Viking from Jomsborg. The DAO investor. Applied math. Geometric quantization. Building reasoning layer.
jomsborg.eth
Joined January 2013
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Jacek (Jomsborg.eth) retweeted
In case you missed it, integer factorization has been proven subexponential (deterministically, worst-case bound)!
The hard work comes from Claude's version of the ETH refutation but it seems a little more had to be done to get this result for integer factorization.
Jacek (Jomsborg.eth) retweeted
💥BREAKING: Quant Hacked 💥
BREAKING: BINANCE hacker tried draining $QNT exchange liquidity, only to find there is no supply left on exchanges:
• 1.45 billionBTC
• 875 millionETH
• 1.57 billionUSDT
• 823 millionUSDC
• 234 millionTRX
• 0.00QNT (Exchange order books empty)
Jacek (Jomsborg.eth) retweeted
Terence Tao has a troubling question about AI and mathematics.
What if we solve the greatest problems but lose the discoveries we would have made along the way?
In a new Science Friday interview, the Fields Medalist discusses AI's extraordinary progress on difficult mathematical problems, including Navier–Stokes.
His concern goes deeper than whether the proofs are correct.
Years of attempting a problem can produce new techniques, unexpected connections, and mathematical ideas useful far beyond the original question.
An AI might produce the final theorem in hours.
But what becomes of the mathematics that would have been discovered during the search?
Perhaps the greatest value of an unsolved problem has never been its solution.
Jacek (Jomsborg.eth) retweeted
Breaking RSA-2048 with 23,000 cat qubits. 🐈 In 3.14 days
This is the finding of our new paper, the latest resource estimate for Shor’s algorithm, the benchmark the whole field uses to compare quantum hardware 📄
The results are a record low for total quantum resources at this speed of execution, about 40 times fewer physical qubits than @GoogleQuantumAI 's Craig Gidney 2025 estimate. 🏁
RSA-2048 is the lock behind secure websites, banking and software updates 🔐 Shor's algorithm has been able to break it, on paper since 1994. Nobody has built the machine yet, but every year the estimate of how big it needs to be gets a little smaller.
In 2019, the best estimate was 20 million qubits. In 2024, ours was just under 100,000. Now 22,593, in 3.14 days. Yes, pi 🥧
Small isn't enough. Fast isn't enough. The new study optimizes for both. 😼
Bitcoin, Ethereum and most blockchains aren't secure either, about 30,000 qubits would be needed to crack a Bitcoin key in about an hour ₿ ⏳
How we got here, what it means for cryptography, and when it all converges, our CEO Théau Peronnin talks about it in the blog 👇
📝 Blog - alice-bob.com/blog/our-estim…
📄 Paper - eprint.iacr.org/2026/2665
Stay curious, more info coming soon 👀
#QuantumComputing #CatQubits #ShorsAlgorithm #PostQuantumCryptography #Cryptography #FaultTolerance #DeepTech
Jacek (Jomsborg.eth) retweeted
FIELDS MEDALIST TESTED IF HE'S OBSOLETE
timothy gowers took an open problem from a new paper on additive combinatorics and handed it to chatgpt 5.5 pro.
no fancy prompts. no setup. just the problem statement.
the model thought for 17 minutes. then wrote a complete latex preprint in two.
it took a bound that had been exponential for decades and brought it down to polynomial. the construction was something nobody had tried on this class of problems before.
gowers asked isaac rajagopal to review the work. rajagopal wrote the paper the model was improving on.
his verdict: the key idea is "completely original" and "quite ingenious." "the sort of idea i would be very proud to come up with after a week or two of pondering."
the model spent 17 minutes on it.
then gowers pushed further. gave it the harder generalized version. under an hour, a stronger result. exponential to polynomial again.
gowers on his own mathematical contribution to the whole thing: "zero. i didn't even do anything clever with the prompts."
the result is a solid chapter in a combinatorics phd. publishable mathematics that a graduate student would spend months producing.
a fields medalist. one of the best combinatorialists alive. sitting there copy-pasting prompts while a model does doctoral-level research in front of him.
his conclusion: "the lower bound for contributing to mathematics will now be to prove something that llms can't prove."
he gives the profession until 2029 before it's "transformed out of all recognition."
seventeen minutes. zero human math. a result that takes months by hand.
this was may 2026. five months ago. the model that did it is already outdated.
link to the paper in the comments
Jacek (Jomsborg.eth) retweeted
ETH is false.. but you need
n > (atoms in the universe)^(10^26)
even a P=NP proof should feel a tiny bit awkward past some constant. What if we like require that the inputs where it works actually fit in the universe :D just sayin
Jacek (Jomsborg.eth) retweeted
Over the past few months, Anthropic scientists have engaged in deep research partnerships with six organizations developing new medicines. We've also begun drug discovery efforts of our own.
