Cal Newport

But basically, they applied a – the LLM said, what would happen if we applied a sort of standard – and they had to generalize this stuff.

It was non-trivial.

But if we applied a standard sort of like algebraic embedding, I guess would be the right word, to the original solution, hey, it turns out this thing has more points with unit distance than Erdos thought, right?

So it was –

The answer was kind of in the near field around the right.

It was around.

It was nearby.

Just no one had found it before.

All right.

So let me go on.

I'm going to read some more from Bloom.

On examining the construction, it becomes more clear how people had missed this before.

It requires the confluence of several different unlikely events.

that a good mathematician is one, spending significant time in thinking about the unit distance conjecture in the first place.

Two, seriously trying to disprove it despite the oft-repeated belief of Erdos that it is true.

Three,

believes that there is mileage in generalizing the original construction to other number fields and so is willing to expend significant time in exploring such constructions.

And four, sufficiently familiar with the relevant parts of class field theory to recognize that the appropriately phrased question about infinite towers and number fields with appropriate parameters can be solved using existing theory.

The AI met all of these criteria and its success here echoes previous achievements.

It often produces the most surprising results by persevering down paths that a human may have dismissed as not worth their time to explore, combining superhuman levels of patience with familiarity with a vast array of technical machinery.