3 ms·

The papers on Inter-universal Teichmueller theory span over 500 pages alone, and they build on material developed earlier that needs to be understood too. Those

by mmarx 11y ago

The papers on Inter-universal Teichmueller theory span over 500 pages alone, and they build on material developed earlier that needs to be understood too. Those papers were published a little over 3 years ago, so claiming that they can't be understood “by experts who concentrate on them for a long time” might be a bit premature.

logicallee 11y ago
but the article doesn't make it sound like it's not "fully understood." the article makes it sound like not even the summary is known - for example, what parts of the other papers are used, what isn't. As though the experts didn't even known what parts of theories were being referred to. very bizarre.
- jsprogrammer 11y ago
  The summary is known. Have you read the abstracts?
  - logicallee 11y ago
    Did you even read our article, jsprogrammer? That's what I'm reacting to. It says: >A consensus emerged that the highlight of the workshop was a lecture on 9 December by Kiran Kedlaya, an arithmetic geometer from the University of California, San Diego. He zeroed in on a result from a 2008 paper by Mochizuki that linked the statement of the abc conjecture to another branch of maths called topology. The link was immediately recognised as a crucial step in Mochizuki’s grand strategy. This is why I'm making the reference to ancient lost texts. I mean, if the result of a 2008 paper is crucial, you'd think the guy would have just mentioned this fact. It's as though they're investigating some long dead guy's hidden thoughts. This is a direct quote: "There is still no clear answer to lingering questions about how things are ultimately going to fit together." What? Wouldn't the guy just tell you how they're ultimately going to fit together? I'm utterly perplexed at the process the article describes, when the author is available and can give hints.
    - shmageggy 11y ago
      What I understood from http://mathbabe.org/2015/12/15/notes-on-the-oxford-iut-workshop-by-brian-conrad/ http://mathbabe.org/2015/12/15/notes-on-the-oxford-iut-works... (posted elsewhere here), is that the problem stems from differing motivations. On one hand, Mochizuki wants to make his proof fullyt complete and correct (being both fully general and covering all special cases), but the community wants broad strokes intuitions. From Mochizuki's perspective, he has told everyone how things fit together, but fit together means something different for others. The workshop attendees want to know what things they can gloss over to get the big picture, but as of yet, nobody who understands the proof has succeeded in communicating that information, probably because they don't share the same motivation.
    - jsprogrammer 11y ago
      I did read the article. It wasn't clear that you were referring to that specific paragraph. > I mean, if the result of a 2008 paper is crucial, you'd think the guy would have just mentioned this fact. Maybe he did? Or maybe it is just not crucial.∎ The article just states "The link was immediately recognised as a crucial step in Mochizuki's grand strategy."...that is just the writer's opinion. Linking these papers to topology is trivial. The word "topological" alone occurs 111 times in the first paper. A lot of what I'm reading in this article, and others, is people complaining about not understanding something that they (probably/apparently) have not even read.
jug 11y ago
Personally I find this more mind boggling than that it can't be communicated easily. Clearly, a proof of 500 pages will be extremely difficult to verify or even understand. However... That a concept taking just a paragraph to explain* for people who know math requires a proof of over 500 pages. THAT is what I find mind boggling and I find hard to understand. That it can just balloon in size like that, especially given that mathematics is a language of logic. * https://en.wikipedia.org/wiki/Abc_conjecture https://en.wikipedia.org/wiki/Abc_conjecture
- im2w1l 11y ago
  The halting problem proves that mathematics is hard. There is no algorithm that can prove/disprove any decidable statement. Not even a a superslow algorithm. Maybe ballooning is related to that...

by mmarx 11y ago

logicallee 11y ago

but the article doesn't make it sound like it's not "fully understood." the article makes it sound like not even the summary is known - for example, what parts of the other papers are used, what isn't. As though the experts didn't even known what parts of theories were being referred to. very bizarre.

jsprogrammer 11y ago
The summary is known. Have you read the abstracts?
- logicallee 11y ago
  Did you even read our article, jsprogrammer? That's what I'm reacting to. It says: >A consensus emerged that the highlight of the workshop was a lecture on 9 December by Kiran Kedlaya, an arithmetic geometer from the University of California, San Diego. He zeroed in on a result from a 2008 paper by Mochizuki that linked the statement of the abc conjecture to another branch of maths called topology. The link was immediately recognised as a crucial step in Mochizuki’s grand strategy. This is why I'm making the reference to ancient lost texts. I mean, if the result of a 2008 paper is crucial, you'd think the guy would have just mentioned this fact. It's as though they're investigating some long dead guy's hidden thoughts. This is a direct quote: "There is still no clear answer to lingering questions about how things are ultimately going to fit together." What? Wouldn't the guy just tell you how they're ultimately going to fit together? I'm utterly perplexed at the process the article describes, when the author is available and can give hints.
  - shmageggy 11y ago
    What I understood from http://mathbabe.org/2015/12/15/notes-on-the-oxford-iut-workshop-by-brian-conrad/ http://mathbabe.org/2015/12/15/notes-on-the-oxford-iut-works... (posted elsewhere here), is that the problem stems from differing motivations. On one hand, Mochizuki wants to make his proof fullyt complete and correct (being both fully general and covering all special cases), but the community wants broad strokes intuitions. From Mochizuki's perspective, he has told everyone how things fit together, but fit together means something different for others. The workshop attendees want to know what things they can gloss over to get the big picture, but as of yet, nobody who understands the proof has succeeded in communicating that information, probably because they don't share the same motivation.
  - jsprogrammer 11y ago
    I did read the article. It wasn't clear that you were referring to that specific paragraph. > I mean, if the result of a 2008 paper is crucial, you'd think the guy would have just mentioned this fact. Maybe he did? Or maybe it is just not crucial.∎ The article just states "The link was immediately recognised as a crucial step in Mochizuki's grand strategy."...that is just the writer's opinion. Linking these papers to topology is trivial. The word "topological" alone occurs 111 times in the first paper. A lot of what I'm reading in this article, and others, is people complaining about not understanding something that they (probably/apparently) have not even read.

jug 11y ago

Personally I find this more mind boggling than that it can't be communicated easily. Clearly, a proof of 500 pages will be extremely difficult to verify or even understand. However... That a concept taking just a paragraph to explain* for people who know math requires a proof of over 500 pages. THAT is what I find mind boggling and I find hard to understand. That it can just balloon in size like that, especially given that mathematics is a language of logic. * https://en.wikipedia.org/wiki/Abc_conjecture https://en.wikipedia.org/wiki/Abc_conjecture

im2w1l 11y ago
The halting problem proves that mathematics is hard. There is no algorithm that can prove/disprove any decidable statement. Not even a a superslow algorithm. Maybe ballooning is related to that...