welcome to the singularity | engineering biology @ https://xitter.cf/t.co/tEHm5co0eN

Bay Area
Joined November 2011
Jonathan Hales 🚀🕊🥳 retweeted
"How do my cells compare to clinical reference data?" We use Glass Bio's reference catalog to follow a case study of cancer immunotherapy, uncovering increased immune activity that exceeds all public references!
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Sympathetic to this take from Tao. I think the "industrial era" is going to be pretty great though.
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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I keep rewatching this in awe.
Turns out the future does have flying cars
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Jonathan Hales 🚀🕊🥳 retweeted
We're releasing Astral, a map of healthy and diseased cell types in the human body.
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Catastrophizing is now an even more potent substitute for argument than claiming victimhood.
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Wow. First big AI proof of a problem I am familiar with from my previous life as a mathematician!
Please welcome to the world a beautiful new geometric object, to do with a problem i’ve always loved. claude really contains multitudes:D Does S^6 admit a complex structure? Yup
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Jonathan Hales 🚀🕊🥳 retweeted
1/6 Frontier models outperform open-weights models on bio/science tasks. We're figuring out which tools and harness can elevate open-weights models to par! Our first finding shows that access to web or the @firecrawl paper search index improves model performance.
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i've yet to hear a convincing argument that RSI will work for capabilities but not for safety.
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> The total number of tokens needed to find solutions to these problems would cost roughly $2,000 at Sol API rates. Surprising to me that these problems are so "cheap" to solve relative to how much we spend on software engineering projects.
yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model. We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann algebras (disproof of Connes' Rigidity Conjecture) to better bounds for high dimensional sphere packing, for circuit complexity, for monochromatic triangles in multicolored graphs, and more. More thoughts here: openai.com/index/ten-advance…
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@vamsiprithamp like I would think these would be an order of magnitude higher. Maybe that's my own biases, or maybe LLM capabilities are just very spiky.
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Can god create a rock so heavy he can’t lift it?
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If this was bio, it would still be another 2 years before they published it on a paywalled 2010 era journal website. 17 coauthors too.
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
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Wow, was not expecting this. Incredible.
A technical dive inside our new "Midjourney Scanner"
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Jonathan Hales 🚀🕊🥳 retweeted
In my doctorate, I proved the Erdős Primitive Set Conjecture, showing that the primes themselves are maximal among all primitive sets. This problem will always be in my heart: I worked on it for 4 years (even when my mentors recommended against it!) and loved every minute of it. [Primitive sets are a vast generalization of the prime numbers: A set S is called primitive if no number in S divides another.] Now Erdős#1196 is an asymptotic version of Erdős' conjecture, for primitive sets of "large" numbers. It was posed in 1966 by the Hungarian legends Paul Erdős, András Sárközy, and Endre Szemerédi. I'd been working on it for many years, and consulted/badgered many experts about it, including my mentors Carl Pomerance and James Maynard. The the proof produced by GPT5.4 Pro was quite surprising, since it rejected the "gambit" that was implicit in all works on the subject since Erdős' original 1935 paper. The idea to pass from analysis to probability was so natural & tempting from a human-conceptual point of view, that it obscured a technical possibility to retain (efficient, yet counter-intuitve) analytic terminology throughout, by use of the von Mangoldt function \Lambda(n). The closest analogy I would give would be that the main openings in chess were well-studied, but AI discovers a new opening line that had been overlooked based on human aesthetics and convention. In fact, the von Mangoldt function itself is celebrated for it's connection to primes and the Riemann zeta function--but its piecewise definition appears to be odd and unmotivated to students seeing it for the first time. By the same token, in Erdős#1196, the von Mangoldt weights seem odd and unmotivated but turn out to cleverly encode a fundamental identity \sum_{q|n}\Lambda(q) = \log n, which is equivalent to unique factorization of n into primes. This is the exact trick that breaks the analytic issues arising in the "usual opening". Moreover, Terry Tao has long suspected that the applications of probability to number theory are unnecessarily complicated and this "trick" might actually clarify the general theory, which would have a broader impact than solving a single conjecture.
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Jonathan Hales 🚀🕊🥳 retweeted
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Jonathan Hales 🚀🕊🥳 retweeted
What’s just as important as biotech innovation? Policy innovation. I speak about it at length with @IanHuyett 0:00 New Hampshire’s Biotech Potential and Right‑to‑Try Origins 09:30 Preventative Pre‑Birth Care and the Case for Policy Change 19:30 Faith, Ethics, and the Christian Perspective on Technology 28:30 Donum Vitae, IVF Ethics, and Embryo‑Focused Therapies 37:30 Building a Pro‑Innovation Hub: Next Steps for New Hampshire
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Candle light Nick Land acknowledgment 🕯️🚀
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