5 ms·
This has been a long time coming. There is an infamous MathOverflow thread about the proof (also linked in the article), with the following comment summarizing
by spekcular 5y ago
This has been a long time coming. There is an infamous MathOverflow thread about the proof (also linked in the article), with the following comment summarizing the state of affairs ~10 years ago:
> There is no other evidence. In fact there is absolutely no evidence what so ever. I have never met a mathematician who could convince me that he or she understood Freedman`s proof. I attempted to read that monstrosity of a paper a number of times by myself and quite a few times with a group of other mathematicians. We never were able to finish checking all of the details. Such seminars always ended before we could make it through even half of his paper. No other expositions on the subject seem to be any better. It is truely an odd state of affairs that after all of these years no one has managed to write a clear exposition of this so called proof, and that no one seems to question the claim that there ever was a proof. I remember thinking as a young mathematician either this "proof" is sheer nonsense or someone will eventually write out a clear and detailed explanation. As of April of 2011 I have understood that the so called proof is full of errors and they can not be fixed. I mentioned this to several mathematicians during the summer of 2011 and I believe these conversations are directly linked to the dialogue seen here on math overflow.
Also on that thread, Brendan Guilfoyle raised the issue of writing a complete book-length treatment of the proof. I found the following response an interesting commentary on incentives in academia.
> Promotion committee: "What have you done in the last 5 years?"
> B.G.: "I've been writing a book about a paper published in 1982."
> Promotion committee: "How is that groundbreaking overachieving hyped research?"
> B.G.: "It is not, but I am preserving the knowledge of the elders."
> Promotion committee: "Who told you that was a good idea?"
> B.G.: "A guy on the internet, and 24 people liked his suggestion."
> Promotion committee: "We will call you, don't call us. Good bye."
- auntienomen 5y agoThat comment on incentives is funny, but I'm not sure it captures the situation here: The mathematicians who wrote The Disc Embedding Theorem have been quite successful. All are on the tenure ladder (or tenured already) and publishing novel research in a field they revitalized. I can see how sinking time into this is risky, but that's generally true of choosing a field of research. I think the authors deserve credit for doing it well. Likewise, Peter Teichner should get a little credit for helping to create the space for them to do so.
- spekcular 5y agoI agree, actually. I think a book published by a major academic press is a plus for any tenure/promotion committee. Further, this is definitely not just "expository" work; as the article notes, they had a bunch of gaps/errors to fix. I expect the importance of those contributions would be reflected in strong recommendation letters for promotion.
- agf 5y agoThread in question: https://mathoverflow.net/questions/87674/independent-evidence-for-the-classification-of-topological-4-manifolds https://mathoverflow.net/questions/87674/independent-evidenc...
- OGWhales 5y ago> (also linked in the article) Would never have seen that without your telling me. It was well hidden until you moused over it
- Koshkin 5y ago> what so ever I've always thought it was connected.
- est31 5y agoThis is more due to the inability of promotion committees to capture the usefulness of scientific work than due to the uselessness of this for science. Sure, if you have nothing else to show for yourself, it might be bad for your career. But I feel like people who work in academia already forego many career opportunities. That being said, you still need to put food onto the table. But posterity will remember you. Today, Bach is considered one of the most prolific musical composers of history. But back when he lived, he didn't receive that much fame. In fact, after his death, people forgot about him. And Bach lived in a time before copyright. He used existing themes by other people and rearranged them for the instruments he used. Many of those folks might have been famous back then, but now many their names are only known to historians (exceptions exist, e.g. Vivaldi).
- conistonwater 5y agoIt's worth noting that the consensus in the MathOverflow thread seems to have been that it was a complete waste of time to spend any further time on that paper and the proof. That's the opinion that they reached based on the general issues with the proof itself, and not any promotion committee decisions: specifically the fact that multiple mathematicians tried to read the paper in detail, in seminars, to understand it, and reported that they failed. That would certainly do it! I don't have an opinion myself on whether it was a mistake to spend more time on it, but you can clearly see professional mathematicians deciding not to work on something "important" for the legitimate reason that they thought it was unsalvageable. If that's correct, then a promotion committee should penalize people for doing it anyway.