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"The proof ends up being remarkably elementary." Dude then proceeds to dump about 16 A4 pages worth of heavy-duty algebra which 99.999% of the humans on the su

"The proof ends up being remarkably elementary." Dude then proceeds to dump about 16 A4 pages worth of heavy-duty algebra which 99.999% of the humans on the surface of this planet are completely unable to read past the first two lines. LOL, I guess language is a "remarkably" vague tool, where "elementary" means vastly different things to different people. That doesn't diminish the achievement of course, but ... please, easy on the "remarkably elementary" next time, that's borderline insulting.

zem 29d ago
"elementary" does not mean simple or easy, it refers to the domain of mathematics involved in the proof. https://en.wikipedia.org/wiki/Elementary_proof https://en.wikipedia.org/wiki/Elementary_proof
- ur-whale 29d ago
  Your definition of "elementary" is the one used by the other 100.0 - 99.999 % Thank you for making my point for me. Ivory tower much?
  - bananaflag 29d ago
    It's not the OP's definition, it's the definition of the word as used in mathematical practice, as evidenced by the Wikipedia article cited.
ifethereal 29d ago
It's a habit of the community. Tao actually elaborates on what he means by this in the same paragraph. I'd like to offer a charitable interpretation. By Tao labelling it as "remarkably elementary", he encourages less experienced mathematicians (including students) to go and read the proof for themselves. He's advertising a low barrier to entry for certain parts of his audience. This isn't always the case with whatever he reports on, so it's worth pointing out when it's true.
GPerson 29d ago
“Remarkably elementary” in mathematics means accessible to people who have finished the first 1-3 years of grad school where you go through the canonical entry level courses in research level mathematics. There’s no reason to think Terence’s blog is aimed at a general audience.

zem 29d ago

"elementary" does not mean simple or easy, it refers to the domain of mathematics involved in the proof. https://en.wikipedia.org/wiki/Elementary_proof https://en.wikipedia.org/wiki/Elementary_proof

ur-whale 29d ago
Your definition of "elementary" is the one used by the other 100.0 - 99.999 % Thank you for making my point for me. Ivory tower much?
- bananaflag 29d ago
  It's not the OP's definition, it's the definition of the word as used in mathematical practice, as evidenced by the Wikipedia article cited.

ifethereal 29d ago

It's a habit of the community. Tao actually elaborates on what he means by this in the same paragraph. I'd like to offer a charitable interpretation. By Tao labelling it as "remarkably elementary", he encourages less experienced mathematicians (including students) to go and read the proof for themselves. He's advertising a low barrier to entry for certain parts of his audience. This isn't always the case with whatever he reports on, so it's worth pointing out when it's true.

GPerson 29d ago

“Remarkably elementary” in mathematics means accessible to people who have finished the first 1-3 years of grad school where you go through the canonical entry level courses in research level mathematics. There’s no reason to think Terence’s blog is aimed at a general audience.