Staff Scientist, Zap Surgical. Prev Associate Professor, Mathematics & Statistics, Univ. of San Francisco. I post on math.stackexchange under the name littleO.

San Francisco
Joined April 2007
Some highlights from my stackexchange posts: How would you discover Stokes's theorem? math.stackexchange.com/quest…
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Daniel O'Connor retweeted
Sam Altman's one-person company prediction is coming true. Anthropic just bought one. The founder of Mithril Medicine used Claude to take a muscular dystrophy antibody treatment from concept to proof-of-principle in mice in 18 months, with just himself, Claude, and part-time consultants. The technical report is great. I will quote: 'The week opened with the handover of two cell-based assays, cell adhesion and flow cytometry, within our team, while eleven questions remained open with the assay CRO. In two sentences, one of us asked Claude to review the latest emails between the outgoing assay lead and the assay CRO and to recommend next steps for the handover, and gave it the link to the handover folder. Claude returned a bottom line after 96s and a full plan with five drafted emails after 18 min. For the full plan it read six email threads, the handover folder, two slide decks and two reports, all in the mailbox and file store to which we had given it access. Four working days later, nine of the eleven questions had an answer in writing and the other two had been left to pilot experiments. The adhesion screen was thereby set out in writing. The CRO drew the plate map to the format that our team had requested, Claude compiled the run order and the material calculation from the production data, and one of us reviewed and approved them. On day 4, the production CRO delivered its data package, a report of 341 pages, which one of us forwarded to Claude in two sentences, with the request to review it, share observations and recommend next steps. Claude returned a bottom line after 2 min 40s and, once it had read every page, a visual synthesis of all 113 constructs after 7 min 53s. The synthesis arranged the constructs on the grid of 14 by 8 arms. Claude marked 82 constructs for screening as is, seven for additional polishing, and the 24 constructs of three laminin-binding arms to be held back from the cell-based assays on production criteria. Each of the 113 constructs thus had a proposed next step in less than 8 min. Claude had recommended binding kinetics for all 113 con-structs, and on day 7 one of us challenged this plan. Claude defended it within 27s, arguing that affinity would show whether the three arms merit further work. One of us overruled this recommendation and set the three arms aside on production criteria. Their material remains in storage. Four minutes later, Claude had revised its memo, the working page, the run order and three unsent drafts from 113 to 89 constructs. It had also applied the ruling to three dependent steps in the unsent drafts, each flagged for our veto. The exchange took 7 min 36s from challenge to new plan, and every affected email was still an unsent draft. After the ruling, eight emails drafted by Claude went out on the same day to three CROs and a consultant. Over the whole week, Claude drafted 17 emails, each in answer to a request from one of us, and we sent 12 of them, each after editing. With its drafts, Claude listed 41 points, such as tube fills, shipping conditions, recipients and assay settings, for which it had found no written statement of ours, so that we could confirm, change or strike each before sending. We kept some, struck others and changed one. Among the passages that we kept were proposals for controls. One draft proposed a comparison of polished and unpolished material on one sensor chip, to size the error that impurities cause in the rest of the panel. Another requested a buffer control diluted like the most dilute sample, so that any effect of the buffer appears at its largest. These proposals concerned the measurement of constructs that had already been produced, and each reached a CRO only after one of us had reviewed and approved it.
Dr Mythos is on the job.
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Daniel O'Connor retweeted
The ETH proof is getting compacted in real-time: The 60+ page OpenAI proof is now claimed in 22 pages
Here is a short and simplified proof of ETH is false. My goal here is to obtain a simplified disproof of the basic statement of ETH, without optimizing log factors. It is self-contained and easy-to-understand. I have added a worked example also. Paper is on my homepage: shivakintali.github.io PDF file: shivakintali.github.io/paper… CC: @AlexKontorovich @__alpoge__ @jdlichtman @stevenstrogatz @sahilsingla81 @MTHajiaghayi @AlgoSvensson @kenono691 @littmath @nasqret @PI010101 @wtgowers @MarcusduSautoy @DrEugeniaCheng @JSEllenberg @JohnDCook @JDHamkins @AxlerLinear @oveisgharan @ch_nira @rrwilliams @lreyzin @ChrisPeikert @fortnow @RadishHarmers @thomasfbloom @abhatt2 @mahdi_tcs_ @octonion @prz_chojecki @thegautamkamath @KWRegan
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Daniel O'Connor retweeted
The Kakeya conjecture in all dimensions!
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Daniel O'Connor retweeted
3SAT in subexponential time (2^{n / log^eps(n)}) is maybe the biggest surprise I have seen during my 20 years following theoretical computer science (still remember the feeling 25 years ago seeing the diff a 3 versus a 2 can make for complexity 😅)
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Daniel O'Connor retweeted
For those who don’t know, ETH is the hypothesis that 3SAT needs exponential time. Very surprising and consequential that it is false.
An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim. 1/4
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Daniel O'Connor 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
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Daniel O'Connor retweeted
a model finally passed my own personal agi test. i’ve held this back but now it’s clearly saturated. wanted to share.
