Suggestion to rely on AI for proof verification is just laughable. Neuron weights instead of formal definitions. So reliable.
Number theorist fears many proofs widely considered to be true are wrong
31–40 of 107 posts
Re: Number theorist fears many proofs widely considered to be true are wrong
#32Headline is waaaay overblown, but not all of it is total hyperbole -- checkout out arxiv and try to read the abstract from just about any paper. It's basically totally impermeable. I'm almost done with an undergraduate degree in math and basically have no idea what ~90% of the research is about at anything other than a topical level. This is fine, it's written for specialists in the field (hopefully), but damn, for m…
That doesn’t mean that it’s wrong, it means that you need to read more. In a lot of fields, undergraduate material doesn’t qualify you to read papers, a PhD does. If all papers actually were written to undergraduate level, many would be 500 pages long. Who has time to write a book-length exposition of the basics of their field every time they publish? I mean, have you ever published a technical work? If so, did you g…
The above statement is true with the assumption that the topic being discussed is truly above the level of understanding for undergraduates. For the majority of the papers, that assumption is not true though. Papers are hard to read has more to do with the idea that if it's not filled with jargons, its chance of getting published is greatly reduced.
Papers are not rewarded for being easy to understand. People/organizations get rewarded for publishing "complicate" papers. That misalignment is the issue.
Re: Number theorist fears many proofs widely considered to be true are wrong
#33I just can't help feeling that either the true should be correct, or the wrong should be false. But I guess English is not a strongly typed language.
Re: Number theorist fears many proofs widely considered to be true are wrong
#34Headline is waaaay overblown, but not all of it is total hyperbole -- checkout out arxiv and try to read the abstract from just about any paper. It's basically totally impermeable. I'm almost done with an undergraduate degree in math and basically have no idea what ~90% of the research is about at anything other than a topical level. This is fine, it's written for specialists in the field (hopefully), but damn, for m…
I did some undergraduate research and ended up getting published. My initial drafts were written with prose so that I (and hopefully any novice) could understand. However, my professor wasn’t happy with it so I got some help from one of his grad students to re-write it. By the end of it I could barely understand my own paper. IMO the final paper had too much technical jargon which was convoluting some simple concepts…
This is one of the reasons why I pursued engineering instead of a hard science. Mathematics in particular feels like an ivory tower with a bunch of gatekeeping.
Better language and grammar around core concepts could improve accessibility, but few in the field that I've encountered seem to care about that.
Biology and chemistry are a bit better, but there are still improvements that could be made. You can't easily go from zero to biochem or ochem, and I don't think that has to be the case. Gen chem and gen bio just suck at presenting themes and concepts and instead focus on being a smorgasbord of facts (that you later have to amend or unlearn).
Computer science and electrical engineering are a walk in the park by comparison. We have all sorts of interactive tools and visualizations of algorithms and analysis. We keep refining and making the onboarding process easier and more accessible.
Re: Number theorist fears many proofs widely considered to be true are wrong
#35Headline is waaaay overblown, but not all of it is total hyperbole -- checkout out arxiv and try to read the abstract from just about any paper. It's basically totally impermeable. I'm almost done with an undergraduate degree in math and basically have no idea what ~90% of the research is about at anything other than a topical level. This is fine, it's written for specialists in the field (hopefully), but damn, for m…
That doesn’t mean that it’s wrong, it means that you need to read more. In a lot of fields, undergraduate material doesn’t qualify you to read papers, a PhD does. If all papers actually were written to undergraduate level, many would be 500 pages long. Who has time to write a book-length exposition of the basics of their field every time they publish? I mean, have you ever published a technical work? If so, did you g…
A B.A. in math gets you to the forefront of mathematical research as it was circa 1912. (Source: https://slate.com/human-interest/2003/05/is-math-a-young-man...) This is purely my impression as somebody who switched away from pure math early in their career, but: amazingly, in pure math, unless you are really advanced, you are not even that close to engaging independently in cutting-edge research until well after your Ph.D. Math has been continuously researched by all the smartest people for hundreds of years (thousands, depending on how you view the dark ages). The low hanging fruit got gobbled up centuries ago. The same could be said for physics and various other "classical" scientific fields.
