3 ms·

The problem is that the base "axioms" (really, definitions) he's working off of are basically alien language, and almost nobody understands why they are relevan

by ttz 7y ago

The problem is that the base "axioms" (really, definitions) he's working off of are basically alien language, and almost nobody understands why they are relevant. Add to that he is not saying "turn the crank like this", but is effectively saying "trust me when I say the cranks turn and out pops the answer, but if you dig into the machinery yourselves you'll see what I mean". On the other hand, there was a similar case with a German mathematician beforehand, and he turned out to be correct.

throwaway_pdp09 7y ago
I don't buy that the base axioms are alien and it doesn't matter anyway. I can give you an alien language of logical axioms, and a series of steps, none of which a random person wouldn't be able to understand, but could still lead them through a series of steps, showing that the outcome could be derived from the input via the axioms. Now, if nobody could understand the axioms and steps of this but they still got a consistent outcome, mathematicians would still be interested if for no other reason than it was self-consistent. That alone would be a result. But if they had that, I suspect that would also give them a framework for understanding it. > "trust me when I say the cranks turn and out pops the answer, but if you dig into the machinery yourselves you'll see what I mean". automate that and there'll be no need to trust him.
- Someone 7y ago
  This (purported) proof is 500+ pages. For a mathematical proof, that’s enormous. Sampling a few of the issues of the journal in question, its longest papers seems to be about 40 pages (http://www.kurims.kyoto-u.ac.jp/~prims/pdf/43-1/contents-43-1.pdf http://www.kurims.kyoto-u.ac.jp/~prims/pdf/43-1/contents-43-..., http://www.kurims.kyoto-u.ac.jp/~prims/pdf/42-3/contents-42-3.pdf http://www.kurims.kyoto-u.ac.jp/~prims/pdf/42-3/contents-42-...) And those are papers that an expert can skim to get an idea about the flow of the proofs. This one, if you jump in, says you things like “every fooable bazz is a bar”, where foo, bar and baz are new terms no mathematician has any intuition for that, likely, got defined in terms of other hitherto unknown terms qux, quux and quuz, making it impossible to judge whether that statement has merit, or how it leads to proving the abc conjecture. And yes, an automated proof checker would be nice to have, but we aren’t there yet, by a wide margin. Getting there would make this proof a lot longer. (For a loose analogue: imagine that the published solution to a “mate in 2” problem in chess wouldn’t just be “Queen g1, check, King h8, rook h2, mate”, but “whites queen is on field d1, by rule r queen can move horizontally across empty fields, there are no empty fields between d1 and g1, that doesn’t bring white’s king in check (blacks pawn on e4 can’t take it because…, blacks knight on c6 can only move to… because of rules…, so white can move their queen to g1. That brings black in check because of rules…, etc)
heavenlyblue 7y ago
> On the other hand, there was a similar case with a German mathematician beforehand, and he turned out to be correct. Who is that?
- highergeometer 7y ago
  Maybe thinking of Heegner (https://en.wikipedia.org/wiki/Kurt_Heegner https://en.wikipedia.org/wiki/Kurt_Heegner)? I give this example (that I learned from a book of van der Poorten) in my Inference piece.

by ttz 7y ago

throwaway_pdp09 7y ago

I don't buy that the base axioms are alien and it doesn't matter anyway. I can give you an alien language of logical axioms, and a series of steps, none of which a random person wouldn't be able to understand, but could still lead them through a series of steps, showing that the outcome could be derived from the input via the axioms. Now, if nobody could understand the axioms and steps of this but they still got a consistent outcome, mathematicians would still be interested if for no other reason than it was self-consistent. That alone would be a result. But if they had that, I suspect that would also give them a framework for understanding it. > "trust me when I say the cranks turn and out pops the answer, but if you dig into the machinery yourselves you'll see what I mean". automate that and there'll be no need to trust him.

Someone 7y ago
This (purported) proof is 500+ pages. For a mathematical proof, that’s enormous. Sampling a few of the issues of the journal in question, its longest papers seems to be about 40 pages (http://www.kurims.kyoto-u.ac.jp/~prims/pdf/43-1/contents-43-1.pdf http://www.kurims.kyoto-u.ac.jp/~prims/pdf/43-1/contents-43-..., http://www.kurims.kyoto-u.ac.jp/~prims/pdf/42-3/contents-42-3.pdf http://www.kurims.kyoto-u.ac.jp/~prims/pdf/42-3/contents-42-...) And those are papers that an expert can skim to get an idea about the flow of the proofs. This one, if you jump in, says you things like “every fooable bazz is a bar”, where foo, bar and baz are new terms no mathematician has any intuition for that, likely, got defined in terms of other hitherto unknown terms qux, quux and quuz, making it impossible to judge whether that statement has merit, or how it leads to proving the abc conjecture. And yes, an automated proof checker would be nice to have, but we aren’t there yet, by a wide margin. Getting there would make this proof a lot longer. (For a loose analogue: imagine that the published solution to a “mate in 2” problem in chess wouldn’t just be “Queen g1, check, King h8, rook h2, mate”, but “whites queen is on field d1, by rule r queen can move horizontally across empty fields, there are no empty fields between d1 and g1, that doesn’t bring white’s king in check (blacks pawn on e4 can’t take it because…, blacks knight on c6 can only move to… because of rules…, so white can move their queen to g1. That brings black in check because of rules…, etc)

heavenlyblue 7y ago

> On the other hand, there was a similar case with a German mathematician beforehand, and he turned out to be correct. Who is that?

highergeometer 7y ago
Maybe thinking of Heegner (https://en.wikipedia.org/wiki/Kurt_Heegner https://en.wikipedia.org/wiki/Kurt_Heegner)? I give this example (that I learned from a book of van der Poorten) in my Inference piece.