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Some time ago I found my "own" proof of the fundamental theorem of Galois theory. You can find a pdf with the proof here. It is quite short, self-contained, and uses a neat combinatorial argument:

A field cannot be written as a union of finitely many proper subfields

Most users of mathoverflow can simply skip most of it and only read the combinatorial Lemma 3.3. which leads to Prop. 4.2, as well as Lemma 5.5 which leads to to Prop. 6.3. The rest is easy.

I wonder if this proof is new or not. For sure I have never seen it before, and I checked a bit the literature and couldn't find it so far. But also I am not really an expert on the history of algebra at all, and my days as an "active mathematician" are over anyway. Hopefully somebody else has a better overview?

Update. It's now on the arXiv.

Some time ago I found my "own" proof of the fundamental theorem of Galois theory. You can find a pdf with the proof (link removed, see arXiv). It is quite short, self-contained, and uses a neat combinatorial argument:

A field cannot be written as a union of finitely many proper subfields

Most users of mathoverflow can simply skip most of it and only read the combinatorial Lemma 3.3. which leads to Prop. 4.2, as well as Lemma 5.5 which leads to to Prop. 6.3. The rest is easy.

I wonder if this proof is new or not. For sure I have never seen it before, and I checked a bit the literature and couldn't find it so far. But also I am not really an expert on the history of algebra at all, and my days as an "active mathematician" are over anyway. Hopefully somebody else has a better overview?

Some time ago I found my "own" proof of the fundamental theorem of Galois theory. You can find a pdf with the proof here. It is quite short, self-contained, and uses a neat combinatorial argument:

A field cannot be written as a union of finitely many proper subfields

Most users of mathoverflow can simply skip most of it and only read the combinatorial Lemma 3.3. which leads to Prop. 4.2, as well as Lemma 5.5 which leads to to Prop. 6.4. The rest is easy.

I wonder if this proof is new or not. For sure I have never seen it before, and I checked a bit the literature and couldn't find it so far. But also I am not really an expert on the history of algebra at all, and my days as an "active mathematician" are over anyway. Hopefully somebody else has a better overview?

Edit. The response so far indicates that the proof might be new. I think this suffices to justify putting it up to arXiv. (?)

Some time ago I found my "own" proof of the fundamental theorem of Galois theory. You can find a pdf with the proof here. It is quite short, self-contained, and uses a neat combinatorial argument:

A field cannot be written as a union of finitely many proper subfields

Most users of mathoverflow can simply skip most of it and only read the combinatorial Lemma 3.3. which leads to Prop. 4.2, as well as Lemma 5.5 which leads to to Prop. 6.3. The rest is easy.

I wonder if this proof is new or not. For sure I have never seen it before, and I checked a bit the literature and couldn't find it so far. But also I am not really an expert on the history of algebra at all, and my days as an "active mathematician" are over anyway. Hopefully somebody else has a better overview?

Some time ago I found my "own" proof of the fundamental theorem of Galois theory. You can find a pdf with the proof here. It is quite short, self-contained, and uses a neat combinatorial argument:

A field cannot be written as a union of finitely many proper subfields

Most users of mathoverflow can simply skip most of it and only read the combinatorial Lemma 3.3. which leads to Prop. 4.2, as well as Lemma 5.5 which leads to to Prop. 6.4. The rest is easy.

I wonder if this proof is new or not. For sure I have never seen it before, and I checked a bit the literature and couldn't find it so far. But also I am not really an expert on the history of algebra at all, and my days as an "active mathematician" are over anyway. Hopefully somebody else has a better overview?

Some time ago I found my "own" proof of the fundamental theorem of Galois theory. You can find a pdf with the proof here. It is quite short, self-contained, and uses a neat combinatorial argument:

A field cannot be written as a union of finitely many proper subfields

Most users of mathoverflow can simply skip most of it and only read the combinatorial Lemma 3.3. which leads to Prop. 4.2, as well as Lemma 5.5 which leads to to Prop. 6.4. The rest is easy.

I wonder if this proof is new or not. For sure I have never seen it before, and I checked a bit the literature and couldn't find it so far. But also I am not really an expert on the history of algebra at all, and my days as an "active mathematician" are over anyway. Hopefully somebody else has a better overview?

Edit. The response so far indicates that the proof might be new. I think this suffices to justify putting it up to arXiv. (?)