A Historical Discovery & a Bunch of Lies

TLDR;

Welcome back! This week, we have the first truly AI-only discovery in history, and it’s one of the greatest mysteries in maths.

We also discuss a new model trained at a millionth of the cost of frontier models, which is still very competitive with models tens of times larger, as well as a rundown of market news, including a review of Anthropic's claim that it’s about to become operationally profitable.

We’ll end with CEO digital twins and Google’s I/O event.

Enjoy!

FRONTIER RESEARCH

A First in AI Discovery

As published by OpenAI, the company says one of its internal reasoning models has disproved a longstanding conjecture tied to the “planar unit distance problem,” a famous question in discrete geometry first posed by Paul Erdős in 1946.

The problem asks how many pairs of points in a plane can be exactly one unit apart. For decades, mathematicians believed the best constructions were essentially based on square-grid arrangements. OpenAI says its model has found a new infinite family of constructions that outperform those assumptions, yielding a polynomial improvement over the previously accepted approach.

According to OpenAI, the proof was reviewed by external mathematicians. Princeton mathematician Noga Alon described the problem as one of Erdős’s favorite open questions, while researchers including Arul Shankar and Jacob Tsimerman said the construction was unexpectedly sophisticated and difficult to derive manually.

Timothy Gowers, Fields Medal recipient, called it a huge milestone in AI’s push toward mathematics.

TheWhiteBox’s takeaway:

This is actually a first in the industry, and I’m not exaggerating.

For the longest time (very likely until this event), AI has shown zero capability to improve the frontier of human knowledge autonomously. Previous Erdős solutions in which AI participated included the active involvement of renowned mathematicians. Instead, here the AI was just given the problem and the goal, as you can see below:

Source

Interestingly, OpenAI claims this model is not a specialized model for maths but a general-purpose model that happened to be incredibly good at maths, a claim very similar to the one made by Anthropic regarding Mythos's cybersecurity capabilities.

The only caveat to all of this is that, while OpenAI published the reasoning (125 pages long), it was a redacted version, summarized from the original. Why OpenAI chooses not to disclose the actual reasoning trace is unknown, but it certainly reduces trust in its claims.

That said, it’s important that we reflect on why this happened in the first place. As the researchers explain, the key here is exploration. Intelligence is commonly described as a mixture of intuition and search: our minds suggest possible directions, and we explore them to find the best solution.

What this release suggests is that AI, which obviously has a much higher capacity for exploration (we humans can only consider a few options at any given time; an AI can explore millions), is developing good intuition too (suggesting good directions).

Interestingly, three hours later, the proof had already been improved by a human. From what I’ve been told,…

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