Sabine Oechsner

Sabine Oechsner

@proofnerd.bsky.social

cryptography and pretty proofs | PL-curious | everything is MPC | assistant professor @ VU Amsterdam

278 followers220 following81 posts

Sabine Oechsner reposted

Sophie Huiberts
@sophie.huiberts.me

Virginia's writing is very informative! She and Josh received the original (shitty) proof from Anthropic's internal model, but she could easily reproduce it using her own old proposed strategy and <2 hours of publicly available Claude.

Hung Le@hunglv.bsky.social

Virginia Vassilevska Williams reflected on the recent 3SUM and APSP: people.csail.mit.edu/virgi/though...

people.csail.mit.eduhttps://people.csail.mit.edu/virgi/thoughts.txtA week has passed since Josh and I posted our write-up on the arXiv, and I decided to write a few things. Much was said about our write-up. Some were excited, others enraged. Most everyone was scar...

Sabine Oechsner reposted

Clément Canonne
@ccanonne.github.io

We should also keep track of the number of AI-generated results desk-rejected from conferences and journals due to being of subpar quality, to help keep things in perspective. "OpenAI announces 722 desk-rejections from leading scientific venues!" would not have the same ring, I know.

Sabine Oechsner reposted

Joshua Grochow
@joshuagrochow.bsky.social

"The apparent complete lack of care to do undergraduate-level code clean-up is striking, even if the code compiles ok. One can then perhaps extrapolate to the quality of the English writing that the system has put out."

theHigherGeometer@highergeometer.mathstodon.xyz.ap.brid.gy

I felt like I had come to a place to actually say something worth saying about last week's dump of AI-generated claimed results. https://thehighergeometer.wordpress.com/2026/10/12/what-even-is-mathematical-output/

