Maybe infinite monkeys at infinite typewriters hitting the statistically most likely next key based on their training.

Someone actually mathed out infinite monkeys at infinite typewriters, and it turns out, it is a great example of how misleading probabilities are when dealing with infinity:

"Even if every proton in the observable universe (which is estimated at roughly 1080) were a monkey with a typewriter, typing from the Big Bang until the end of the universe (when protons might no longer exist), they would still need a far greater amount of time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10500 chance of success. To put it another way, for a one in a trillion chance of success, there would need to be 10^360,641 observable universes made of protonic monkeys."

Often infinite things that are probability 1 in theory, are in practice, safe to assume to be 0.

So no. LLMs are not brute force dummies. We are seeing increasingly emergent behavior in frontier models.

The real question is how to define intelligence in a way that isn't artificially constrained to eliminate all possibilities except our own.

I hired an artist for an oil painting.

The artist drew 10 pencil sketches and said "hmm I think this one works the best" and finished the painting based on it.

I said he didn't one shot it and therefore he has no ability to paint, and refused to pay him.

You learned what was unsuitable over your entire life until now by making countless mistakes in human interaction.

A basic AI chat response also doesn't first discard all other possible responses.

How often do you self edit before submitting?

because commenting is easy and solving hard problems is hard

That's just not true at all. There are entire fields that rest pretty heavily on brute force search. Entire theses in biomedical and materials science have been written to the effect of "I ran these tests on this compound, and these are the results", without necessarily any underlying theory more than a hope that it'll yield something useful.

As for advances where there is a hypothesis, it rests on the shoulders of those who've come before. You know from observations that putting carbon in iron makes it stronger, and then someone else comes along with a theory of atoms and molecules. You might apply that to figuring out why steel is stronger than iron, and your student takes that and invents a new superalloy with improvements to your model. Remixing is a fundamental part of innovation, because it often teaches you something new. We aren't just alchemying things out of nothing.

More often than not, far, far, far more often than not, we do not already know that it will work. For all human endeavors, from the beginning of time.

If we get to any sort of confidence it will work it is based on building a history of it, or things related to "it" working consistently over time, out of innumerable other efforts where other "it"s did not work.

AI can one shot problems too, if they have the necessary tools in their training data, or have the right thing in context, or have access to tools to search relevant data. Not all AI solutions are iterative, trial and error.

Also

> humans are a lot better at (...)

That's maybe true in 2026, but it's hard to make statements about "AI" in a field that is advancing so quickly. For most of 2025 for example, AI doing math like this wouldn't even be possible