Sentos Australibia retweeted
Or my email for thar matter about Brendon Hiers from October last year. Did you even bother to read it, Ali?
Sentos Australibia retweeted
Test your device with dv-g3b-emudhra.we-have-a-pro…
I still remember that my PhD collaborator's paper was rejected for "it is practically impossible for modern PKI to fail."
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They run script that did this on purpose in the middle of key ceremony...it was deliberate.
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Here is M, Misanthropy aka Mercury, CIA, talking how he trusts Brendon because he worked for Builders Door & Trim in Las Vegas (for 27 years 6 months Russel Radke was admin there). This suggests Radke is CIA asset.
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This fork now repairs all of the effected proofs except for DefocusingNLS. I need to sleep, but will hopefully be fixed by tmrw morning
If anyone is reading this, I would appreciate if you also run comparator on these 10 challenges to double-check the results
Sentos Australibia retweeted
Today I released a preprint answering a 60-year old problem dating back to Bourbaki. I was originally motivated to work on this problem because it is needed to define differential forms in Mathlib.
I will give a talk at NYU tomorrow presenting the proof.
github.com/Deicyde/alternati…
Sentos Australibia retweeted
Finitely presented infinite amenable simple group. Amenability seems to be a technique from probability theory. Finite presentation seems to be an idea that we tried to implement (unpublished), but we missed a simple trick. All preliminary impressions (it is really hard to read).
Sentos Australibia retweeted
I am announcing an update on this 3SUM problem.
We now have the fastest deterministic 3SUM algorithm known: n¹·⁹⁹⁶¹
That's 4.5× the deterministic saving below n², with zero randomness, and it matches the best randomized bound.
Truly Subquadratic 3SUM and Truly Subcubic APSP via Triangles in Sparse Lopsided Graphs
(Josh Alman)@firebat03 , Virginia Vassilevska Williams
This is really a huge breakthrough result in fine-grained complexity.
arxiv.org/abs/2610.06783
Sentos Australibia retweeted
c = 4/33 proven in 36 pages!
This inspired me. I set out, with GPT6-Pro of course, to find a short proof for a larger value of c. Mine isn't 27 pages, but it's a much larger half-plane!
Formalization locally verified in Lean, NanoDa, and con-ron.
PDF & formalization links in reply.
Thank you for the inspiration and starting point, Shiva!
More QRH news to come ;)
Here is a Short Proof of the Quasi-Riemann Hypothesis.
My goal here is to substantially simplify OpenAI’s proof and focus only on proving the Quasi-Riemann Hypothesis for some 1-c, without worrying about maximizing the value of the c.
I obtained a much shorter proof for c=1/48. This proof is easy to understand and it can be taught in math courses in one lecture.
It is self-contained. It is only 21 pages including abstract, proof overview, all proof details and references.
Paper is on my homepage: shivakintali.github.io
PDF file: shivakintali.github.io/paper…
CC: @AlexKontorovich @__alpoge__ @jdlichtman @cremieuxrecueil @danielmarinq @stevenstrogatz @kenono691 @littmath @nasqret @PI010101 @nechita_ion @Isaac__kim @FryRsquared @wtgowers @MarcusduSautoy @DrEugeniaCheng @JSEllenberg @JohnDCook @JDHamkins @AxlerLinear @emilyriehl @hollykrieger @Kit_Yates_Maths @PoShenLoh @robertghrist @AlexKontorovich @kenono691 @ch_nira @rrwilliams @lreyzin @ChrisPeikert @fortnow @RadishHarmers @thomasfbloom @abhatt2 @mahdi_tcs_ @octonion @prz_chojecki @thegautamkamath
Sentos Australibia retweeted
Would it be possible for someone at @OpenAI to put them up on the repo? I really would like to read through this proof!
- seed.cpp
- covout.cpp
- ub.cpp
- patchx.cpp
- atlas.cpp
- stageB.cpp
- stageC.cpp
Sentos Australibia retweeted
I'm keeping track of similar cases, I can upload them to GitHub if you like see e.g. mehmetmars7.github.io/Erdosp…
Sentos Australibia retweeted
人間の讃歌は『勇気』の讃歌ッ / A hymn to humanity is a hymn to courage -- to the pioneers at the pre-scaling era 🍻
Only after seeing the Fermat’s Last Theorem visualization (fig. 1) did I truly understand how long Wiles persevered. In the long silence, four crossed lemma clusters were peeled back layer by layer, then pushed further. Night after night in that Princeton attic, he couldn’t even know whether “dawn” existed at all. There are tons of theorems seemingly correct in the history.
The densely packed web of nodes amounts to an epic genealogy of mathematics: a single branch — sometimes even a single point — will take a math PhD’s lifetime to explore. While countless lemmas serve as bridges across ridges and straits, frequently spanning three or four different domains to make breakthroughs. For nearly 300 years, successive generations of seekers keep pursuing the Grail — until, at last, Andrew Wiles, eventually lit the path that led to Fermat’s Last Theorem.
Visualization: fermat.lzhu.me/
Sentos Australibia retweeted
I also want to point out that the paper has a GitHub containing supplementary material, which is unheared of in mathematics.
There I also share the chat transcript of the session during which I first found a solution. What is nice about that, is that I can pinpoint the exact moment where the breakthrough was made, as shown in the picture.
The initial model draft Sam and I used as a basis of our paper is also shared. So everyone can asses for themselves what exactly we have contributed.
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The results, including notes, exact certificates, source patches, and the routing audit are published here:
github.com/CrocSwap/integer-…
Sentos Australibia retweeted
We are publishing an update to OpenAI Problem #109 (integer multiplication) with a substantial further tightening:
T(n) = O(n (log n)^(1 − κ)),
With κ = 2⁻⁷⁸ (tightened from κ = 2⁻¹⁸²)
Approximately 570 million fold improvement over our previous result and a 2¹⁰⁴ fold improvement over original OAI result.
Our earlier ceiling applied to a cubic bottleneck in the network. The new witness scales quadratically; we haven't established a new ceiling.
The key was using nonadjacent axis swaps to route around the cubic bottleneck. The original manuscript already supported nonadjacent axis swaps. Using them directly reduces layout routing from O(d²) to O(d) swaps.
We're publishing a result demonstrating a substantial tightening to the results from OpenAI Problem #109 (integer multiplication).
Conditional on OpenAI's algorithmic interfaces, our parameter and network refinements improve the exponent saving in:
T(n)=O(n(\log n)^{1-\kappa})
from κ=2⁻¹⁸² to κ=5.8×10⁻³³ (between 2⁻¹⁰⁸ and 2⁻¹⁰⁷).
This represents a nearly 2⁷⁵ fold increase in the algorithm's exponent saving parameter.
We also establish a ceiling of κ<5.838×10⁻³³ for the stated network-counting family and cost inequalities. Our result exceeds 99% of that ceiling. Surpassing this ceiling would require improving the network bounds or cost analysis from the original result.
Sentos Australibia retweeted
oh yeah btw guys we can do integer multiplication faster than n log n lol
I was definitely very surprised when this one came in lol
github.com/openai/math/tree/…