thehighergeometer.wordpress.comWhat even is mathematical output?It’s been nearly a week since the dump of the GitHub repository with over 700 documents and (far fewer) Lean formalisations of AI-generated proofs, but it’s felt a lot longer. My own views on use of AI are mixed. I use it for my day job, we formalise things (previously in Isabelle, now in Lean) that we are implementing, and which will never be made public. I have played around with AI to fill in my understanding of background material for a research paper I’m writing, and to try to hunt for references for things that are difficult to find, and to generate some code that calculates something in a specialist language I didn’t know. I have used it to translate and extract material out of old scanned documents. But I am loath to just get it to prove things I want to know. A couple of years back I did, when the systems were much more flaky, and eventually I ended up just deriving what I got out of it by hand from scratch, as I lost the transcript and I needed a proof anyway. I choose not to get it to draft or write my papers for me, as I find it just insufferable. I have spent perhaps more time that I should have trying to get a measure of people’s takes; I didn’t want to comment at the time. Some are obviously really interested in mining the 700+ documents for insights, or for taking them and improving the result (for instance the multiplication algorithm complexity bound has been dropping rapidly, but these are perhaps mostly just announced in posts on X/Twitter). Some people want to run AI over the system and give appropriate credit rather than letting authors of cited work be buried under the size of the pile. Perhaps an even more worthy task would be figuring out who _wasn’t_ cited for their ideas that were used. This is aside from people who had already worked on and solved the problems, sometimes with AI, and whose work wasn’t recognised. Others would like to ignore the material and not donate their expertise and time freely to help the company disseminate or (more likely) give feedback to the model that produced the material in the first place to improve it. A lot of ink has been spent trying to think about what it is that the pure mathematics research community actually values, if being suddenly having hundreds of claimed results being dropped on us isn’t actually what we wanted. Many have said, rightly, that the mere fact of the theorem being true or false is not actually that useful. The value in that binary piece of information is that it gives confidence that there really is a fact of the matter that is (apparently) known, and can liberate people to really let rip. But the actual benefit comes from _understanding_ the mathematics, because it adds to our toolkit, triggers associations to other parts of mathematics, opens new questions etc. But one might, as an outsider, feel that saying that no, the AI can say it’s true, but we want this fluffy concept of “understanding” instead, is a bit of a soft, reactionary excuse. It’s actually very difficult to pin down on paper what clarity and understanding is for research mathematics. To step back, it’s really nontrivial to assess students’ understanding of mathematical ideas they are learning and being assessed on, and those are ideas that people have known for centuries or even millennia, in some form, and which the assessors (teachers, lecturers, examiners) have expertise, fluency, mastery etc in. Now try to imagine how you assess someone’s understanding on mathematics when they have just synthesized a new theoretical framework that only _they_ (or a small group of collaborators) understand. What is the actual method by which we can appreciate someone’s understanding of ideas you are hearing for the first time? I argue that it is in the _communication_ of those ideas. To draw a parallel, when Shinichi Mochizuki released his four papers on Inter-universal Teichmüller Theory in 2012, the excitement that he had built a framework to prove the abc conjecture was real, but the papers themselves as written did not help communicate the ideas. There were eventually workshops, and in-person communication (via video feed) did not improve matters. Leaving aside the actual correctness or otherwise, if experts in the topic are getting frustrated with the exposition for being unclear, and can’t tell if you have actually proved the claims or not, that’s a failure of process. My long-held view is that the papers could and should have been rewritten to be simpler (they absolutely could have been) and clearer, in the years that followed, as a form of service to the community that was trying to understand them. It was a common position that if experts can’t read the papers because they are not written clearly enough, the proof hasn’t been communicated, and as a result the theorem cannot have been held to be established. I have said before that I like the fact even pure mathematics actually produces material output. For most research, this is not images, or physical objects: the thing that is created is the _writing_ , the paper, or, sometimes, the board presentation or slides. One of the best talks I ever saw was a keynote at CT2014, which use the blackboards in the lecture hall to perfection, the layout and design of the talk as presented used exactly all the available space once, and material that needed to be referred to late in the talk was just there to be gestured at. Sadly, I can’t quite recall who it was! One stand-out creator of slides, if he’ll pardon me for singling him out, is Bryce Clarke (eg, these slides from his CT2025 talk). But, on the whole, it is mathematical _writing_ that stands the test of time. I can pick up (a translation of) Richard Dedekind’s 1872 paper introducing what are now called _Dedekind cuts_ in order to define the real numbers, and it is a masterpiece (in my opinion) of insightful and clear writing. I can read Grothendieck’s 1957 _Tôhoku_ paper (even though my French is very impoverished) and the brilliance of it shines through. I once wrote: > Mathematical exposition, if it is to be effective, must give both an intuitive picture of difficult ideas and a precise technical description of their meaning. The best writers do this seamlessly. > —A Crisis of Identification Even though mathematical ideas get digested, get filtered though many minds, there is a reason reading old mathematical texts is still worthwhile. I recall Manjul Bhargava was inspired by reading Gauss’ 1801 monograph _Disquisitiones Arithmeticae_ to come up with new insights that were left to be gleaned by generations of mathematicians who had only read downstream treatments. It is (largely) by our writings that the quality of a mathematician’s work is assessed, though it’s recognised that this is sometimes by the proxy of a journal, whose referees and editors have ideally given the paper its best chance. And it is the permanent record by which they can create a legacy. So this brings us back to the dump. Like many others last week, I trawled through this list, even just out of curiosity. A standout to me was the uniform zero-free region in the critical strip of the Riemann zeta function, as I’m aware from the work of my Australian colleague Tim Trudgian and colleagues (eg this paper from March this year) on getting larger, but still decaying, such regions. The other one was the establishment of the Grothendieck’s homotopy hypothesis for the version of -groupoids extracted from the first part of Grothendieck’s _Pursuing Stacks_ , the actual original letter to Daniel Quillen. This was interesting purely from the point of view of history: it establishes that Grothendieck’s definition of -groupoids, which is used by practically no one, was actually correct. The actual result proved was a technical lemma conjectured by Simon Henry, which by a longer chain of reasoning suffices to establish the homotopy hypothesis in this setting. I will say that I have not actually read any of the papers, largely because none of them are on things I actually work on, or are close enough that I need to read them. Having established that mathematicians care about what each other actually write, then what do we say about the over 700 pdf documents that landed last week? Certainly people expect AI to write slop. But you get assessments like this from experts on the material they are looking at: > A senior colleague of mine found one of his favourite problems among those solved and attempted to read the accompanying paper. He told me it was so unintelligible that, had he received it as an editor at a mathematics journal, “**it would have gone straight into the bin** ”. > —Melissa Lee, Monash University (writing at The Conversation) and this: > I took a brief look at the preprint released by OpenAI […]. **It sucked. It is unclear, muddled, and has a strange structure.