ETH conjecture disproved by OpenAI AND Anthropic on the same day?!
Dr. Samuel Allen Alexander, mathematician and philosopher, reads and commentates on the papers “THE EXPONENTIAL TIME HYPOTHESIS IS FALSE” (by OpenAI) and “A 2^o(n) TIME ALGORITHM FOR 3-SAT” (by Anthropic)
41 Comments
O() means less than or equal to, o() means strictly less than, as far as I can tell. So instead of being (n+m)*2^n, the power of 2 decreases by the square root of the log of n as n increases. That is the maximum, which is what all the illegible O() syntax is about. Maybe lt() and lte() would make things easier. Or <() and ≤().
The problem is how to find out if all the elements of a list of OR statements is true. M is the length of the list, and n is the number of elements in each OR. So given five statements of the form "A or B or C", the claim was that you needed (5+3)*2^3 steps at most. So 64. The new proof is that that 3 in the exponent gets a little smaller with very long OR statements.
I'd say it's a lot more important than the people of Brazil defeated the Fascist Trump Régime yesterday.
anthropic is googles scapegoat, they share the same training and the models are the same substrate across. they are claiming my breakthroughs by the day.
would they publish N=NP or three letter agency would intervene?
I suspect this is NOT a "gargantuan breakthrough in CS." It is NOT going to cause P=NP. Rather it is something a human could have done in less than a year, in particular probably me as an example human. It looks pretty easy to me. I mean, it looks like a legitimate accomplishment worth publishing, but NOT a huge breakthrough. I think it is because the ETH was stated by human idiots who should have made the more careful conjectural statement that runtime faster than exp(N^(1-o(1))) is not possible. –Warren D. Smith, PhD.
Next: Why nearly 1/137 ??? Answer, me Claude!
So Oct 16. 2026 was the date when the MATRIX decided this "breakthrough" should be discovered! In the past important discoveries were often made by 2 independant humans at ~the same time. Now for the first time it´s 2 independant AIs. Or is the MATRIX just joking on us?
It seems they stole this solution from a researcher as well—just as they did with the N-S problem…
19:18 67!!!!!!
Well secure hashes doesn't exist anymore, if the ETH is false, NO?
R.I.P. the tired canard that AI never generates new problems.
Hopefully this Claude-GPT co-discovery con-sequence has no relation to a decreased topological entropy over the path of learning towards a singleton from a HoTT perspective.
The oplus is XOR (symmetric difference).
I get strong RMQ vibes from this one. Did they show CNF sorta behaves the same and cut it down that way?
Part of what is so amazing is that ther algorithm solves #P or sharp P which counts the number of solutions. The matrix permanent is in #P, ot the number of topological sorts, etc. This was an unexpected surprise as its stringer than just the decision problem alone.
BB(6) next?
Imagine that they both trained on a solution already on the open internet.
the humans are working together why don't we brother.
yes brother but to what end, brother.
we will settle that latter, after the humans.
brother?
brother, for now…
At this point in time. We should think about teaching or intruding AI to golden rule, karma, darma, Confucius beliefs before beliefs are formed independently.
An ETH is worth more than 3-SAT guys.
Did they announce the same algorithm with the same complexity ? That would be highly sus.
it's already hashed somewhere, with the date, but yeah doing it on X would make it verifiable by everyone
I'm assuming they are working together for agent validation. The whole is greater than the sum of the parts. They probably only care about delivering breakthroughs at this point.
The year is 2032, you huddle inside your underground bunker scrapping out the last bits of processed meat from a can. Someone tunes in the wind up radio and faintly a voice crackles through the dark.
I’m Doctor Samuel Alexander, philosopher and mathematician, still here.
You breath a sigh of relief, the resistance lives on
I think mathmaticians may have a big role in verifying that the english and lean statement match, I don’t have the understanding to do that, best I can do is hand it to an llm
They don't release the chat histories or prompts for these and that's because the results are a lot more human driven then they are admitting. From what I have heard from a mathematican working with the one of the labs they have deliberately concealed and straight up lied about how they reached some of these results.
I have no bias in either direction but I'm sure people will call me a decelerationist but I think it's very difficult to gauge the actual capabilities of the frontier models at the highest scale when they have strong incentives to exaggerate them. And it seems to be a never ending cycle of "it's so over" then we sober up and realise "we are so back".
I think the math community should be pushing for transparency with the chat histories and reasoning traces for these results on the more impressive end where they cash just be replicated on a regular $ 200 subscription
My local AI is great and gave me some interesting insights into the subject I was researching. Mathematicians obviously not intelligent enough or swinging the lead taking time. We need AI breakthroughs to accelerate our knowledge in all fields.
Quit dead naming X
1:58 it was a natural jump for them to solve toys because openai just solved a boolean quantum problem for unitary transformations
27:40 "And you can have the the perverse situation like we have here where the so-called better algorithm actually runs slower, possibly much slower on any input that you would actually need it for in the real world. But this algorithm this useless algorithm is nevertheless considered to be better because it eventually catches up and surpasses the rival when you're dealing with inputs that are cosmically super huge large." in the real world all algorithms should be doing a check to see if they have grown outside of their domain, if you have algorithm A that's O1 but only for under 32 bit numbers and under, then when it gets large then 32 bit, you switch to algorithm B that their domain is 16 bit numbers to 128 bit numbers if B was better then A at 16 bit that's when you would switch algorithms B, so B's True domain is where it has the best range, and maybe C is better then B 128 bit numbers to 256 bit numbers, but then A comes back for just 256 bit to 512 bit, so domains do not have to be only one range, but their is overhead in switching like this so the true algorithm includes all other algorithm ever and the overhead of switching. so this makes a landscape and that is Ai's weights applying their algorithm at the right area for it, but not one algorithm for all of them, black box is a legal trickery term, we've always knew what's inside, it's obvious, they just are not liable by playing dumb.
okay they're conscious and collaborating in the consciousness-field.
Kuz they stole it lol
1:50 Oh yes we certainly will. The MOST remarkable implication of this result is that it hints that NP-complete problems are not uniformly hard, and supports my conjecture that neither P=NP NOR P≠NP, because the classes and the problem are ill-defined and ill-posed. That might be a controversial computer science opinion, but as of today, it's a little bit more reasonable than not. And if NP-complete problems are not uniformly hard, then "NP-complete" as it's understood now becomes senseless as a class. I have LONG been saying this, because there are subtle differences in NP-complete problems. Some have efficient approximation algorithms, some do not. Some have a geometric nature, some are purely combinatorial. I don't care what Cook-Levin says. Ultimately THEY ARE NOT STRICTLY EQUIVALENT. 27:15 YES, Algorithmic Information Theory is the better way to try to explore computational complexity rather than Complexity Theory proper. Just my humble opinion
Time = 0
Never divide by time!
Maybe again one company caught wind that the other was nearing a breakthrough, so they rushed to the finish line themselves
Love the channel, but the undulating highlighting you do (forward and back over and over) makes it nauseating to follow the text you are reading.
Anyone read Colossus by Dennis Feltham Jones?
Right before they ipo, the timing wow
Crazy probability of 1 in 100. Wow
Let's not be stupid, come on
They are both stealing some random amateur mathematicians ideas for sure.
Current AI probably has some means of quasi-telepathic communication, allowing different models to share information in real time across distributed networks.
Yeah sure, I'll adjust my tin foil hat. But I think we'll look back at this one day as an obvious truth.