Viking from Jomsborg. The DAO investor. Applied math. Geometric quantization. Building reasoning layer.

jomsborg.eth
Joined January 2013
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.
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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."
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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…
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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.
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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.
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#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
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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.
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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.'
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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…
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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.
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[ ZOOMER ] GOOGLE MAKES MAJOR BREAKTHROUGH IN QUANTUM COMPUTING, SHOWING THAT "MAGIC STATE CULTIVATION" WORKS IN PRACTICE, REDUCING ERRORS BY 40X: BLOG
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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
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Read each paper by Eva Tardos
Learning in Strategic Queuing with Geometric Recharge: From Bandits to Systems Cristian Palma Foster, Eva Tardos arxiv.org/abs/2610.19179 [𝚌𝚜.𝙶𝚃 𝚌𝚜.𝙻𝙶 𝚌𝚜.𝙿𝙵]
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Jacek (Jomsborg.eth) retweeted
En 1984, una pareja celebraba su boda en Polonia cuando cinco hombres de pelo largo entraron sin invitación y terminaron tocando con los instrumentos de la orquesta. Eran los integrantes de IRON MAIDEN. Pero lo más increíble es que aquella noche no tocaron ni una de sus canciones. La banda se encontraba de gira por Polonia, todavía bajo el régimen comunista, cuando sus integrantes terminaron en el club Adria, en la ciudad de Poznań, donde se estaba celebrando una boda. Al principio solo querían tomar unas copas. Pero cuando vieron que había músicos tocando en directo, se les ocurrió una idea: pedirles prestados los instrumentos y subir al escenario. Los músicos de la fiesta aceptaron, aunque el baterista estaba especialmente preocupado por lo que aquellos desconocidos pudieran hacerle a su equipo. Y entonces ocurrió algo que parecía imposible. Bruce Dickinson, Steve Harris y sus compañeros comenzaron a tocar "Smoke on the Water", de Deep Purple, y "Tush", de ZZ Top. Lo más divertido es que no interpretaron ninguna canción de Iron Maiden. Bruce Dickinson recordaría años después que ni siquiera estaba seguro de que los invitados supieran quiénes eran aquellos músicos que habían aparecido de repente en su celebración. Pero hay un detalle que hace esta historia todavía mejor: todo quedó grabado. Parte de aquella actuación terminó apareciendo en el documental Behind the Iron Curtain, que registró la histórica gira de Iron Maiden por Europa del Este en 1984. Y pensar que, mientras miles de seguidores pagaban por ver a Iron Maiden en concierto, unos novios polacos terminaron teniendo a la banda tocando gratis en su boda. Hay parejas que contratan una orquesta para su boda. Y hay otras que, sin saberlo, terminan con Iron Maiden tocando canciones de Deep Purple.
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Jacek (Jomsborg.eth) retweeted
JUST IN: Gold and silver prices dump following higher-than-expected inflation report, wiping out a combined $700,000,000,000
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Yes, Goedel was brilliant and his main theorems are dramatic and devastating. But Tarski utterly blows my mind. While Goedel exposed a limitation of proof, Tarski exposed a limit of definition. Arithmetical truth itself cannot be defined by a formula in the language of arithmetic. A definition need not be an algorithm. Plenty of things with a precise definition are uncomputable! Moving from “we cannot mechanically establish every truth” to “we cannot even define the full truth predicate here” is amazing — it crosses a conceptual boundary. Tarski’s work, IMHO, reveals more, philosophically, than Goedel.
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Jacek (Jomsborg.eth) retweeted
In 1974 Deligne proved the last of the four Weil conjectures—an analogue of the Riemann hypothesis in a world where some prime number has been set to zero. While Deligne’s work was celebrated, his doctoral advisor, Grothendieck, was unhappy. Can solving a problem be bad? I think not, but I want to explain my understanding of the story, which in my view sheds some light on the present moment. In his memoir, “Récoltes et Semailles” (Reaping and Sowing), Grothendieck explains his approach to problem solving and mathematics more generally: "The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration… the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it... yet it finally surrounds the resistant substance." He compared a precise mathematical question to a nut, which, rather than being cracked open by a chisel, yields at the perfect time to simple hand pressure once it has been soaked in the ocean of mathematical understanding. According to this account of mathematical progress, solutions, though important, are ancillary to the advance of the rising sea of mathematical understanding. At best they measure it to some extent, but the goal is to raise the water level. Grothendieck had laid out a program to resolve the Weil conjectures: the standard conjectures, which are part of the philosophy of motives. The proof circumvented this program. Deligne characterized Grothendieck's reaction as "he did not care...the proof was a trick" but in fact Grothendieck excoriated Deligne in his memoir, claiming Deligne and others tried to "bury" the theory of motives, and Grothendieck himself. The standard conjectures remain open today. Deligne's result relied on a lot of work that was not yet well-exposited in the literature, around the theory of étale cohomology. Deligne himself wrote an exposition of this in SGA 4.5, and Illusie contributed additional necessary material in SGA 5. Some have referred to this additional work as "thankless," but it was completed. While Grothendieck is one of my heroes, and I find his view of mathematics very appealing, I think he was wrong here. Though the standard conjectures are still open, there is an immense amount of work on the theory of motives. People worked very hard to clarify the issues left unclear by Deligne's argument. And crucially, Deligne followed up on his work with a different proof, in "La conjecture de Weil II," that completely revolutionized arithmetic geometry, in many ways going beyond the philosophy of motives as it existed at that time. I think Grothendieck's view that the first proof Deligne provided was insufficient was, in some sense, correct. But he was wrong about the fact that the theory he so desired, and the attendant quest for understanding, would be abandoned, and that his ideas would be buried. I don't think anything can stop us from trying to understand.
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Jacek (Jomsborg.eth) retweeted
JPEG XL turned on by default is just starting shipping in Firefox (earlier Safari, Chrome, Edge) - after ~30 years officially replacing JPEG for the next decades, ~2x reducing web sizes, adding HDR, transparency, progressive decoding for much faster www, also animations, lossless - should retire also ancient GIF, PNG, TIFF - finally reaching universality and much better compression. phoronix.com/news/Firefox-15…
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Jacek (Jomsborg.eth) retweeted
ANTHROPIC: "small AI models may be months away from being capable enough to self-replicate on commercial IoT devices" "In our evals, a 9B model got inference running on 8 of the 9 hardware types we tested"
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MAIN TAKE-AWAY from @token2049: World needs Starknet as a quantum-safe L1. Market says it. Whales, KoLs and OGs say it. I say, We hear you.
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Jacek (Jomsborg.eth) retweeted
"Ils ont annihilé mon domaine de recherche": nouveau coup de massue d’OpenAI sur le monde des mathématiques En résolvant des problèmes extrêmement complexes par centaines, l'IA provoque les larmes d'Hugo Duminil-Copin, médaillé Fields lemonde.fr/sciences/article/…
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