** The terminology is “a bit off”, there are theorems that I would not expect to be proved, that are also stated in a very strange manner. Lemma 7.4, again, is not something you’d expect to see in a paper like this, the same goes to Lemma 8.1. > [….] > No, **if this was an academic paper submitted to a journal, it should be issued a desk rejection for the quality.** The onus is always on the author to conform and adhere to the communications level. Much like a paper written in Swedish would likely be rejected outright from the Proceedings of the American Mathematical Society, because the onus is on the authors to make it accessible for the readers. > —Asaf Karagila (blog post) and this > “To the extent I have looked, I would not bet any money that either has a correct proof. Both read like **papers I would immediately reject were I a referee** , as both seem mainly filled with awkward proofs of well known facts with nothing that motivates.” > —Nick Kuhn (ALG-TOP mailing list) and this > But the more I thought about it, the more annoyed I became. What bothers me most is the double standard. > > Whenever I referee a paper, or receive a thesis or project from a student, I apply the same standards that most of us do. If a paper or thesis is so badly written that I cannot get past the first page without considerable effort, **I reject it and ask for a new, readable version.** > > With these AI-generated papers, I feel that we, as a community, are not applying the same standards of quality and rigour. They can simply release multiple 100+ page papers claiming to have solved this or that problem, often with **redundant arguments, unclear logical structure, multiple dead ends** , and strange or unsettling terminology — in other words, slop. > —Enrico Fatighenti (self-described as ‘not a Luddite’ who uses AI for various tasks) Proofs and Prompts and this > It’s clear many papers were never reviewed by a human: for instance, I took their example #254 (an Artin group with no CAT(0) action): their group has 116 generators, but after feeding it to Astra, in 10 minutes I got a new example with 12 generators. Clearly, **they were in a rush to post the big drop, prioritizing quantity over quality** …Why? > —Giulio Tiozzo, Proofs and Prompts There are of course reactions by people who are willing to look past the slop, for whom the results are too valuable to ignore. But the fact of the matter is that the output can’t have been refined past the original generation, which is what (ideally) mathematicians do for their own work once the results are generated. One particularly cynical view is that this is like outputting a giant calculation and then leaving the understanding to the people who are trying to get some value out of it. In fact, it _is_ just a giant calculation, just on a scale remote from any kind of personal experience, and then distilled into some output in symbols that approximates ordinary writing. I was much amused by the parody account @Endings500 that sprang up on X/Twitter last week, and this was a small amount of amusement when (unformalised) papers had to be withdrawn from the dump for having errors: > We Are Withdrawing Three Endings from Endings-500, Reaffirm Our Full Confidence in the Remaining 497 > > ** FOR IMMEDIATE RELEASE** > > Today we are withdrawing three endings from Endings-500, our landmark repository containing the final ten minutes of 500 previously unreleased films pic.twitter.com/HxVAts5Ikg > > — Endings FourHundredAndNinetySeven (@Endings500) October 8, 2026 To stretch the film analogy to breaking point, it’s not just that there is some content like a film showing only the last 10 minutes, it’s that the film is of a similar quality to _Plan 9 from Outer Space_ (“justly celebrated for its staggering ineptitude”). One might, however, take heart in the fact that a bunch (by all means not all) of the claims were formalised in Lean. As much as people are getting mileage out of the recent preprint showing that the Navier–Stokes formalisation doesn’t match the pdf describing the proof, that is really just a proof of concept: autoformalisation of a paper argument really needs double-checking against the written version to see if they match, and one or the other should be adjusted so they match. It says little about the results until an expert checks one or both. However, one doesn’t need to be a Lean expert to see that code like this (the entirety of the file `OrdinaryArchimedeanTwistBasic.lean`): import Mathlib namespace OAI noncomputable section open scoped BigOperators open MeasureTheory intervalIntegral open Finset open Finset Nat ArithmeticFunction open scoped ArithmeticFunction.Moebius open Filter open MeasureTheory Filter open MeasureTheory open MeasureTheory Set open Set MeasureTheory Complex open Set open Finset Filter namespace OrdinaryArchimedeanTwist end OrdinaryArchimedeanTwist end end OAI literally does nothing. This is one of the Lean files in the repository for the dump (thanks to Joseph Meyers in the Lean Zulip chat server for pointing some of these ridiculous files out). A basic deterministic code cleanliness linter would have picked these up, let alone an audit by the all-power internal model of its own output. Another one, pointed out by Sébastien Gouëzel in the Lean Zulip goes like this: import OAI.Dynamics.TriangleBilliards.SpatialRigidity namespace OAI open MeasureTheory Set open scoped ENNReal symmDiff noncomputable section open MeasureTheory Set Filter Function Metric open scoped Topology Convolution ContDiff noncomputable section open MeasureTheory Set open scoped ENNReal noncomputable section open MeasureTheory Set Filter BoundedContinuousFunction open scoped ENNReal Topology ComplexConjugate noncomputable section open MeasureTheory Set Filter open scoped Topology ComplexConjugate noncomputable section open MeasureTheory Filter open scoped ComplexConjugate noncomputable section open MeasureTheory Filter Set open scoped Topology ComplexConjugate noncomputable section open Filter Finset Set open scoped Topology BigOperators noncomputable section open MeasureTheory Filter Set open scoped Topology ContDiff NNReal open MeasureTheory Filter Set open scoped Topology ComplexConjugate noncomputable section open Filter Set open scoped Topology noncomputable section Again, the pointless repetition is far below the quality I would expect even in my own use of a less-powerful AI system to generate Lean code locally. The apparent complete lack of care to do undergraduate-level code clean-up is striking, even if the code compiles ok. One can then perhaps extrapolate to the quality of the English writing that the system has put out. And if mathematicians are judged on their writing, as the medium to communicate ideas, to give others the hard-to-describe understanding, and mathematics is judged on how clearly it is written, I hope you, dear reader, can appreciate at least one aspect of why the dump of over 700 long documents of this nature is not just frustrating, but _insulting_. ### Share this: * Share on X (Opens in new window) X * Share on Facebook (Opens in new window) Facebook * Like Loading... ### _Related_

