New math book rescues landmark topology proof

And cheers to Quantum Magazine for regularly publishing popularizations of research mathematics. I know many, at times, take issue with their simplifications and framing, but they’re trying, where almost no one else with their reach covers these areas at all.

> 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."