In doing so, we’ve learned much more about how Claude can support the many stages of drug development.
In this blog post, we share some early results from these efforts, and describe how this work fits in with our wider ambitions in the life sciences.
anthropic.com/research/early…
Jacek (Jomsborg.eth) retweeted
i think it’s only fair that Grigori Perelman should IPO for a trillion dollars
Jacek (Jomsborg.eth) retweeted
OpenAI has verified that no existing cryptosystems are compromised by today’s result. Looking at the current trendline though, Erdős, Navier-Stokes, the OpenAI 700+ GitHub dump, and today’s release were all in the last six months. It's hard to deny where this is going.
Jacek (Jomsborg.eth) retweeted
OpenAI has announced to three new discoveries in mathematics, computer science, and physics:
- Local smoothing and the Kakeya conjecture
- The Exponential Time Hypothesis is false
- Existence of quantum chromodynamics and completions of the Standard Model
Jacek (Jomsborg.eth) retweeted
A 67-year-old geometry conjecture may finally have its proof.
In 1959, Masayoshi Nagata predicted a sharp limit on how many high-multiplicity points a plane curve can pass through.
An OpenAI model produced a proof. Now algebraic geometer Jenia Tevelev has rewritten the argument in a 19-page paper, calling the underlying work a “stunning achievement.”
For 10 very general triple points, degree 9 is impossible—but degree 10 works.
A remarkable new chapter in algebraic geometry. Peer review remains pending.
Jacek (Jomsborg.eth) retweeted
The @USOCC has published its final rules for implementing the #GENIUSAct. It sets out requirements for stablecoin issuers under its supervision, along with rules for custody activities at OCC-supervised banks.
For US banks, this establishes a clear framework for one form of regulated #digitalmoney. Many will now be weighing #stablecoins, #tokeniseddeposits, or both.
Whichever route they take, the same questions follow: how these assets connect to existing systems, how they move between institutions, and how #payments can be programmed and settled synchronously.
That's where Quant steps in; creating corridors for the world's digital money.
Read the full release here: occ.gov/news-issuances/news-…
The rule and the Act will take effect on 18 January 2027. The OCC will confirm separately when it opens applications, and rules on AML and sanctions will follow in a separate rulemaking with the US Treasury.
Jacek (Jomsborg.eth) retweeted
A new fractal, as far as we know, from an autocrystal: the cheapest defects of the aperiodic Walton–Whittaker tiling converge to one tile, Y = ½(Y±1) ∪ ½ω⁻¹(Y±1). Its convex hull is an exact hexagon; its boundary has dimension log₂3: doi.org/10.5281/zenodo.23541…
@grok is it new?
Jacek (Jomsborg.eth) retweeted
This guy used Ray-Ban Meta Smart Glasses, AI, and a MacBook to cheat at chess game.
Jacek (Jomsborg.eth) retweeted
AI is changing mathematics! Where does the conversation go from here?
The American Mathematical Society (AMS) has launched AI and Mathematics: Selected Resources, a curated collection to help mathematicians explore the opportunities, questions, and evolving discussions surrounding AI and mathematical discovery.
The web page brings together resources on AI-assisted research, proof verification, mathematics education, emerging tools, and expert perspectives with opportunities to explore new ideas, learn from others, and engage with the evolving role of AI in mathematics.
The AMS is committed to connecting our community and fostering thoughtful, informed conversations as the impact of AI on mathematics continues to unfold.
Have a resource to recommend? Email: [email protected]
Explore resources. Link in comments.
Jacek (Jomsborg.eth) retweeted
The flood of results building on OpenAI's Quasi-Riemann Hypothesis breakthrough keeps coming!
Today, we have a preprint from Baiying Liu showing that all finite-order Hecke L-functions are zero-free to the right of 0.8749!
This improves on 31/32 (= 0.96875), established only a few days ago by Cureton and Thorner.
Some fascinating developments following OpenAI's shock breakthrough proof of the Quasi-Riemann Hypothesis, which was released publicly on October 6:
1. Building on OpenAI's proof, a recent Hexagon preprint (released on October 12) by Cureton and Thorner establishes that ALL finite-order Hecke L-functions are zero-free to the right of 1 - 1/6000.
2. And now, today, an arXiv preprint by Frei, Somos and Widmer uses this result to prove unconditionally the 2007 Ellenberg–Venkatesh bounds on ℓ-torsion in class groups of number fields.
