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So we don't know if anyone at all has reviewed their proof, do we? Sounds like at this point they are just claiming something.

I guess it will become interesting once it's actually reviewed.

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Which is good! They're backing that claim by submitting it for peer review. It may seem like they're leapfrogging the process by getting published in the Guardian before getting validation but: a. The Guardian is promoting them, not the students themselves, I believe. b. It's genuinely impressive that high school students worked out a proof, (for something so common like the Pythagoreas theorem!) that wasn't immediately rejected on first sight by professionals. Even if is eventually rejected, getting to this point is worth noting and appreciating.

Oh that's the bit I was missing: so professionals did see the proof and did not reject it right away, is that right?

It was not clear to me if they just submitted their work or actually presented it already.

Do undergraduate mathematics journals ever desk-reject sincere attempts?

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