I've been asked: what do I think of @Kalshi & @Polymarket? These are still very early days. My vision, which I started to articulate ~1990, is of a world very different from both the world of then, and the world of today. A world where markets are accepted as offering more accurate estimates on far more useful topics. So I’m mostly interested in the potential of stuff today to enable and cause that future vision. The politics/policy questions on Polymarket and Kalshi trending now seem plausibly like topics where some people might find their estimate useful in making personal or collective choices. But I don’t have great confidence in that, or know who those people are. But if these systems continue to grow in size, and to attract users and competitors, they could lower the many costs of creating and managing such markets, allowing a lot more experimentation with markets like those I find more promising re my long term vision. Or course if these systems induce a backlash that gets them outlawed or drastically shrunk, that may plausibly block or at least long delay my vision. I don’t personally mind people having fun knowingly betting on sports, on actions that celebrities can influence, or on topics where insiders have big info advantages. But I see many people complaining about these things, and I fear a new prudish temperance movement may shut them down, and as a side effect shut down the more promising markets that I’ve envisioned. Robin Hanson

We are on the cusp of a profound change in the field of mathematics. Vibe proving is here. Aristotle from @HarmonicMath just proved Erdos Problem #124 in @leanprover, all by itself. This problem has been open for nearly 30 years since conjectured in the paper “Complete sequences of sets of integer powers” in the journal Acta Arithmetica. Boris Alexeev ran this problem using a beta version of Aristotle, recently updated to have stronger reasoning ability and a natural language interface. Mathematical superintelligence is getting closer by the minute, and I’m confident it will change and dramatically accelerate progress in mathematics and all dependent fields.

Lean is the only program verifier you need. Here’s why. 🧵