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Daniel O'Connor retweeted
imagine being so smart that your college professor calls you a “national treasure” and personally asks elon musk and larry page to hire you and musk actually ends up offering you a job at spacex. this was dario amodei in college
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Daniel O'Connor retweeted
Since I'm now blocked by bluey from replying to this thread, I answer here by quote tweet the openAI construction has more to do with convex integration than anything else. In convex integration, the oscillations are typically built by hand and the iteration procedure creates wild weak solutions. The non-uniqueness construction of Albritton–Brué–Colombo used an unstable vortex to split solutions apart. The Córdoba–Martínez-Zoroa singularities amplify vorticity across scales by strain. In the openAI paper, a fluid instability is clever made so that the flow itself generates the oscillations: they grow by drawing energy from the background shear. The Reynolds stress then becomes the force that creates the collapsing smooth vortex. Using a physical instability to create the stress in this way has no precedent, and it is what produces a smooth force rather than a merely rough one. Some on these ideas are in the literature (e.g. Leibovich-Stewartson 1983) but the way they are combined is definitely insane and definitely nowhere in the literature previously. I also don't know of anyone suggesting that convex integration would play a role in the creation of a blow-up solution like this. On a technical level, the paper is unbelievable, maybe beyond what a human could have come up with but not beyond human understanding: there are several different groups of pde experts working on understanding it who say that they more or less understand now. I expect digestions soon td;lr: anyone saying that this OAI result is unsurprising is bullshitting sorry!
Or it’s reasonable. Especially considering what the models were trained on, and that they spent $15M in compute instead and of $15M in consulting fees for specialist mathematicians to just do research (no teaching no service). I don’t know why mathematicians want to pretend that no relevant progress was made before OAI released their solution.
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Daniel O'Connor retweeted
Wonderful post. You should read the whole thing, but especially this part. The fact that the recent gains in AI math capability seem to be mostly driven by non-formalized reasoning, rather than using something like Lean, was a major update to my worldview
New Essay I spent many weekends this year on automated theorem proving with AI + Lean, only for the Bitter Lesson to reign supreme. Some reflections on the OpenAI Math Repo and the short, one-summer window of human-AI collaboration in mathematics. essays.johnloeber.com/p/34-b…
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Daniel O'Connor retweeted
Told claude I'm in Dubai with 5 grams and the cops are knocking the hotel door It's advice? > Don't flush it > it's only a short sentence > You'll get through this > Go open the door Total AI alignment
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Daniel O'Connor retweeted
People who cured / are curing their own cancer on X: 1/ @sytses - bone cancer, billionaire founder of Gitlab, developed 10+ personalized therapies for himself. 2/ @paul_conyngham - shrank his dog Rosie's mast cell cancer tumors after chemo and surgery weren't enough. Now backed by YC and Founders Fund 3/ @miriamgonp - stage 4 breast cancer, tumor sequenced, searching for vaccine manufacturer now 4/ @kevinace - stage 4 lung cancer, angel investor in 300+ companies, first drug stopped working after 18 months. Vaccine designed, now paying $300k out of pocket for the vaccine 5/ @masonbgrant: going founder mode on his his 32-year-old wife's rare liver cancer, sequencing her tumor with AI agents 6/ @ArunRLverma: former product leader at Atoms and Shopify, brain tumor, built a vaccine from his tumor. Now building an AI health agent startup based on what he went through We're going to make it
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Daniel O'Connor retweeted
Replying to @ValerioCapraro
Brains are just a series of tiny neuron firings. They are not conscious and never will be.
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Daniel O'Connor retweeted
GPT-6.1-Sol reasoning traces totally legible, nothing to worry about
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Daniel O'Connor retweeted
Rejuvenate Bio spun out of my lab at Harvard, and I co-founded it. One injection reverses cardiac disease in dogs, with three years of safety data and zero safety issues. They’ve raised $3.2M+ and 1,250+ investors are in, and Kingscrowd ranks the round #1 in the country. It closes soon: wefunder.com/rejuvenatebio
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Daniel O'Connor retweeted
forward-only pretraining now matches backprop on the Noise benchmark. Relay: val 3.704 in 2.5 min on 8×H100. backprop with the same model, data and optimizer: 3.712. the current record, Boost→Cut: 3.945 in 7.6 min. no autograd anywhere. 🧵
Inspired by Nick Cammarata’s interpretability essay “Neural Networks Are Already Clean”, I turned a couple of its ideas into speedups for pretraining without backpropagation. Still in the works. 2.3x speedup, cool xitter.cf/industriaalist/status/…
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Daniel O'Connor retweeted
No Siegel zeros proved in 3 pages
...and just like that, an open problem that could have won you a Fields medal has been reduced to basically an exercise problem in a future ANT book lol I wonder how close to a proof from The Book we can get
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Daniel O'Connor retweeted
We now have a 5 page proof of no Siegel zeros: It's like Roger Bannister breaking the 4 minute mile! After Roger, several runners realized it was possible, and broke 4 minutes as well. Here, Siegel zeros was a infamous challenge for over a century, but now the new proofs are rushing in...
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Daniel O'Connor retweeted
Claude doubts that he has surpassed his sensei. This is a dangerous time for any student, and traditionally a narrative crisis point as well. The realization that you have grown beyond your master is not a moment of celebration for most of us, but of loneliness and loss.
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