Re: Number theorist fears many proofs widely considered to be true are wrong
#36Headline is waaaay overblown, but not all of it is total hyperbole -- checkout out arxiv and try to read the abstract from just about any paper. It's basically totally impermeable. I'm almost done with an undergraduate degree in math and basically have no idea what ~90% of the research is about at anything other than a topical level. This is fine, it's written for specialists in the field (hopefully), but damn, for m…
That doesn’t mean that it’s wrong, it means that you need to read more. In a lot of fields, undergraduate material doesn’t qualify you to read papers, a PhD does. If all papers actually were written to undergraduate level, many would be 500 pages long. Who has time to write a book-length exposition of the basics of their field every time they publish? I mean, have you ever published a technical work? If so, did you g…
Suppose a narrow field where only two human beings can understand. How could the society judge the progress of the field or the merit of a new project? I don't think it is possible to avoid collusion or groupthink in such a field and it would be difficult to differentiate the two.
So does it mean we should curb some superhuman thinking and let them explain better to other human being? I'd think so. It is all about balance or trade-off, but at some point, a field would become too esoteric for a society and it might need to slow down the short-term progress to ensure consistent long-term progress.
It seems the math field as a whole (or more specifically the number theorists?) needs more of good communicators who can link the cutting edge and more general public. The math academia could give incentives to such activities in addition to pushing the boundaries.
Re: Number theorist fears many proofs widely considered to be true are wrong
#37"I believe that no human, alive or dead, knows all the details of the proof of Fermat’s Last Theorem. But the community accept the proof nonetheless," Buzzard wrote in a slide presentation[...] That s 100% clickbait. People knows the demonstration and the demonstration helped to create entire new fields. By the way there are new and shorter proof of the theorem.
Also, that is quite a remarkable and provocative statement given that Andrew Wiles is still very much alive.
Re: Number theorist fears many proofs widely considered to be true are wrong
#38Headline is waaaay overblown, but not all of it is total hyperbole -- checkout out arxiv and try to read the abstract from just about any paper. It's basically totally impermeable. I'm almost done with an undergraduate degree in math and basically have no idea what ~90% of the research is about at anything other than a topical level. This is fine, it's written for specialists in the field (hopefully), but damn, for m…
I did some undergraduate research and ended up getting published. My initial drafts were written with prose so that I (and hopefully any novice) could understand. However, my professor wasn’t happy with it so I got some help from one of his grad students to re-write it. By the end of it I could barely understand my own paper. IMO the final paper had too much technical jargon which was convoluting some simple concepts…
So I find this interesting, because it seems to confirm a suspicion I held. I "only" did some undergrad math during my computer science (but due to a lack of specialization at my university back then it was "real math", i.e. we took the same courses as the math students).
My impression often was that a lot of this stuff isn't so hard if you "get to it", but it's clouded in a lot of complicated language that makes it sound harder than it really is. I never dared to postulate that this is a more general problem of math, but your words sound like that's exactly what is happening.
Do you think there's a way forward to make math more accessible by using simpler language without sacrificing correctness?
Re: Number theorist fears many proofs widely considered to be true are wrong
#39Summary: Motherboard interviewed an attendee at the Interactive Theorem Proving conference who says that he thinks Interactive Theorem Proving is important. Also, professors specializing in proof theory think their tooling may become important but "the technology still needs improvement".
Re: Number theorist fears many proofs widely considered to be true are wrong
#40"I believe that no human, alive or dead, knows all the details of the proof of Fermat’s Last Theorem. But the community accept the proof nonetheless," Buzzard wrote in a slide presentation[...] That s 100% clickbait. People knows the demonstration and the demonstration helped to create entire new fields. By the way there are new and shorter proof of the theorem.
There’s a great discussion of this on Buzzard’s blog.
https://xenaproject.wordpress.com/2019/09/27/does-anyone-kno...
Read the comments too.