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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

#151
post #121

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.

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

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

#152

Earlier quoted context omitted.

Yes but these will only accept proofs from within the mathematical framework of the multiple verifiers. I'm not saying that having 4 automatic independent verifications of a proof is useless, far from it! Just that, the notion you can "prove" all of mathematics is almost meaningless, or demonstrable false.

I'm not sure what your point is here. If the point is that the provers require a particular format, and not just English sentences, then that is true but not really a problem. Writing programs also requires that you use a particular format, AKA programming language, and that happens all the time. It's true that some things cannot be proven, due to Goedel's incompleteness theorems... but that is a fundamental limitati…

I was responding directly to:

"I don't really understand why the entire known mathematics is not automatically proven yet."

Which I believe is going to be related to English (or whatever natural language) if we really want to talk about what is meant by "entire known mathematics".

edit: I mean it's a crazy proposal, so you get a crazy response. I think somewhat intuitively we know you can't prove everything.

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

#153
The math community can't accept a new result is true without a good proof. As part of good, the proof has to be readable by peer reviewers. Net, if the writing is tough to read by some of the best qualified peers, then the writer has more work to do, in particular, to learn to write better.

We have lots of examples of good writing in math from Bourbaki, W. Rudin, P. Halmos, H. Royden, and more.

Sorry 'bout that: No one wants math to miss out on a great, new result, but the writer has to do their job first, in particular, do good math writing.

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

#154
post #81
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.

I participated in a discussion on /r/math about this a few months ago, and there was surprising resistance to ideas like this. Most of it fell into two categories. The first was people with a paper fetish who refuse to believe that there are now computer display technologies that provide adequate readability and resolution to be a full-time substitute for books. The second was people who can't imagine a usable way to…

Except... it's not a fetish. Paper books have many advantages. It is easily annotable. (none of the current ebook types are easy). It provides tactile feedback, which can be used for organization - folded corners give you two types of indices (top/bottom outer corner). The entire structure of the book as a stack of pages gives you immediate visual feedback where you are, and it's effectively random-addressable. ("Yeah, it's roughly a third in, check there"). Heck, you can color page edges to make it even easier, and that gives you three spatial indices on top of the two tactile ones. It's not as unwieldy as screens. It is flexible, which makes it nicer to handle. It doesn't need to be charged. It doesn't break when you drop it. (Not to mention you can kill a fly with a paper book, ebooks don't work)

Yes, e-books have other advantages - but calling it a paper fetish basically means you're making an uninformed call, because you're not even aware of the advantages.

The second, you could have easily addressed by proposing a markup if it were easy to do so. The fact that you haven't, and aren't even aware why people think it's hard, means you're again coming from an uninformed position.

And you thought the resistance was surprising?

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

#155
post #12

I have a MSc in mathematics so I am by no means an expert in mathematics proofs but I get the gist of it. To me a proof is literally a logical argument that you can follow to "believe" that a theorem is true. I do worry how many people actually understand or verify mathematics proofs. How many people have actually read and verified Perelman's or Wiles' proofs (I'm only singling them out because they're famous, not be…

Agree with this. Don't think there are too many mathematicians who can really argue for or against a really important theorem. My prof has come up with one for Riemann hypothesis[1], but he is not finding anyone willing to engage in a discussion. Most mathematicians seem to believe that the Riemann hypothesis is unsolvable and I don't think it helps that my prof is currently not associated with any reputable university. It's as if proofs can come from only reputable universities and reputable mathematicians.

[1]https://medium.com/@nutanc/the-final-and-exhaustive-proof-of...

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

#156
post #12

I have a MSc in mathematics so I am by no means an expert in mathematics proofs but I get the gist of it. To me a proof is literally a logical argument that you can follow to "believe" that a theorem is true. I do worry how many people actually understand or verify mathematics proofs. How many people have actually read and verified Perelman's or Wiles' proofs (I'm only singling them out because they're famous, not be…

You have an MSc in mathematics but don't consider yourself an expert?

Mathematics is this beautiful and terrifying field where, much like swimming in the Ocean, the further into it you get, the deeper and infinitely more vast it becomes. Now consider that most people can only really swim in one direction at once and this Ocean goes off in all directions.

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

#158

Earlier quoted context omitted.

people with a paper fetish who refuse to believe Maybe there was surprising resistance because you spoke like that?

Nah. I'm only using language that harsh now because of how disappointingly irrational and weak the objections on reddit were. It's odd to see mathematicians resistant to quantifying what they believe to be inferior about computer displays, and improperly generalizing what seemed to be their experience with $500 laptops to also argue against high-quality eInk, OLED and IPS LCDs.

a lot of mathematicians prefer chalkboards over whiteboards too, because 85% of all known whiteboard markers are nearly empty.

love of math and love of technology aren't as closely linked as you believe.

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

#159
post #155
post #12

I have a MSc in mathematics so I am by no means an expert in mathematics proofs but I get the gist of it. To me a proof is literally a logical argument that you can follow to "believe" that a theorem is true. I do worry how many people actually understand or verify mathematics proofs. How many people have actually read and verified Perelman's or Wiles' proofs (I'm only singling them out because they're famous, not be…

Agree with this. Don't think there are too many mathematicians who can really argue for or against a really important theorem. My prof has come up with one for Riemann hypothesis[1], but he is not finding anyone willing to engage in a discussion. Most mathematicians seem to believe that the Riemann hypothesis is unsolvable and I don't think it helps that my prof is currently not associated with any reputable universi…

It appears your professor's work has gotten the attention of at least one other researcher -- a Matthew Watkin at the University of Exeter. He seems to believe that it can be disproven by a student of analytic number theory [0].

[0]: https://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/RHpro...

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

#160
post #12

I have a MSc in mathematics so I am by no means an expert in mathematics proofs but I get the gist of it. To me a proof is literally a logical argument that you can follow to "believe" that a theorem is true. I do worry how many people actually understand or verify mathematics proofs. How many people have actually read and verified Perelman's or Wiles' proofs (I'm only singling them out because they're famous, not be…

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