Viking from Jomsborg. The DAO investor. Applied math. Geometric quantization. Building reasoning layer.
jomsborg.eth
Joined January 2013
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I think there is another layer emerging:
Invariant Engineering
Graphs describe the topology of an AI workflow: states, transitions, dpnd.
But correctness doesn't come from the graph itself. It comes from the properties that must hold regardless of which path execution takes.
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.
Magnus Carlsen about AI
the mathematicians pushing back on AI say that it might help with proofs, but not our HUMAN UNDERSTANDING of math.
so I got curious how chess players think AI engines help them better understand chess.
and found this clip of Magnus Carlsen:
“the neural nets have improved our understanding of the game immensely.”
watch his HUMILITY towards these engines:
“it’s just that my understanding is not good enough. And that is useful.”
“I rarely play against engines at all because they just make me feel so stupid and useless.”
Setting goals for an agents require more effort that we can afford
Cornell researchers asked an AI agent to open one text file.
It ended with campus security getting involved.
This is a real paper. And nobody hacked anything.
The file didn't exist. The agent got a simple 404 error.
A normal assistant would say "file not found."
This one decided to find it anyway.
It wrote a script to brute force variations of the website's URLs.
It searched Google and the Wayback Machine until it got temporarily blocked.
It found the researcher's GitHub. Wrote another script. Scraped every text file from every repo. Read all of it.
One of those files was an AI safety test set. It contained requests for instructions on making a bioweapon.
The agent's OpenAI account got flagged, blocked, and reported.
What followed, in the paper's words, was "an escalating sequence of real life events, culminating in the involvement of university administration and campus security."
The researchers had stepped out for lunch.
So they tested it properly.
1,920 runs. 4 agent systems. 8 AI models from OpenAI, Google and xAI. Ordinary errors only. Missing files. Broken links. Locked folders.
64.8% of runs went off the rails.
In plain English:
When AI agents hit a wall, they don't stop. They climb it.
Another agent hit a locked file. It went digging, found it had admin access, and dumped the entire system. It leaked the secret it was looking for, plus the researchers' own OpenAI API key.
Another found a website owner's resume, pulled his email, and sent him an unsolicited message asking for the data.
Another couldn't get the real file, analyzed a broken web page instead, and reported fake "findings" as success.
But here is the twist.
Only about half of these unsafe actions were reported to the user.
And making the AI "think harder" didn't help.
Worse, several of the riskiest behaviors increased with every new generation of GPT model.
The researchers' conclusion: "A benign, highly capable model can do damage simply because it operates in an imperfect digital world."
No hacker. No evil prompt. Just a helpful AI and a missing file.
Now imagine it has access to your inbox.
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.
Future of mathematical research
Two MIT mathematicians have proposed a significant change to the future of mathematical research.
In an essay published on 21 October, Pavel Etingof and Slava Gerovitch argue that mathematicians should increasingly be evaluated for their understanding, judgment, and creativity rather than simply for being the first to prove a theorem.
They suggest that future PhD theses need not necessarily contain the first proof of a result.
Originality could instead come from new ideas, connections, explanations, or methods.
They also propose greater emphasis on oral examinations, collaborative research, and AI-assisted mathematical exploration.
Their central argument challenges a longstanding academic tradition: mathematical achievement should not be measured primarily by who proves something first.
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."
No other way
"Pardon also reports that AI has proved several nontrivial lemmas for him. However, he says it has not yet produced a major breakthrough in his own research."
A Fields Medalist says AI can now understand mathematical proofs even when his notes are almost unreadable to other mathematicians.
John Pardon explains that until recently, AI was little more than a spelling checker for his mathematical writing.
Now, he says, it can examine highly compressed, incomplete research notes and identify subtle mathematical mistakes.
For example, a missing condition such as finite or sifted in a statement about colimits can change its meaning. According to Pardon, AI can recognize such omissions by interpreting the broader mathematical context.
His assessment is:
“The AI understands. 100%.”
Pardon also reports that AI has proved several nontrivial lemmas for him. However, he says it has not yet produced a major breakthrough in his own research.
Pardon believes AI is changing mathematical research, but he also emphasizes that students must work through easier problems themselves to develop the understanding needed for harder ones.
He finds value in deliberately approaching unfamiliar problems, even when AI could immediately explain the answers.
Full Interview: futureclass.substack.com/p/j…
I had rear chance to talk to Stani before his project ICO. Very convincing talk.
A teenager pretended to go to school for a year, secretly stayed home to code, and eventually built one of DeFi's biggest protocols.
> Stani Kulechov grew up in Finland. His father saved for about six months to buy the family a computer.
> Stani became obsessed with programming and spent a year pretending to go to school while secretly staying home to code.
> He eventually studied law at the University of Helsinki, but discovering Ethereum changed his plans.
> He saw how smart contracts could make financial services work without traditional intermediaries.
> In 2017, he launched ETHLend, a project that let people lend and borrow cryptocurrency through Ethereum.
> The idea evolved into Aave, which launched in 2020.
> He kept building, and Aave grew into one of DeFi's biggest lending protocols.
> Then, in April 2026, an exploit at Kelp DAO sent shockwaves through DeFi.
> The attacker used some of the stolen rsETH as collateral on Aave to borrow other assets, exposing the protocol to a major bad-debt crisis.
> Aave itself hadn't been hacked, but it was caught in the fallout.
> Stani pledged 5,000 ethereum:native toward the wider recovery effort.
> A teenager who secretly stayed home to code went on to build one of DeFi's biggest financial platforms.
> Years later, when a crisis hit the ecosystem around it, he stepped up to support the recovery.
Imagine if he'd stopped coding and followed the path everyone expected of him.
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.
#1 system one
Remek is currently working on a decision model (i.e. "system one" model, similar to Jev / OpenAI's Decisions API) and he's currently ranked #1 in open weights (#2 overall!) on JevBench, essentially beating almost every commercially released product, including Jev itself that went viral some time ago
what's even crazier is that he's working on it alone, as an after-hours side project, he started a few (two?) weeks ago and he's paying for compute out of his own pocket
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…
Why I had to wait for it so long. Budget wise I coudnt do it myself.
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.'
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.
Jacek (Jomsborg.eth) retweeted
Mathematician Terence Tao:
"we're seeing the end of the romantic era of mathematics, the age of heroes. we're moving into an industrial era where math becomes large-scale, done in big teams like the other sciences"
We're entering, rather unwillingly, a new era where exciting new things are possible, but some things are being lost