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So who gets credit for proving it? Freedman, the original author from 1981; or the authors of this book? If Freedman's proof has so many gaps, should it be co

So who gets credit for proving it? Freedman, the original author from 1981; or the authors of this book? If Freedman's proof has so many gaps, should it be considered more of a proof outline, or a motivation for believing a conjecture, and the current book be considered the actual proof? Or does Freedman get the glory? In that case, there's not much incentive for people to do what these book authors did. Which I suppose is why it took 30 years, and is only happening now because they "were captivated by the beauty of Freedman’s proof and wanted to give it new life. "

auntienomen 5y ago
It's not a strict exclusive-or choice. Credit will accrue to both Freedman and the authors of this book, because both advanced the state of the subject. And eventually perhaps further credit to someone who publishes a machine-verifiable proof, or finds a simpler way to understand the theorem.
pfortuny 5y ago
Well, thank God lots of scientists (mathematicians in this case) understand that transmission of knowledge is as important (or more so) as novelty. And that is their incentive.
- ChrisKnott 5y ago
  This distinction has been called an "open exposition problem", versus an "open research problem". Once Freedman's proof was accepted, it was no longer an open research problem; on the publication of this book, it will (hopefully) no longer be an open exposition problem. The phrase was coined by Timothy Chow in his paper A Beginner's Guide To Forcing [0]; > "All mathematicians are familiar with the concept of an open research problem. I propose the less familiar concept of an open exposition problem. Solving an open exposition problem means explaining a mathematical subject in a way that renders it totally perspicuous. Every step should be motivated and clear; ideally, students should feel that they could have arrived at the results themselves." [0] https://arxiv.org/abs/0712.1320 https://arxiv.org/abs/0712.1320
eigenket 5y ago
Freedman gets the credit for the bits of the proof that are his, the authors of this book get the credits for the novel stuff they add.
rPlayer6554 5y ago
According to a sister comment, the paper contains a meta-proof that shows that many of the gaps do not matter in showing the equivalence.[0] I don't know if this is true or not, I'm just connecting the discussions. [0] https://news.ycombinator.com/item?id=28473319 https://news.ycombinator.com/item?id=28473319
throwaway81523 5y ago
It's common for complicated proofs to have little gaps that got past the referees. The basic standard of whether the proof is valid is that if you do find a gap in the written version, the author can say "oh yeah, you can fix that by doing X", making some small patch. It's like finding a bug in a program that the author can fix right away once you file a bug report. If the author is unable to fix the bug despite a reasonable amount of effort, then there is a problem. You get credit if you can fix it where the author couldn't. Otherwise it's almost like trying to invalidate a proof over a misspelling. In the case of Wiles' proof of FLT, someone found a bug, Wiles worked unsuccessfully for something like a year trying to fix it, basically concluded that FLT was not really completely proved after all (i.e. he had "merely" made enormous progress, but not actually closed the ticket). Then right after more or less giving up, he and Richard Taylor figured out how to fix the bug, so it came out ok after all. Of course Taylor now gets a slice of the FLT credit.

auntienomen 5y ago

It's not a strict exclusive-or choice. Credit will accrue to both Freedman and the authors of this book, because both advanced the state of the subject. And eventually perhaps further credit to someone who publishes a machine-verifiable proof, or finds a simpler way to understand the theorem.

pfortuny 5y ago

Well, thank God lots of scientists (mathematicians in this case) understand that transmission of knowledge is as important (or more so) as novelty. And that is their incentive.

ChrisKnott 5y ago
This distinction has been called an "open exposition problem", versus an "open research problem". Once Freedman's proof was accepted, it was no longer an open research problem; on the publication of this book, it will (hopefully) no longer be an open exposition problem. The phrase was coined by Timothy Chow in his paper A Beginner's Guide To Forcing [0]; > "All mathematicians are familiar with the concept of an open research problem. I propose the less familiar concept of an open exposition problem. Solving an open exposition problem means explaining a mathematical subject in a way that renders it totally perspicuous. Every step should be motivated and clear; ideally, students should feel that they could have arrived at the results themselves." [0] https://arxiv.org/abs/0712.1320 https://arxiv.org/abs/0712.1320

eigenket 5y ago

Freedman gets the credit for the bits of the proof that are his, the authors of this book get the credits for the novel stuff they add.

rPlayer6554 5y ago

According to a sister comment, the paper contains a meta-proof that shows that many of the gaps do not matter in showing the equivalence.[0] I don't know if this is true or not, I'm just connecting the discussions. [0] https://news.ycombinator.com/item?id=28473319 https://news.ycombinator.com/item?id=28473319

throwaway81523 5y ago

It's common for complicated proofs to have little gaps that got past the referees. The basic standard of whether the proof is valid is that if you do find a gap in the written version, the author can say "oh yeah, you can fix that by doing X", making some small patch. It's like finding a bug in a program that the author can fix right away once you file a bug report. If the author is unable to fix the bug despite a reasonable amount of effort, then there is a problem. You get credit if you can fix it where the author couldn't. Otherwise it's almost like trying to invalidate a proof over a misspelling. In the case of Wiles' proof of FLT, someone found a bug, Wiles worked unsuccessfully for something like a year trying to fix it, basically concluded that FLT was not really completely proved after all (i.e. he had "merely" made enormous progress, but not actually closed the ticket). Then right after more or less giving up, he and Richard Taylor figured out how to fix the bug, so it came out ok after all. Of course Taylor now gets a slice of the FLT credit.