Biggest mystery in mathematics in limbo after cryptic meeting • Hacker News Board

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#31

Post by bhaak » Thu, Dec 17, 2015, 11:44 AM UTC

guard-of-terra wrote: post #20

bhaak wrote: post #18

Earlier quoted context omitted.

Just because his proof is long, convoluted, and cryptic doesn't mean that there won't be a simpler proof down the road. Maybe some of the tools just haven't been developed yet. Look for example at how the Greeks and Romans struggled with mathematical problems many of which are today easily solvable in high school because we have advanced techniques and a positional notation for numbers. As far as I understand it, a l…

What if there won't be? What if, for many of questions, the only proof is as decipherable as MD5 of question?

That's probably highly improbable. Look at how many different proofs the are for the pythagorean theorem: http://www.cut-the-knot.org/pythagoras/

I'm not mathematician but I guess if there is really only one possible proof for a given question (Gödel might have proven that this is impossible but I don't know for sure), then the question isn't actually an interesting one. Because this would mean that the question touches only very few topics.

But the abc conjecture is interesting because it has lots of links with deep questions in number theory.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#32

Post by jsprogrammer » Thu, Dec 17, 2015, 11:49 AM UTC

logicallee wrote: post #17

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.

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.

The summary is known. Have you read the abstracts?

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#33

Post by MrQuincle » Thu, Dec 17, 2015, 12:07 PM UTC

enewc wrote: post #15

ryporter wrote: post #12

I view some of these math researchers like startup founders who are absolutely brilliant technically, but who lack almost all ability to interact with customers, investors, etc. As a solo founder, they will fail. However, if they attract a co-founder who complements their skills, they can be wildly successful. It sounds like Mochizuki would have benefited greatly from such a co-author, in order to truly prove his res…

Math is objective. The proof is either correct or not. Human interaction doesn't matter, except for perhaps marketing the importance of the results. In this case, the history of the problem itself has done the marketing, so any valid solution would be a wild success regardless of how socially eccentric the researcher is. Another recent example of such a mathematician is Grigori Perelman.

If the proof cannot be understood, it might very well be the case that another researcher more concerned with advancing knowledge for us all, will be credited. There are many roads to Rome.

Proofs that cannot be grasped are like unproven truths. Worth very little... They only stand through the credibility of the inventor. It downgrades the mathematician to a politician.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#34

Post by chriswarbo » Thu, Dec 17, 2015, 12:14 PM UTC

enewc wrote: post #15

ryporter wrote: post #12

I view some of these math researchers like startup founders who are absolutely brilliant technically, but who lack almost all ability to interact with customers, investors, etc. As a solo founder, they will fail. However, if they attract a co-founder who complements their skills, they can be wildly successful. It sounds like Mochizuki would have benefited greatly from such a co-author, in order to truly prove his res…

Math is objective. The proof is either correct or not. Human interaction doesn't matter, except for perhaps marketing the importance of the results. In this case, the history of the problem itself has done the marketing, so any valid solution would be a wild success regardless of how socially eccentric the researcher is. Another recent example of such a mathematician is Grigori Perelman.

The proof is a human interaction: it is a series of papers written by one person to transmit their ideas to other people.

If it were a giant Coq term then sure, you can ignore those pesky details like "understandability".

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#35

Post by williamjennings » Thu, Dec 17, 2015, 12:15 PM UTC

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 negligible.

For the record, Oswald Teichmüller is a fraudulent Nazi war criminal who robbed Felix Hausdorff during the Holocaust.

The undeniable fact that Oswald Teichmüller is solely published in a journal of racial propaganda makes Mochizuki's choice of terminology questionable at the very least.

The fact that I am being suppressed for this demonstrates unambiguously that Mochizuki's proof is nothing more than media hype and puffery.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#36

Post by guard-of-terra » Thu, Dec 17, 2015, 12:27 PM UTC

bhaak wrote: post #31

guard-of-terra wrote: post #20

Earlier quoted context omitted.

What if there won't be? What if, for many of questions, the only proof is as decipherable as MD5 of question?

That's probably highly improbable. Look at how many different proofs the are for the pythagorean theorem: http://www.cut-the-knot.org/pythagoras/ I'm not mathematician but I guess if there is really only one possible proof for a given question (Gödel might have proven that this is impossible but I don't know for sure), then the question isn't actually an interesting one. Because this would mean that the question touc…

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

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#37

Post by [deleted] » Thu, Dec 17, 2015, 12:27 PM UTC

bhaak wrote: post #31

guard-of-terra wrote: post #20

Earlier quoted context omitted.

What if there won't be? What if, for many of questions, the only proof is as decipherable as MD5 of question?

That's probably highly improbable. Look at how many different proofs the are for the pythagorean theorem: http://www.cut-the-knot.org/pythagoras/ I'm not mathematician but I guess if there is really only one possible proof for a given question (Gödel might have proven that this is impossible but I don't know for sure), then the question isn't actually an interesting one. Because this would mean that the question touc…

[deleted]

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#38

Post by Al-Khwarizmi » Thu, Dec 17, 2015, 12:34 PM UTC

zbyszek wrote: post #7

mipapage wrote: post #2

I remember at university how, when attending the few multi-disciplinary meetings or get-togethers, I would marvel that these people - on the same campus! - didn't get together more often in order to share and stimulate growth or share strategies, which inevitably occurred during these meetings. I wonder why a handful of qualified mathematicians couldn't get together and go to Japan to sort this proof out...

Having worked in a university mathematics department I noticed that the pure mathematicians tended to keep themselves to themselves, for instance not attending talks by visiting mathematicians unless it was of direct relevance to their research. In contrast, we theoretical physicists would listen to any visiting speaker just for fun - even on occasion experimental particle physicists, applied mathematicians or comput…

I think it's probably because it's very difficult to understand a pure math talk if you didn't already have significant understanding of the subject before the talk.

I don't work on pure mathematics, but I work in a field of computer science where there is both theoretical and empirical/applied research, and I do, and enjoy doing, both.

However, when it comes to attending talks, I do go to a lot of talks on empirical subjects just for fun, but I hardly ever go to a highly theoretical talk for fun. I only do that if the talk is highly related to the specific work I do; if you see me in a theoretical talk otherwise, it's probably just for social compromise.

The reason is that I can perfectly understand the gist of an empirical paper in 20 or 30 minutes, where there is no way I will understand a piece of theoretical research by listening to a talk if I haven't gone through the paper carefully before (and if you have done that, there is often no point in going to the talk anyway). Honestly I think the talk format doesn't lend itself too well to highly theoretical work. I have learned a lot about empirical research and obtained many useful ideas from talks, but in the theoretical field, the useful ideas and insights I got from talks are few and far between, and I would probably have obtained them more efficiently from reading papers anyway...

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#39

Post by moron4hire » Thu, Dec 17, 2015, 12:38 PM UTC

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

It's the only pure way to describe existence. That isn't meaningful? Mathematics is a language, first and foremost. To argue otherwise is to fundamentally misunderstand its goals, methods, and form.

You can draw all the squiggly lines on paper that you want, but it won't mean anything until someone else interpets it. You cannot prove logic that only exists in your own head, because you cannot prove yourself rational. Your very existence does not even make sense without other people perceiving you.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#40

Post by logicallee » Thu, Dec 17, 2015, 1:07 PM UTC

jsprogrammer wrote: post #32

logicallee wrote: post #17

Earlier quoted context omitted.

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.

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 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.