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.
Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
151–160 of 275 posts
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#152Earlier 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 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
#153We 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
#154Earlier 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…
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
#155I 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…
[1]https://medium.com/@nutanc/the-final-and-exhaustive-proof-of...
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#156I 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?
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#157Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#158Earlier 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.
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
#159I 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…
[0]: https://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/RHpro...
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#160I 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…