Lemma for the Fundamental Theorem of Galois Theory

Re:Lemma for the Fundamental Theorem of Galois Theory by xanderlewis on Saturday March 15, 2025 @04:38PM (#43374992)

You mean like a dependency tree? There isn’t a comprehensive one — it would be way too big and we don’t have all mathematical knowledge written down in one place anyway.

But if you’re interested in any given classical result, if you ask I’m sure a mathematician can give you a rough idea of what the path back down to first principles is. If you’re not literally interested in starting by assuming the existence of the empty set, say, then opening any introductory book on the topic will give you an idea. Just look at the proof of the result and follow its references back. It won’t go that deep.

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Re:Lemma for the Fundamental Theorem of Galois Theory by galaxyLogic on Saturday March 15, 2025 @06:46PM (#43375646)

I see. I was just thinking I would personally appreciate seeing a big graph of proof-dependencies. A bit like "Seeing the Forest from the Trees".

Every mathematician is working on their own TREE, I assume. But might be useful if somebody was looking at how the FOREST is doing.

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Re:Lemma for the Fundamental Theorem of Galois Theory by lupire on Sunday March 16, 2025 @12:59PM (#43380432)

> it would be way too big and we don’t have all mathematical knowledge written down in one place anyway.

Yet somehow Google managed to index the Internet.

And the human genome is indexed.

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