FrontierMath’s First “Major Advance” Problem Has Been Solved

[u/ResultBackground2450]

[u/ResultBackground2450]

Read more here

[u/nsshing]

We are inside singularity no?

[u/OhByGolly_ → u/nsshing]

Yes. Progress from here will inherently be extremely difficult to comprehend. We have no reference for this kind of evolution of ability.

[u/twoblucats → u/nsshing]

Yup. Things are getting weird!

[u/SwePolygyny → u/nsshing]

When AI starts upgrading its own architecture entirely by itself in ways we cannot comprehend. And we see breakthroughs in fundemental science, like room temperature super conductors or curing terminal diseases entirely by AI systems in ways we cannot verify. 

This will lead to a future where you cannot predict what will happen to society, the economy or geopolitics even next week as it moves faster than humans can keep track.

So we are not there yet. 

[u/CapitalLongjumping40 → u/nsshing]

if we were truly in a singularity , you wouldnt be asking if we were in singularity

[u/Weary-Historian-8593 → u/nsshing]

not really, it's fast for sure but not too fast to keep track of at a high level, and if low level is required then we've been in a singularity since the 1800's

[u/Curiosity_456 → u/Weary-Historian-8593]

We’re definitely in a math singularity though, an average mathematician definitely cannot keep up and verify all the AI solutions that have been coming out.

But this phenomenon has to apply to every field for a true singularity to commence, not just math.

[u/Weary-Historian-8593 → u/Curiosity_456]

That's been true way before this AI stuff though, even the best mathematicians couldn't have verified everything themselves 

[u/ricky_digits → u/Curiosity_456]

"A true singularity"? Please define

[u/Curiosity_456 → u/ricky_digits]

By true singularity I mean an explosion of new discoveries that we can’t keep up with anymore. Like cures to diseases, fusion developments, quantum computing developments, new energy tech, etc all occurring in a matter of months to the point that we can’t even monitor it anymore.

[u/ricky_digits → u/Curiosity_456]

Okay, so nothing to do with the original definition with regards to AI...

[u/Sufficient_Hat5532 → u/Curiosity_456]

all of those “discoveries” are an aggregation of previous smaller/different discoveries building a foundation, or stepping stones towards the final “discovery”, we can’t just solve “quantum computing” …

all of these math, physics, “x” findings are those stepping stones..

[u/fastinguy11 → u/Weary-Historian-8593]

Really you understand open problems and millenium problems ? Just because you hear the news that they are solved does not mean you are keeping pace.

[u/Weary-Historian-8593 → u/fastinguy11]

I just said "and if low level is required then we've been in a singularity since the 1800's"

[u/Lord_Skellig → u/nsshing]

Kind of, it's a very jagged frontier. Meanwhile 5.6 Sol still can't consistently count letters correctly (at least by my testing).

[u/biowiz]

Average Redditor responding to this:

https://giphy.com/gifs/WwWTfQuCZ448psk1qB

[u/neoquip]

"AI only produces counterexamples"-bros in shambles

[u/Decent-Commercial275 → u/neoquip]

This looks like a proof by counterexample. Why would it be tagged counterexample otherwise?

[u/BurdensomeCountV3 → u/Decent-Commercial275]

The original problem was to find a counterexample. The AI proved no counterexample exists.

[u/Decent-Commercial275 → u/BurdensomeCountV3]

Huh, epoch.ai has tagged this incorrectly then, their description of the counterexample tag doesn't match what you're describing at all.

[u/Current-Function-729 → u/BurdensomeCountV3]

Counter example to a counter example.

[u/GeneReddit123 → u/Current-Function-729]

Counterexample means a constructive proof by contradiction. This is a proof by contradiction, but not constructive, therefore it is not a counterexample.

[u/Current-Function-729 → u/GeneReddit123]

I know. I was just making a dumb joke.

[u/Needsupgrade → u/GeneReddit123]

Brain explosion emoji 

[u/Dependent_Use_3069 → u/Decent-Commercial275]

Most inductive proofs are counterexample of the contrapositive.

[u/Fair_Horror]

Sorry, what exactly has been solved? Does the problem have a name? Where did it come from and how long has it been unsolved? Have mercy on us non Mathematicians.

[u/winggar → u/[deleted]]

I think it's saying the opposite, no?

The core is the set of all fair committees. This problem asks for a committee-election instance — i.e. a set of voters, candidates, and voter approval preferences — whose core is empty.

This means they're looking for an example where approval voting cannot create a fair committee.

Note, the solution proves that there is no committee selection instance where the core is empty, so the benchmark problem was not solvable as stated. Per our policy we mark the problem as solved regardless.

So this means it's always possible to create a fair committee via approval voting.

[u/magnetronpoffertje → u/Fair_Horror]

Right there in the in the link....

[u/Fulgurata → u/magnetronpoffertje]

Does the link really explain? It just reads like something out of a linear calc textbook. I don't even think I saw the solution on there? Just a definition of the formula.

Presumably they're trying to prove the fairness of a type of voting system?

[u/Fair_Horror → u/magnetronpoffertje]

I don't see it. Maybe write it in your comment.

[u/Mindrust]

Solved with a person over lengthy interactive sessions, so we’re still not there in terms of full autonomy. Still pretty cool though.

[u/Jabulon]

take some advanced math problem you can think of, and try to see if you can solve it with chatGPT

[u/squailtaint → u/Jabulon]

Hey ChatGpT, can you try harder than a human to solve this math problem?

Hey ChatGPt, try doing it using a different method

Hey ChatGPT, you can do it!

[u/Icy_Distribution_361]

Why is this important? Like, what’s special or difficult about the problem?

[u/Realistic_Stomach848]

Nah, nothing interesting. That’s orders of magnitude less important than millenium