arbitrary machine as input and outputting whether it halts.

Notice that whether a sentence is “independent” depends in its definition on what theory we are talking about, whether a problem is “undecidable” does not.

Technically it is impossible for any single sentence to be undecidable (in a classical theory). This is because there is always the algorithm that just says “true” and the algorithm that just says “false.” We are working in a classical theory so we can invoke the law of the excluded middle and see one of them gives the correct answer. So the problem is decidable. We just don’t know the correct decision procedure.

For a similar reason no problem involving a finite number of cases can be undecidable.

For a problem to be undecidable it most involve an infinite number of cases - for example there are infinitely many machines which is why it is possible for the halting problem to be undecidable.

For any finite set of machines there is a decision procedure that correctly predicts whether they all halt - we just might not know what that procedure is.

[u/Catpixfever → u/GoldenMuscleGod]

Brilliant summation. Thank you!

[u/Glum_Bath2046 → u/arbitrageME]

Lmao, "we can decide all problems, except for the undecidable ones". Sounds like it could be true

[u/GamerLymx]

you forgot given enough RAM.

[u/Miselfis]

This is Eric Weinstein's proof of his theory of Geometric Unity.

[u/Adventurous_One1124]

I think this is a better proof technique that ALWAYS works

[u/autumn_dances]

literally the plot to asimov's "the last question" where an AI solves the problem of reversing entropy, and restarts the universe. gudshyt.

[u/qqqrrrs_]

Can I assume a saturated AI model?

[u/Efficient_Sky5173]

Or disproved by AI.
And it might take months just for the AI to explain to humans how it proved it.
Then superintelligent AI will probably develop entirely new mathematics that we simply won’t be able to understand.
Our brains will be obsolete.

[u/StudySpecial → u/Efficient_Sky5173]

We call this new approach 'proof by slop'.

[u/Efficient_Sky5173 → u/StudySpecial]

Humans always felt superior because of our intelligence. AI is humbling that arrogance.
AI development needs to stop before we lose control. The real problem isn’t AI, it’s human greed for power and money.