1/5 Necroing this cast from a fortnight ago (which, in the age of the singularity, is eons). There's now visible tension in the math community between two fundamental views of the craft: is math about problem solving, or about deepening our (human) understanding? It even made the HN front page today, so it's grabbed the attention of even pedantic nerds. To be clear, I'm not a mathematician, but the question strikes me as an epistemological one.

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One of the 21st-century first-world annoyances of the modern web is that I rarely can make sense of the source code of any website anymore. It’s often all a jumbled, obfuscated framework mess that has no obvious bearing with the contents. Like I could search for a keyword that I’m seeing on the page, and it doesn’t even show up in the source because it’s part of some dynamic call. Factoid about me: while studying for my Masters (98–00), I was a part-time webmaster for the university. Having to manually open and close HTML tags in a text editor, figure out the right CSS declarations through trial and error, manage the proper indentation, optimize images so they’d load fast, actually think about the design of the page elements in relation to each other, etc. was an exercise in meticulousness and patience, but also a great learning experience. I’m very happy with the modern state of HTML5, advanced CSS capabilities, JS-free UI, etc. I just wish we stuck to those simple standards without bloat.

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Mood rn

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So Claude just casually formalized the proof of Fermat’s Last Theorem in 13M LOC (the largest Lean proof ever produced). We’re heading toward this kind of feat being a monthly, then weekly, then daily occurrence; which is a defining trait of the singularity btw. We’re just missing the recursive self-improvement in AI… for now. 2027 is going to be wild. https://github.com/anthropics/fermats-last-theorem

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Terence Tao has this superb analogy for AI — initially in the context of math, but with applicability to other domains. Adapting a bit, it goes something like this: Let’s say you go on a hike, and you want to visit a particular waterfall. You brought a map, but you still get a bit lost on the way, and in doing so, you come across other noteworthy landmarks. Perhaps you find a cave, which you plan on sending your spelunking friend to explore another day. Eventually, you chart a path to the waterfall, and even if you don’t, it’s been a gratifying and productive journey. AI is like the helicopter that will take you directly there. You do reach your goal, and faster too, but you haven’t learned much about the terrain and you missed those features that only reveal themselves to those who wander by foot. So be deliberate and intentional about whether any particular journey is worth experiencing on your own, or if you just need to shortcut your way to your destination

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I’m increasingly thinking of LLMs as Libraries of Babel. As their training set asymptotically approximates all human outputs ever recorded, they gain the ability to churn out every possible permutation of extant knowledge in a multidisciplinary, nexialist, polymathic way (connecting every dot to every other dot). But if we raise the models’ temperature, they can also provide every possible hallucination, including one that predicts your future to a tee, or contains Satoshi’s private key, etc. — which is pretty exciting in its own right, even as we tend to view hallucinations as aberrations to squash. The Library of Babel always had the capacity to do all of the above. The hurdle, of course, was to find meaning in a googolplex number of outputs that are mostly gibberish. So just like the librarians in Borge’s story are tasked with curating meaningful outputs, the best LLM whisperers are those who know exactly *what* to ask in a near-infinite search space, and how to critically parse the answers.

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1/5 The news about a cancer mRNA vaccine successfully completing a Phase 3 trial tracks with the emerging consensus from the last few years that virtually all human diseases could be either prevented, stabilized, or cured within the next few decades, with obvious implications not just to average life expectancy, but to healthier living in old age (equitable access to medication notwithstanding). Having said that, I was never sold on the immortality proposition.

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Farcaster didn’t fail because of onboarding friction, a crypto bias, token rugs, node centralization, spooky VC money, or poor stewardship. Farcaster ultimately failed because of LinkedIn-level PGness in the feed. Everyone here (myself included) was just too polite, polished, and milquetoast (which is not the same as mid). We didn’t have enough open controversies and spicy takes on sex, drugs, crime, morality, religion, wars, pop culture, and your mom. Even the occasional outrage tended to be collective instead of factional, because we were too neighborly to turn on one another. With a few exceptions, we’ve been casting to each other as if we might meet later that day at a VC luncheon in the Bay Area, and had a FID-reputation to maintain. To be clear, I’ve thoroughly enjoyed this very aspect of an intellectual and nuanced cozy corner of the internet. But it was a PvE experience, and PvE servers are stuck with low player counts

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Back to myspace I guess

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My autocorrect now recommends “hodling” as the default syntax I may have been in crypto for too long

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It’s dawning on me that markets can remain irrational longer than I can stay alive Maybe the grandkids will get to enjoy the Lambo

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hello so the hilbert–pólya conjecture is true thus proving the riemann hypothesis, Fable and i found a self-adjoint operator whose eigenvalues are the riemann zeros i have a truly marvelous demonstration of this which this cast is too narrow to contain

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There’s an insane acceleration happening at the confluence of AI, crypto, and quantum right now. In March of this year, Google proved that the bar to make Shor’s algorithm (the quantum algo that would break 256-bit elliptic curves) is much lower than expected. Interestingly, Google didn’t provide the details of the attack vector, but only a ZK proof, in the interest of “responsible disclosure”. See the paper at https://arxiv.org/abs/2603.28846 The so-called qday (when quantum computing finally breaks elliptic curves used in mainstream crypto) is now estimated for 2029, barely three years from now. But then independent researchers have used frontier AI models to reverse engineer Google’s findings and have reached 80% of the way. There’s even an open competition at https://www.ecdsa.fail where you can join the search by contributing your own tokens. Further improvements have been discovered in the span of hours thanks to collaborative AI research, including by complete lay people. There’s an amazing X thread by @justindrake which summarizes all this at https://x.com/drakefjustin/status/2061793725299224676 So two things are happening at once. First, it’s getting more urgent than ever to move to post-quantum cryptography through forks. But even then, dormant BTC wallets from the Satoshi era (P2PK) will remain vulnerable, because their public key is already known (from which their private key will eventually be quantum computable). Same goes for P2PKH wallets if they spent once (exposing their public key). There’s around 1.7–1.9M BTC contained in P2PK wallets alone. Thats twice as many BTC as even Microstrategy owns… and we’ve seen how the markets just reacted to MSTR selling a mere 32 BTC. This won’t be pretty for Bitcoin. I don’t expect there’ll be another cycle, and if that prophecy comes true, Saylor is well and truly cooked. Second, agentic AI science is now in full swing, and hobbyists / lay people are contributing almost on par with large and well-funded FAANG labs. The acceleration looks exponential from just this year alone. We’re going to see breakthroughs happen faster than we can fully digest them. What a time to be alive

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I visited Cuba nearly 20 years ago; I wanted to see the country for myself before American capitalism rolled in on the back of a military takeover and changed the landscape forever. Back then, I assumed that scenario was about five years away. I guess I was fifteen years early.

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The shift from cars being depreciating assets to cars being disposable consumables continues. The bestselling entry level Geely EX2 now sells for $10K in China. https://www.reuters.com/business/autos-transportation/average-price-car-us-you-could-buy-5-new-chinese-evs-2026-04-28/

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