Dave-Thinking

Some reflections on AI in math. I found it helpful to simply list out the various parts of what a mathematician does, why math is valuable, and where the funding comes from. From there, what happens if AI gets more capable? youtu.be/LKrwhjOI8Nc

OSINT analysts who have been bashing @ElonMusk for days over this don't get it. Russia has the capacity to blow up satellites in space. They proved this on November 15, 2021, by firing a PL-19 Nudol missile at an old satellite of their own. The impact created a large debris cloud—more than 1,500 trackable fragments plus hundreds of thousands of smaller pieces. The International Space Station was forced to implement safe-haven procedures: the seven-person crew (including Russian cosmonauts) sealed hatches and sheltered in the docked Soyuz and Crew Dragon spacecraft for several hours as the debris cloud repeatedly crossed their orbital path. The ISS even had to perform thruster burns on multiple occasions over the following months to avoid the debris cloud orbiting the Earth. If Russia decides that the civilian Starlink satellite network is weaponized and fair game, we risk a serious Kessler syndrome. First modeled by NASA’s Donald Kessler and Burton Cour-Palais in 1978, it describes a scenario in which the density of objects in low Earth orbit gets so high that collisions start producing debris faster than natural processes (mainly atmospheric drag) can remove. Each collision creates more fragments, which raise the odds of further collisions, leading to a self-sustaining cascade, a runaway cloud of satellite debris that can make certain orbital bands increasingly hazardous. Space could become unusable for years to centuries. You like driving around with GPS? Starlink MUST remain a civilian entity.

Claude isn't a great musician (yet) But this kind of video would be unfathomable to make even 6 months ago with previous LLMs "Claudia Explains: Euclid"

People asked for me to upload the Bitter Lesson video from this piece to YouTube, so here you are: youtu.be/OAwat51S_Sk

I think this is an emotional moment for a lot of people, and the math community itself isn't of one unified mind on what should happen. Perhaps the latest is the 3SUM/APSP result that came out last week. I'm not sure how carefully many people read that preprint, but the most bizarre part of the episode to me is what the prompt was: there was no prompt to solve 3SUM. The agent was working on something else, and decided to attack 3SUM on its own as a side quest then solved it (see page 63 of the preprint). Its solution purported to resolve 3SUM and APSP simultaneously, via a unifying problem that both reduce to. So then, Anthropic is sitting on the refutation of 2 of the 3 major building blocks of fine-grained complexity. Just sitting on them and not telling the world doesn't seem right. Some mathematicians feel poorly written (by AI) manuscripts should be released as they are, and just let the community digest it. Dan Spielman, who I respect a lot, wrote in mathadjacent.com/p/the-big-r… the exact opposite: AI companies should "find experts who are interested in the problems and the solutions, and to offer them the opportunity to write good solutions", which is exactly what Anthropic did. Again, it's impossible to please everyone when there's no consensus amongst reasonable people. I think we’re in a phase of process experimentation while everyone is digesting the new world we're in.