OpenAI 未发布前沿模型产出大量数学结果，Azeem Azhar 谈机器数学与人类数学的分层
🔮 What is left to do - by Azeem Azhar - Exponential View
OpenAI 发布了一批由未发布前沿模型产出的数学结果，共 722 篇手稿、372 个家族，覆盖数论、复杂性理论和数学物理，平均每项结果相当于 ChatGPT Pro 思考三小时。作者 Azeem Azhar 引用 Derya Unutmaz 的说法称，这相当于过去三年主要数学发现的 81%；部分结果已在 Lean 中验证，但并非全部。他援引 Steve Hsu 的观点提出，数学可能分为机器数学与人类数学两层，前者规模庞大且由 AI 消费，后者只是人类能理解的一小部分压缩理论。
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围绕未发布前沿模型产出的数学结果，讨论机器数学与人类数学可能分层这一判断。
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The future of science may be provable, profitable and incomprehensible
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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?
Steve Hsu 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.