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Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

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Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#241

Post by WilliamEdward »

ssmmww wrote: post #121
WilliamEdward wrote: post #49

Earlier quoted context omitted.

see: monty hall problem But anyway, mathematics is not any more unhealthy than any other field, but it does have toxicity like all others do as well.

My understanding is that the Monty Hall problem was just a cute puzzle published in a pop-sci magazine that confused a few professors who perhaps ought not to have been confused by it. I don't think it says anything at all about the health of the mathematical community.

Your understanding of the history of the problem is lacking and you've caused me to get downvoted as a result, thanks for that. The professors were misogynistic towards her as they could not believe a woman could solve this problem. She even addressed this.

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#242

Post by mannykannot »

Jweb_Guru wrote: post #231
Retra wrote: post #169

Earlier quoted context omitted.

The painful part is that you're using tools which are trying to bridge between wildly different logical foundations. Just because a computer beeps and says "proof correct" doesn't mean you've proven what you thought you have, so we need to first translate the logic in which your assumptions are derived into the logic of the machine. That is a complex and subtle project. In other words, it's actually very easy to prov…

Oh, come on. "It's not any easier than writing a bug-free program" is not even remotely true. Getting the spec right is way easier than getting the implementation right, in almost all cases. And the logic isn't that different from set theory--there's even a set theoretic model (which you get when you use Prop, to which you can add classical axioms).

If getting the spec right is way easier than getting the implementation right, then strict waterfall would be the most effective way to write programs, and the holy grail of software engineering would be to automate the process of generating implementations from formal specs (there are some people who think exactly that, but that has been the case for about five decades, with effectively no impact on how software is actually made.)

The reality is that we often overlook issues with the spec until we try to implement it, or try using what we have implemented, even when we are trying to get the spec right first.

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#243

Post by wolfgke »

ur-whale wrote: post #211
auntienomen wrote: post #126

Earlier quoted context omitted.

Two points: 1) Mathematicians write all over the papers and books they read. Electronic versions of this exist (e.g., Xournal, written by a well known mathematician), but they tend not to be as convenient as simply scribbling on paper. 2) Mathematicians digest papers nonlinearly. Digital presentations don't usually lend themselves to flipping back and forth between pages. At times, I suspect mathematicians use papers…

> Mathematicians digest papers nonlinearly. That's a fairly weak argument: you can browse an electronic document in a non-linear fashion way easier than a book. And also: books don't have CTRL-F

> That's a fairly weak argument: you can browse an electronic document in a non-linear fashion way easier than a book.

How do I make handwritten side notes? How can I create a bookmark for a specific page? How can I view multiple non-contiguous pages next to each other? How can I reference a specific part in an electronic text (in non-electronic text "3rd paragraph on page 11") and send it to a collaborator?

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#244

Post by mannykannot »

rocqua wrote: post #105
mrob wrote: post #57

Earlier quoted context omitted.

Why can't textbooks use code-folding style display to hide unwanted detail? Paper books are basically obsolete except as a master copy for archival.

In all of my papers, I have attempted to include an indent-based hierarchy of the argument. Adding code-folding to this would allow for so much more detail here. I don't think we should have papers being nothing but folds, but there is definite value in presenting proofs in this way. One potential downside is that there is no longer an order that guides the reader through the paper. Because it isn't quite clear how d…

I think the idea is that you go deeper only if you are stuck or unsure about something at your current level.

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#245

Post by mannykannot »

fjsolwmv wrote: post #151
ssmmww wrote: post #121

Earlier quoted context omitted.

My understanding is that the Monty Hall problem was just a cute puzzle published in a pop-sci magazine that confused a few professors who perhaps ought not to have been confused by it. I don't think it says anything at all about the health of the mathematical community.

It was also ambiguously worded, which is the bane of probability problems posed by people who think they are clever (like vos Savant).

I will repeat what I wrote about this point a couple of weeks ago: According to vos Savant, in most of the cases where the correspondent actually had a correction to offer for her alleged error, they were assuming the intended interpretation of the puzzle.

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#246

Post by mannykannot »

jim777 wrote: post #6

> When he told colleagues the nature of Scholze and Stix’s objections, he wrote, his descriptions “were met with a remarkably unanimous response of utter astonishment and even disbelief (at times accompanied by bouts of laughter!) that such manifestly erroneous misunderstandings could have occurred.” Is this normal in advanced Math or is this guy kind of a jerk?

If the objections really were founded on a basic misunderstanding, then one would expect a straightforward clarification to be forthcoming (where 'straightforward' should be read in the context of the formidable mathematical abilities of the parties to this dispute.) Its absence suggests that this is bluster (though that interpretation is made through the filter of my western/English-speaking cultural background.)

