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Number theorist fears many proofs widely considered to be true are wrong

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Re: Number theorist fears many proofs widely considered to be true are wrong

#21

Post by hgtr »

Hasz wrote: post #9

Headline 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. Kinda made me disenchanted with the academic world. Still have to give credit to my prof and the grad student, without their edits it probably wouldn’t have been published.

Re: Number theorist fears many proofs widely considered to be true are wrong

#22

Post by enjoyyourlife »

colorincorrect wrote: post #19

This short pdf which the article cites is more useful than anything the article itself contains: http://wwwf.imperial.ac.uk/~buzzard/one_off_lectures/msr.pdf

Discussion: https://news.ycombinator.com/item?id=20909404

Re: Number theorist fears many proofs widely considered to be true are wrong

#23

Post by hiphop »

Hasz wrote: post #9

Headline 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'm almost done with an undergraduate degree in math and basically have no idea what ~90% of the research is about

Find a grad student who are just about done with their studies in, say, analysis and the odds are they understand jacksquat about anything in current research in Number Theory either.

This post is in support of your point :)

Re: Number theorist fears many proofs widely considered to be true are wrong

#24

Post by lidHanteyk »

breck wrote: post #12

Anyone interested in this topic, I have a prediction that the time is right for a new math, that starts from just 1 and 0, and builds every symbol up in a rigorous way. We're working on the infrastructure to make such a thing easier, but the project does not currently have a leader: https://github.com/treenotation/jtree/issues/83

Disregard cranks, acquire Metamath: http://us.metamath.org/downloads/metamath.pdf

Re: Number theorist fears many proofs widely considered to be true are wrong

#25

Post by knzhou »

Hasz wrote: post #9

Headline 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 go out of your way to make it completely accessible to high schoolers? If you didn’t, you get why professors don’t do the same for undergrads.

Re: Number theorist fears many proofs widely considered to be true are wrong

#26

Post by parsimo2010 »

asaph wrote: post #17
ummonk wrote: post #15

Extreme clickbait headline. The subheading is '"I think there is a non-zero chance that some of our great castles are built on sand," he said, arguing that we must begin to rely on AI to verify proofs.'

But, more consistent with the alarmist headline: > “I’m suddenly concerned that all of published math is wrong because mathematicians are not checking the details, and I’ve seen them wrong before,” Buzzard told Motherboard while he was attending the 10th Interactive Theorem Proving conference in Portland, Oregon, where he gave the opening talk.

Someone who says that is, ironically, not concerned with the details. All of published math is wrong? No, a lot of is is understandable and verifiable by advanced undergraduates.

Most of the fundamental theorems in each field are understandable by humans. As you get more and more abstract, and get into more and more obscure areas, you start to see non-understandable proofs built on top of non-understandable proofs. There's a danger that those are wrong, but when they collapse it just means that one professor has wasted their life, not that all of mathematics will suddenly collapse.

Re: Number theorist fears many proofs widely considered to be true are wrong

#27

Post by kevinzz »

kurlberg wrote: post #11
gowld wrote: post #3

Headline is of course absurd hyperbole that does not belong here. > "I think there is a non-zero chance that some of our great castles are built on sand," Buzzard wrote in a slide presentation. "But I think it's small."

Well, they also quote him as saying: "I’m suddenly concerned that all of published math is wrong because mathematicians are not checking the details, and I’ve seen them wrong before,”

https://xenaproject.wordpress.com/2019/09/27/does-anyone-kno...

Re: Number theorist fears many proofs widely considered to be true are wrong

#28

Post by Ceezy »

"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.

Re: Number theorist fears many proofs widely considered to be true are wrong

#29

Post by dang »

ummonk wrote: post #15

Extreme clickbait headline. The subheading is '"I think there is a non-zero chance that some of our great castles are built on sand," he said, arguing that we must begin to rely on AI to verify proofs.'

We've replaced that with a more measured sentence from the article, in accordance with the HN guidelines ("Please use the original title, unless it is misleading or linkbait")

https://news.ycombinator.com/newsguidelines.html

Re: Number theorist fears many proofs widely considered to be true are wrong

#30

Post by madez »

I'm currently working on the formalization of Catalan's conjecture (or Mihăilescu's theorem) in Isabelle/HOL/Isar.

My personal impression is that more formal verification is necessary in math, and it should be tought to every student of Mathematics in introductionary courses because it gives an unforgiving but also rewarding learning experience with formal proofs.

Feel free to ask questions.

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