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Biggest mystery in mathematics in limbo after cryptic meeting

nature.com

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Re: Biggest mystery in mathematics in limbo after cryptic meeting

#61

Post by mturmon »

mipapage wrote: post #5
hgibbs wrote: post #4

Earlier quoted context omitted.

There is literally only a handful of mathematicians that are qualified and they have gone to Oxford to sort it out - bar mochizuki.

Yes, part of what I was trying to say is why not get that handful of folks together and go to Japan, to the source. Logistics? Ego? Funding? Perhaps a trip is in the cards...

There was an earlier workshop in Japan. From wiki:

"A workshop on IUT was held at RIMS [Japan] in March 2015 and in Beijing in July 2015. A CMI workshop on IUT theory of Mochizuki was held in December 2015 in Oxford, IUT-Oxford (2015). A workshop on IUT will be held in July 2016 at RIMS."

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#62

Post by im2w1l »

jug wrote: post #49
mmarx wrote: post #13

Earlier quoted context omitted.

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.

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 give…

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...

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#64

Post by guard-of-terra »

bhaak wrote: post #48
guard-of-terra wrote: post #36

Earlier quoted context omitted.

Okay. What if there's a lot of proofs, but the shortest of those is still not within reach of human intellect?

So far, we don't know if there are any proofs that are beyond the human intellect. I don't think that we currently believe such a thing to exist theoretically. Every provable conjecture should be understandable in principle by a generic human mind. Now, there for certain systems that are so complex that proofs within those systems are beyond us. Not because we couldn't understand them but because learning and applyin…

I'm talking about practical limitations. It turns out human exploration becomes impractical :(

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#66

Post by jsprogrammer »

logicallee wrote: post #40
jsprogrammer wrote: post #32

Earlier quoted context omitted.

The summary is known. Have you read the abstracts?

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 immed…

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.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#67

Post by dang »

williamjennings wrote: post #35

I just learned about Math 55 and would trade plenty to teach that course. The problem here is that Mochizuki uses too many German Nazi references. Those people had no academic integrity whatsoever; and their works are exclusively stolen, through war crimes and the Holocaust. After you do the right thing, and translate Mochizuki's nomenclature into French and Slavic; the proof is no longer valid, and the problem is ne…

We detached this subthread from https://news.ycombinator.com/item?id=10750422 and marked it off-topic.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#68

Post by bhaak »

guard-of-terra wrote: post #64
bhaak wrote: post #48

Earlier quoted context omitted.

So far, we don't know if there are any proofs that are beyond the human intellect. I don't think that we currently believe such a thing to exist theoretically. Every provable conjecture should be understandable in principle by a generic human mind. Now, there for certain systems that are so complex that proofs within those systems are beyond us. Not because we couldn't understand them but because learning and applyin…

I'm talking about practical limitations. It turns out human exploration becomes impractical :(

Practical limitations can be overcome.

At first it was artificial light sources, then glasses, then machines speeding up calculation and now machines that do calculations themselves.

There is certainly a practical limit of what a human mind can grasp but that limit is far away and with tools, it is even much farther.

We won't run out on difficult problems to solve anytime soon.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#69

Post by imh »

webkike wrote: post #29
moron4hire wrote: post #16

Earlier quoted context omitted.

Mathematics, being a human endeavor, is fundamentally about human interaction. There's no point to doing math if there is no communicating it to other people.

You can argue that everything can be reduced to human interaction, but mathematics is certainly not about human interaction in any meaningful sense

Math? No.

Math in the form of a research community which has built up centuries of work for each other to further build on? Absolutely.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#70

Post by williamjennings »

late2part wrote: post #41
williamjennings wrote: post #35

I just learned about Math 55 and would trade plenty to teach that course. The problem here is that Mochizuki uses too many German Nazi references. Those people had no academic integrity whatsoever; and their works are exclusively stolen, through war crimes and the Holocaust. After you do the right thing, and translate Mochizuki's nomenclature into French and Slavic; the proof is no longer valid, and the problem is ne…

I dont understand what you mean. Can you clarify?

Oswald Teichmüller stole technical documents from Felix Hausdorff and then published the written material in a Nazi pseudoscience journal, alongside racial propaganda.

It is therefore incorrect to cite Oswald Teichmüller, because his words are criminal plagiarism presented in an abhorrent context.

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