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Disclosure: I’m working with Bruno on a company around this.

In the past few weeks, AI labs have reported solving long-standing problems, including OpenAI’s claimed Navier–Stokes proof. Mathematicians fear for their jobs, and others hope math education will finally become unnecessary.

Bruno Buchberger, who invented Gröbner bases in 1965, gave his answer in the inaugural lecture of ACM SIGSAM. There will be no “math winter”: mathematics has always aimed to trivialize itself, and by Gödel there’s no upper bound to automation, so human genius just moves up a level.

He’s also done this before. In 2002 his Theorema system re-invented the Gröbner bases algorithm automatically from the bare specification, by analyzing failed correctness proofs. That’s proof generation, not proof checking. He argues logic + LLMs should beat Lean + LLMs with far less compute. Terrence Tao’s latest video ends with a strikingly similar proposal a few days later.

Given the surge of interest, he’s resuming Theorema and founding a company around it.

Is logical synthesis the next layer, or will “LLM + Lean + compute” win anyway?

What happens to shares? Are people getting IBM stock or cash?

On implications of what is AI and how we can achieve automated programming.

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and tips for going above level 4? something clever seems not be enough, so does prompt hacking start here already?

Are they happy to sell less for this price?

There is a saying in japanese that ideas don't come from kami but from kami. Kami in the first meaning means god. In the second it means paper.

So ideas don't come from god but from paper.

How does memory bandwidth between M1 Pro and M1 Max affect CPU (not GPU) performance?

The thing is that Postico was explicitly made for Postgres so it works flawlessly with it.