Alex Dabrowski

Finetuning LLMs @ Google. AI, Math.

[Nassim Nicholas Taleb @nntaleb]

To generalize from the Kasparov & the math debacle: as a rule, all performative skills will be destroyed by AI. A computer will always outperform a human, so chess is no longer a skill.

Same w/mathematical acrobatics.

What's left is what makes us human.

[Alex Dabrowski @alexdbrw]

@MartinShkreli @AndrewCurran_ An LLM could have fixed this easily… ironic

[Alex Dabrowski @alexdbrw]

From https://t.co/6pn7p5mXMu

[Alex Dabrowski @alexdbrw]

A map of the Hilbert-Smith proof

[Sean McClure @sean_a_mcclure]

Because I am Trying to Save Math

We have a cabin on the lake.

It's been in the family for a long time.

It used to have a nice old rustic look. With a ton of nostalgia attached to it. So many memories.

But it's time had come. The walls, the pipes, the rotting wood. The attempt to preserve what no longer worked, for the sake of nostalgia, did not preserve the cottage. It did the opposite: it risked losing it all together.

Inevitably, it would rot and be lost to time.

The only way to keep it was to modernize it. To make it up-to-date, stable, useable, maintainable. To bring it into the 21st century.

The memories are still there. The space, the geography. The shape of things. But now preserved and given new life, for many more generations.

Because we embraced the evolution of things.

I don't celebrate the use of AI in math and science for their demise. I do it to save them.

[Alex Dabrowski @alexdbrw]

https://t.co/sCBP9jsczJ

[Alex Dabrowski @alexdbrw]

An AI-generated under human guidance proof of Hilbert-Smith, together with complete Lean4 formalization (100k LOC), on which I have worked independently over the last few weeks in my free time. It’s the first Lean4 formalization available afaik, since openai didn’t publish it. Planned on cleaning it up, but had to rush it out after openai’s release. You don’t need the latest biggest models to do research (but it helps).

[Alex Dabrowski @alexdbrw]

@AlanJCoppola @OpenAI I have an independently derived, fully formalized, proof of Hilbert-Smith, together with instructions on how to run Lean4 verification at https://t.co/sCBP9jsKph

[Alex Dabrowski @alexdbrw]

@ElliotGlazer It's very hard to formalize 1-1, sometimes the machinery simply does not exist in Lean4. See e.g. https://t.co/wHPRmWivLp, where a lot of results from the paper have to be restated in specific settings, or an alternative route is MUCH simpler

[Alex Dabrowski @alexdbrw]

@rperezmarco @wtgowers @AcerFur Nothing is within the convex hull in high dimensions (see e.g. https://t.co/g1MeC30AeV). This is a very low-dimensional way of thinking, to which LLMs are immune, but humans definitely not

[Alex Dabrowski @alexdbrw]

If the computer is a bike for the mind, AI is a rocket

[Alex Dabrowski @alexdbrw]

@rperezmarco @HdjDd65233682 Random self promotion of an alternative proof (shorter and Lean4 validated) https://t.co/sCBP9jsKph

[Alex Dabrowski @alexdbrw]

Many LLMs (both commercial and open source) were used for nearly every task, but with occasional human guidance. The core idea and Lean4 formalization were obtained by Opus 5.5. This was a personal project with a small budget, total costs were below $1k.