Azeem Azham 评 OpenAI 未发布模型的数学成果：人类还剩什么可做

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Yesterday, OpenAI released a range of mathematical results produced by an unreleased frontier model. It’s a remarkable range: 722 manuscripts in 372 families, across number theory, complexity theory, and mathematical physics. The average result took the equivalent of three hours of ChatGPT Pro thinking.

As scientist Derya Unutmaz points out, it comprises 81% of the major math discoveries in the past three years.

Many of the results have been verified in Lean, but not all. Even if the real number is half of that, it’s staggering. Problems that have stumped the best human minds for decades fell to one afternoon of compute.

How should we think about this?

suggests:

Imagine millions of superhuman research agents at work. Formal systems may verify the proofs, but humans won’t have enough context to understand the underlying web of machine-invented concepts.
Mathematics could split into two layers:
Machine mathematics: vast, verified, mostly consumed by AIs.
Human mathematics: a compressed “effective theory” of the machine frontier—the small subset of ideas we can understand.

A turning point

It might be an intriguing turning point in how we, as humans, understand the world.

We’ve only had three hundred years of making sense of the world through natural rather than supernatural explanations. The Enlightenment gave us that – a way to use reason and empiricism to understand what had previously been inexplicable.