41–50 of 74 posts
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 After you do the right thing, and translate Mochizuki's nomenclature into French and Slavic; the proof is no longer valid, and the problem is ne…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 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 After you do the right thing, and translate Mochizuki's nomenclature into French and Slavic; the proof is no longer valid, and the problem is ne…
BUT - how does that affect it from a purely scientific perspective? Is the quoted stolen material also incorrect? Because it would be equally bad, IMHO, to ignore an important and correct scientific finding just because it was produced in an unacceptable way.
If I exaggerate a bit, it's similar to someone experimenting on babies to discover a cure for AIDS - sure, they're a terrible person and should not receive praise/compensation for their discovery, their actions should be condemned. But should we also throw away the discovered cure?
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…
Earlier quoted context omitted.
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.…
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 mean people are really, really good at communicating. 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 auth…
Such omissions should be forbidden. Writing down the context in comments and in any other ways available should be a minimum requirement for any new code written. I do enjoy a good puzzle once in a while, but I don't want to reverse engineer someone's brain every time I read code. We should really focus more on helping other people understand the code we write. Some tools can help, but if the original author keeps most of the information to himself it's going to be really hard to follow the code.
Earlier quoted context omitted.
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?
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 applying all the rules of that system takes longer than a human mind is able to live (currently).
But that's just a practical limitation, not a theoretical one.
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.
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.
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…
Shame on you for bringing subjective issues into an objective issue.