New book about Freedman’s proof

Today I learnt from an article in the QuantaMagazine (link to article) that there is finally a new book trying to explain Freedman’s proof of the 4-dimensional Poincaré conjecture (link to book).

The article is fun to read since it contains statements of the involved people about how the whole ‘situation’ about the non-understandable write-up of the proof came to be.

I also want to mention (and comment) the following statements from the article in the QuantaMagazine:

  1. “Truth in mathematics means you convince the experts that your proof is correct. Then it becomes true,” said Teichner.
    • I know that this is true, but it bothers me a bit: It means, exaggerating, that the rest of us (the non-experts) do not matter.
  2. In that same 2019 interview Edwards explained that finally, he told the journal the proof was right, even though he knew he hadn’t had time to fully check it out. “The next time the secretary called I said ‘Yes, the paper is correct, I assure you. But I can’t generate a proper referee’s report any time soon.’ So they decided to accept and published it as it was,” he said.
    • So even back then in the 80s the journal & referee system was already unreliable. Unfortunately, it didn’t get better since then …