11–20 of 74 posts
Same way as we can't really reason about inner workings of machine learning model that yields useful results.
Talk about transhumanism.
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 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…
On my experience, people are usually really bad at communicating. It requires additional effort to imagine what information might be required for somebody else to follow your train of thought. Think of code documentation: What the original author percieves as obvious is cryptic to somebody else because context has been omitted for the sake of brevity. The author needs to invest a lot of time to actually dump his entire mindstate into documentation. Even if he does make an effort, not everybody is a good writer. If he doesn't care about others understanding his stuff (which also seems to be the case with Mochizuki) it gets even worse.
Also remember that Mochizuki basically worked alone on his stuff for 20 odd years. He built his own world to work in and it's just as hard for collegues to catch up to his level in that world as it is for e.g. non-programmers to understand programming (which takes years).
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…
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.
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…
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.
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.
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.
This workshop was crucial that it showed several people that trying to understand the proof could be a worthwhile task.
This is part I — http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20...
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…