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Biggest mystery in mathematics in limbo after cryptic meeting

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Re: Biggest mystery in mathematics in limbo after cryptic meeting

#21

Post by raverbashing »

logicallee wrote: post #8

I don't understand how something, that anyone understands, can be this cryptic. Someone some time ago mentioned that all of Einstein's major papers on special and general relativitiy can be covered in a semester or two. Isn't the hard part discovering this stuff? How can anyone discover mathematical proofs but it is so impossible to communicate them that nobody in the world can follow your train of thought? I mean pe…

I agree

It's a bit obscurantist, to be honest.

While people make source code to be as clear as possible, mathematicians go the other way.

One idea would be to invert the proof, going top-down, instead of bottom up (in the explanation), then clearly dividing the subproofs instead of one big "wall of text" (yes, I know, there are numbered proofs/lemmas, but still it is not very well organized)

Edit: looking at the paper above it seems the author really tries to be helpful, the paper seems very organized (but it is long)

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#22

Post by erostrate »

guard-of-terra wrote: post #11

I guess we can now ask a lot of simple questions in math for whose there can be answer, but the solution itself is untenably long to be produced or understood by mere mortal, not a computer or computer-like individual. Same way as we can't really reason about inner workings of machine learning model that yields useful results. Talk about transhumanism.

I agree. More generally I have often wondered if pure mathematics (and theoretical physics [1]) will reach such a level of abstraction that it becomes impossible to digest all the established ideas in order to build on it. The mathematicians attending this workshop have an ability to manipulate extremely abstract concepts that is superior to the vast majority of humans, and even they can't seem to handle this proof.

[1] http://www.staff.science.uu.nl/~gadda001/goodtheorist/index....

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#23

Post by eveningcoffee »

moron4hire wrote: post #16
enewc wrote: post #15

Earlier quoted context omitted.

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.

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.

There's no point to doing math if there is no communicating it to other people.

I would not agree with that. One can do math for personal pleasure.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#24

Post by randomsearch »

bhaak wrote: post #18
guard-of-terra wrote: post #11

I guess we can now ask a lot of simple questions in math for whose there can be answer, but the solution itself is untenably long to be produced or understood by mere mortal, not a computer or computer-like individual. Same way as we can't really reason about inner workings of machine learning model that yields useful results. Talk about transhumanism.

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…

> As far as I understand it, a lot of the problem stems from the fact that Mochizuki is quite a hermit. And that's a problem if you want others to understand what you have done for years.

Interesting. Reinforces the idea that you should attend conferences and talk to others in your field, to ensure that you speak the same language and don't miss out on helpful advice or new tools that may (for instance) make a proof easier to follow.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#27

Post by OJFord »

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...

This was just one workshop that happened to be at Oxford. Probably it occurred the other way around to you imagine - "let's host a workshop here [at Oxford], what shall be the topic?"

Article says there is another one planned in Japan that will no doubt be attended by a (proper, less those put off!) subset of those at Oxford.

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#29

Post by webkike »

moron4hire wrote: post #16
enewc wrote: post #15

Earlier quoted context omitted.

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.

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

Re: Biggest mystery in mathematics in limbo after cryptic meeting

#30

Post by ilitirit »

IshKebab wrote: post #26
lelf wrote: post #19

If you don't follow how it came mathematicians have so much trouble with some papers: This is part I — http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20...

Jesus. This surely requires a computational proof.

It is essentially a communications problem. Brian Conrad summed it up:

For every subject I have ever understood in mathematics, there are instructive basic examples and concise arguments to illustrate what is the point to generally educated mathematicians. There is no reason that IUT should be any different, especially for the audience that was present at Oxford. Let me illustrate this with a short story. During one of the tea breaks I was chatting with a postdoc who works in analysis, and I mentioned sheaf theory as an example of a notion which may initially look like pointless abstract nonsense but actually allows for very efficient consideration of useful ideas which are rather cumbersome (or impossible) to contemplate in more concrete terms. Since that postdoc knew nothing about what can be done with sheaf theory, I told him about the use of sheaf cohomology to systematize and analyze the deRham theorem and topological obstructions to construction problems in complex analysis; within 20 minutes he understood the point and wanted to learn more. Nobody expects to grasp the main points of IUT within 20 minutes, but if someone says they understand a theory and does not provide instructive visibly relevant examples and concise arguments that clearly illustrate what is the point then they are not trying hard enough. Many are willing to work hard to understand what must be very deep and powerful ideas, but they need a clearer sense of the landscape before beginning their journey.

http://mathbabe.org/2015/12/15/notes-on-the-oxford-iut-works...

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