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  https://youtu.be/ZHizu-koBDA Wonderful.

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  If I repeat the question in a different session, sometimes it answers correctly.

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  Is the open internet worth keeping alive?

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  **At most** $1T is my rough, back of the envelope, estimate of what Anthropic's market capitalization should be. This is based on the reported quarterly **revenue** (not profit) of $16.8B and some very, very rough arithmetic. One can imagine an annual revenue of about $100B which means, at 50% margin, annual earnings of about $50B, and let's say we value them at a P/E ratio of 20. This yields $1T. For me this would be an upper bound, since I think I have been generous with ever...

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  To a first approximation, OpenAI's proof dump is sort of denial-of-service attack on mathematicians. This is analogous to how social media overwhelms our minds. There's simply too much stuff that demands attention. -- Whenever a binding constraint is relaxed (or _removed_ which is practically the case here) the system will move to a very different state. Typically, there will be some other constraint which will newly become binding. (And since this new binding constraint wasn&...

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  I can now use Gemini 4 (Argon) to use several overlapping pictures of an individual shelf, and generate a CSV file with titles and authors (in order). I will now try this with a shelf containing books in many languages. I'd previously assumed that this was already a solved problem, about 1-2 years ago, but when I tried it, it didn't work well enough. Now it seems that it does.

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  https://ai-security-letter.org/ I haven't seen it on Mathstodon, so I figured I should share it. Signatories include Yoshua Bengio and Geoffrey Hinton.

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  Here's an interview with the leader of a country (Germany). If you are not German, please compare it with how a similar interview with your country's leader would have sounded. https://youtu.be/fku17_fFjiI

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  A brilliant proof by Conway: https://youtu.be/S75VTAGKQpk

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  Whoever becomes the next US President will inherit huge problems, which they will be ill-equipped to solve. This is primarily because of the size of the problems. To be addressed properly, they require a degree of political consensus and functioning institutions, neither of which seem to be on the horizon. So either it will be another Obama who will then be blamed for either not doing enough or of being directionally wrong, or it will be someone truly horrible like J.D. Vance who will continue...

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  I recommend this YouTube channel: https://youtube.com/@sholto_david . He's doing some great work uncovering scientific mistakes and fraud, and his videos deserve to be watched by many more people. Watch his last 3-4 videos (about scientific fraud, etc), and also his most popular video (about cycling very very long distances).

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  News is broken. If it's not Trump in the headlines, it's AI. They drown out everything else.

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  If you build a world for machines, you'll find that machines will do better in it than animals (including humans) and plants. But machines are suited to flat, predictable, boring worlds. They will thrive as long as their environment is flat and predictable and boring. https://youtu.be/013zp1Ry4qA

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  A great documentary by Le Monde, about how some people (social climbers) grow their networks. In this case, the person growing his network was Jeffrey Epstein. And at least two of the nodes in the network are great mathematicians: Misha Gromov and Cedric Villani!! His connection to them was very weak, and I don't think they did anything unsavory. I don't blame them, It's extremely easy to to agree to meet, or to reply to an email from, a friend of a friend. Sometimes, yo...