Sabine Oechsner reposted

Chris Peikert
@chrispeikert.bsky.social

“Now Lean, particularly in Navier-Stokes papers, is being used as a time-stamp, a way to claim your theorem before having to write it up properly in an explainable way.” A sentence that would’ve been seen as the ravings of a madman just ~1 year ago. blog.computationalcomplexity.org/2026/09/navi...

blog.computationalcomplexity.orgNavier-Stokes and LeanI was working on this week's post on Lean after reading Kevin Hartnett's book  The Proof in the Code: How a Truth Machine Is Transforming Ma...

Sabine Oechsner reposted

Seny Kamara
@senykamara.com

Fantastic thread on math’s over-indexing on problem solving but applies to theoretical CS and crypto as well (in fact I think TCS and crypto are worse than math in this regard). Took me a few years after my PhD to converge to this viewpoint as well but I always thought I was just odd

Gro-Tsen@gro-tsen.bsky.social

Let me expand upon this 🔽 and say something about AIs, mathematics, proofs, conjectures, problem-solving, goalposts, paperclips, genii and, more importantly, Campbell/Goodhart's law. 🧵⤵️ •1/38

Sabine Oechsner reposted

🇵🇸Tim Henke (tɪm 'ɦɛŋ.kə)
@timhenke.bsky.social

I kinda consider this a soft confession to what I was theorising 1) He admits they only care about maths in so far as it brings good PR 2) they're only interested in announcing results that make it sound like they're gonna replace mathematicians ∴) they're optimising for impressive-soundingness

🇵🇸Tim Henke (tɪm 'ɦɛŋ.kə)@timhenke.bsky.social

I think if I were an AI company trying to create a perception that AIs were going to replace mathematicians, what I would do is grab a large set of high-profile open problems and just start grinding counterexamples until I've found one, and then only report what went into finding that specific one

Sabine Oechsner reposted

Matthew Green
@matthewdgreen.bsky.social

If you haven’t seen it, this new paper is great. They expand on a blog post I wrote that showed you could replay encrypted reasoning blobs from AI models. And they turned it into a full jailbreak. stolen-thoughts.com

stolen-thoughts.comStolen ThoughtsEncrypted chain-of-thought blocks returned by Anthropic, OpenAI and Google APIs are interchangeable across sessions, users and models. We exploit this to decode hidden reasoning at scale.

Sabine Oechsner reposted

Tressie McMillan Cottom
@tressiemcphd.bsky.social

Replying to @tressiemcphd.bsky.social

Anyway, your problem isn‘t finding the time to take notes. The problem is that taking notes is thinking and thinking has to be done by someone. women have been doing a lot of metacognition that looks like a task when it’s really thinking.

Sabine Oechsner reposted

Nils Fleischhacker
@cryptomaeher.bsky.social

I'm looking for a job! I'm an experienced researcher in cryptography. My focus is on the transition to post-quantum cryptographic protocols and protocols related to blockains. If that sounds like someone you might want to hire or you know someone who might, let's talk!

Sabine Oechsner reposted

Miro Haller
@mirohaller.bsky.social

The Workshop on Attacks in Cryptography 8 (WAC8) website is finally up, and our call for talks is open. Submit your cool cryptanalysis before July 3! We'll also invite speakers. If you had a favorite cryptographic attack from the last two years that we should invite, please put it in the comments.