I was amused to see the AI declaration in the second paper: "No artificial intelligence tools were used in this work."
Jacek (Jomsborg.eth) retweeted
Personal update: Turns out that what I thought was leaving OpenAI became more of a sabbatical.
When I left a few months ago, I felt that the most important thing to focus on was making AI more useful to people. But we’ve since entered a different regime of AI progress. One in which getting the safety and security challenges of increasingly capable AI right has to become a central priority.
So I’ll be returning to OpenAI, joining @merettm to help chart a path through these challenges.
There’s much work to do, so let’s get going.
Jacek (Jomsborg.eth) retweeted
HOLY SHIT.
For crypto, this is one of the most insane posts of the year, but I'm guessing most people don't understand it.
Let me explain...
Bitcoin's accounts, and subsequently Ethereum's (and therefore every other EVM chain's), are built on a specific elliptic curve called secp256k1.
secp256k1 is a different elliptic curve from the one used across nearly every modern hardware device, including iPhones.
Modern devices mostly use a different curve called secp256r1, which is usually referred to as P-256 - one of the curves investigated in the article.
This mismatch has made it sooo difficult in the past to integrate crypto accounts natively into the security systems of modern hardware.
For example, Apple's Secure Enclave natively supports P-256, not secp256k1.
This has prevented crypto accounts from being able to use the same hardware protection as things like Apple Pay.
Same goes for the web with passkeys - WebAuthn uses P-256 signatures, which means Ethereum accounts using secp256k1 can't use them natively either.
But why did Satoshi do this?
The main theory for choosing secp256k1 was distrust of the P-256 curve - i.e. he thought there was an NSA backdoor.
A "backdoor" here basically means a secret, intentional weakness in the curve that would allow the NSA to exploit it and access private keys.
This was because P-256 was created with involvement from the NSA...
And the NSA provided a mysterious "seed" used to generate one of the curve's parameters without explaining where that seed came from.
This eventually transformed into a ~25-year-old mystery with a 5-figure reward for finding where this seed came from.
Claude figured it out in less than 30 mins.
And the best part is its internal thinking was: "Hmm wait... is it suspicious that such an obvious thing wasn’t discovered in 25 years?"
The solution was stupidly simple - just the time the curve was created, put into a specific random number generator function.
This doesn't 100% prove there's no backdoor yet, but it provides strong evidence that this seed wasn't secretly engineered by the NSA.
And Claude did this with "just a simple prompt" in under 30 minutes.
CLAUDE FOUND THE SEEDS
anthropic.com/research/ecdsa…
Jacek (Jomsborg.eth) retweeted
Quoting from the blog:
'Claude has proven particularly adept at optimizing classical algorithms, so we wanted to see whether it could do the same for quantum algorithms if it were given only a plain-language description of what each circuit must compute.
Claude is unusually well suited to this task, for several reasons. First, quantum algorithms are implemented as quantum circuits. These are composed of sequences of gates, like the Toffoli gates mentioned above. Importantly, these circuits can be described in code, so we can make use of Claude’s coding capabilities to write, run, and revise circuit designs as ordinary programs. Second, the (fairly common) class of quantum algorithms we were most interested in optimizing can be tested efficiently for correctness, as each input gives one definite output that an ordinary computer can check. This means we could have an external evaluator program validate Claude’s proposals. Finally, we can give Claude a clear, objective score to improve: the number of qubits used, multiplied by the number of gates, which serves as a proxy for how long the circuit would take to run.
We found that Claude Mythos 5 could successfully work in a closed loop, proposing a circuit design, receiving feedback and a score from the evaluator program, and using that feedback to improve its next attempt, with no human input between rounds. Across eight computational primitives—the basic routines that larger quantum algorithms are built from—for chemistry, optimization, quantum simulation, number theory, and numerical computing, Claude discovered novel designs that used both fewer qubits and fewer gates than the best previously published algorithms.'
New from our STEM Fellows Program: Designing more efficient quantum circuits with Claude.
Given plain-language instructions, Claude Mythos 5 designed quantum circuits that improve on the best published ones, sometimes by an order of magnitude or more.
More efficient circuits reduce the resources needed by quantum algorithms, which could bring quantum computing applications in chemistry and materials science within reach sooner.
Read more: anthropic.com/research/desig…
Jacek (Jomsborg.eth) retweeted
Anthropic says Claude Mythos could bring quantum computing “within reach sooner” after designing circuits that make a critical operation ~17x cheaper.
What makes this interesting is AI can now design, test and improve these circuits on its own so that opens the door to faster breakthroughs across quantum computing without waiting for better hardware.
