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The reasoning traces were traditionally keept secret by legacy mathematicians as well.

"When the architect completes a fine building, he removes the scaffolding." - Carl Friedrich Gauss

Legacy mathematicians can nontheless remember much of how they came up with their proof. Even though they (as Gauss says) usually don't publish this, they can still answer questions about it at conferences and workshops, or otherwise use the knowledge of the creation process to explain their proof. It's not a secret in the sense of OpenAI.

I don't believe legacy mathematicians kept their reasoning secret after they published. Quite the opposite—they were giving talks and lectures, responding to criticisms, and generally convincing the community that they were right. OpenAI has done none of that.

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