Sabine Oechsner reposted

COSIC
@cosic.bsky.social

Check out the latest blog post on our website by Neus Vayà, who attended #TPMPC 2026 in Denmark. In the post, she discusses the paper “When Trying to Catch Cheaters Breaks the MPC” by Andreas Brüggemann and Thomas Schneider: www.esat.kuleuven.be/cosic/blog/t...

esat.kuleuven.beTPMPC 2026: “When trying to catch cheaters breaks the MPC” - COSICCOSIC - TPMPC 2026: “When trying to catch cheaters breaks the MPC” (COSIC Cryptography Blog )

Sabine Oechsner reposted

Marcel Keller
@mkskeller.bsky.social

UNSW Sydney is hiring an associate professor and a lecturer in cryptography, and the description explicitly mentions *secure computation*. Didn't you want to live in the sunniest of the most livable cities in the world?

external-careers.jobs.unsw.edu.auAssociate Professor in CryptographyJoin an organisation that is shaping the future direction of cryptography and secure computation in Australia, in a senior academic role that combines research leadership, strategic contribution, and ...

Sabine Oechsner reposted

Clément Canonne
@ccanonne.github.io

And the website with details and registration form is up! sites.google.com/view/sydney-... Join us on July 22–24 at #USyd, in the @sydneycompsci.bsky.social, for a 3-day (free) intensive winter school on Interactive Proofs and the PCP Theorem! [Remote participation possible]

sites.google.comSydney TCS Winter School 2026📅 July 22—24, 2026 🌏 Sydney (Australia)
Clément Canonne@ccanonne.github.io

Teaser: a colleague (Sasha Rubin) and I are planning a 3-day (free) "intensive Winter school" at #USyd on computational complexity: specifically, interactive proofs (IP=PSPACE) and the PCP theorem. July 22-24! I don't know how many people here are nearby and keen, but if you are: please do join!

Sabine Oechsner reposted

Clément Canonne
@ccanonne.github.io

Teaser: a colleague (Sasha Rubin) and I are planning a 3-day (free) "intensive Winter school" at #USyd on computational complexity: specifically, interactive proofs (IP=PSPACE) and the PCP theorem. July 22-24! I don't know how many people here are nearby and keen, but if you are: please do join!

Sabine Oechsner reposted

Pavel
@spavel.bsky.social

Thinking about why women might not want to use a product that has forced itself into every software interface to confidently shout things that are wrong

blair@blairaf.com

One of the more misogynistic takes currently trending in the AI policy space is "women use less AI than men because they have less tech literacy" Ok but have you considered that women use less AI than men because we have more tech literacy?

Sabine Oechsner reposted

Matthew Green
@matthewdgreen.bsky.social

Last week I discovered that ChatGPT and Claude will send you their “encrypted raw reasoning” and of course I immediately wasted a weekend trying to do something bad with it. What I got for my trouble was this blog post: blog.cryptographyengineering.com/2026/05/29/f...

blog.cryptographyengineering.comFooling around with encrypted reasoning blobsThis is a quick post I wanted to write about a “hobby project” I spent a weekend on. It has little to do with real cryptography, and mostly doesn’t expose a particularly exciting …

Sabine Oechsner reposted

Gro-Tsen
@gro-tsen.bsky.social

Very insightful short essay by Petra Schwer ( mathstodon.xyz/@PetraSchwer ): ‘The meaning of doing mathematics’ “(Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving?)” arxiv.org/abs/2509.15998

arxiv.orgThe meaning of doing mathematicsCan AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these question...

Sabine Oechsner reposted

Tianxin Tang
@koptxin.bsky.social

For anyone interested in being a tadpole reviewer (interesting concept, suitable for PhD students and early post-docs) for PETS 2027, you can submit an application using the following link: cryptpad.fr/form/#/2/for.... The PC application form can also be found on the website.

Sabine Oechsner reposted

Nalini Joshi
@monsoon0.bsky.social

You may find the comments by Melanie Matchett Wood on the discovery of a counter example to Erdős’ Unit Distance Conjecture as interesting as I did 👇🏼(see previous post for a link)

Sabine Oechsner reposted

Clément Canonne
@ccanonne.github.io

The OpenAI breakthrough on the unit distance problem seems genuinely impressive to my semi-layman eye. (It is!) One possible takeaway, though, is that if you throw an incredible amount of money and resources at focused research, there WILL be impressive progress. I wish we tried that, too.