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#247

Post by ur-whale »

wolfgke wrote: post #243
ur-whale wrote: post #211

Earlier quoted context omitted.

> Mathematicians digest papers nonlinearly. That's a fairly weak argument: you can browse an electronic document in a non-linear fashion way easier than a book. And also: books don't have CTRL-F

> That's a fairly weak argument: you can browse an electronic document in a non-linear fashion way easier than a book. How do I make handwritten side notes? How can I create a bookmark for a specific page? How can I view multiple non-contiguous pages next to each other? How can I reference a specific part in an electronic text (in non-electronic text "3rd paragraph on page 11") and send it to a collaborator?

I was specifically addressing the "non-linear" part, and none of the things you list have anything to do with that.

However, to nevertheless address your points:

>How do I make handwritten side notes

There is a number of applications to do this (e.g. xournal), and when combined with a touchscreen on a decent hirez modern device, we're getting close to what paper can do. I'll grant you: this is still the weak point of computers as compared to pen and paper (especially for scribbling diagrams), but it won't be for long.

>How can I create a bookmark for a specific page

I'm not sure if you're trolling here, all e-book readers I've used have this feature.

>How can I view multiple non-contiguous pages next to each other?

Multiple windows ? CTRL+N ?

>How can I reference a specific part in an electronic text (in non-electronic text "3rd paragraph on page 11") and send it to a collaborator?

Cut and paste?

Or ... sending him an email with ""3rd paragraph on page 11"" in the body?

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#248

Post by gspetr »

wolfgke wrote: post #243
ur-whale wrote: post #211

Earlier quoted context omitted.

> Mathematicians digest papers nonlinearly. That's a fairly weak argument: you can browse an electronic document in a non-linear fashion way easier than a book. And also: books don't have CTRL-F

> That's a fairly weak argument: you can browse an electronic document in a non-linear fashion way easier than a book. How do I make handwritten side notes? How can I create a bookmark for a specific page? How can I view multiple non-contiguous pages next to each other? How can I reference a specific part in an electronic text (in non-electronic text "3rd paragraph on page 11") and send it to a collaborator?

I think if you reframe the problem it can be much easier (if not trivial) to find solutions.

If you present a 100 page book as a folder of 100 image files instead, most of these become image manipulation problems:

>How do I make handwritten side notes?

The same way you'd edit an image.

> How can I create a bookmark for a specific page?

Create a subdirectory with the page or a link to the page.

> How can I reference a specific part in an electronic text (in non-electronic text "3rd paragraph on page 11")

Cut and paste the excerpt into a new image file.

> and send it to a collaborator?

File sharing is a solved problem. Hell, you can even share it on Instagram if you so choose.

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#249

Post by cycrutchfield »

cxseven wrote: post #176
cycrutchfield wrote: post #26

Earlier quoted context omitted.

Per Peter Scholze (from https://galoisrepresentations.wordpress.com/2017/12/17/the-a... ): >One final point: I get very annoyed by all references to computer-verification (that came up not on this blog, but elsewhere on the internet in discussions of Mochizuki’s work). The computer will not be able to make sense of this step either. The comparison to the Kepler conjecture, say, is entirely misguided: In that case, th…

For the Kepler Conjecture, human mathematicians first found a way to show that it could be proved by checking a finite (but long) list of computer-verifiable claims. Here Scholze is saying that part of the proof simply hasn't been written, so there's nothing to verify. I think he's missing that computer verification proponents are also aware of that and are either 1. trying to motivate the camp that claims to underst…

It took like a decade to produce a computer verified proof for the Kepler Conjecture. And that was just for a relatively well-defined exhaustive search. That sounds like a molehill compared to Mochizuki’s Everest of a proof.

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#250

Post by lacker »

mrob wrote: post #205
lacker wrote: post #177

Earlier quoted context omitted.

I don't really understand why the entire known mathematics is not automatically proven yet. I think the problem is that this would be a significant amount of programming and data entry work, and there's no incentive for anyone to put in this work. There are many important math papers that are written at a level that is enough for a human math professor to understand, but not for a symbolic mathematics program to unde…

Formal proofs increase trust in mathematics. E.g. Fermat's Last Theorem is supposedly true, but I can't understand the proof. I have to trust the mathematicians who say the proof is correct, and I know that in other fields (most notably with the replication crisis in psychology) people accepted things as true when they weren't. If I had a formal proof I could run it through a theorem checker and see that it was corre…

But who is demanding this sort of increased trust in abstract mathematics? Mathematicians don't seem to be demanding it, as this sort of work/research is not in high demand for publications. Non-mathematicians don't seem to be demanding it, because this sort of mathematics doesn't yet have much application outside of mathematics.
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