Fun fact. Max Zorn was at Indiana University when I was a grad student there in the '80s. He hated to be known for Zorn's Lemma instead of the other work he did. He thought that was just a fairly trivial observation.
Hah. Only on HN does one mention a pseudorandom mathematician, then run into someone who was a student in their department 35-40 years ago lol....
You know how the joke goes, right? “The axiom of choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn’s lemma?” [0]
I'm honestly not sure I could have resisted the temptation to ask him "What's yellow and equivalent to the axiom of choice?"[1] one day.
Okay, nevermind. I would have resisted, but I'd be chuckling about it off and on the whole time when I was sure he wasn't around, while I was doing my degree.
In all seriousness, though, proving the equivalence of AC, ZL, and WO was probably my first venture into "real" abstract mathematics in undergrad. For essentially the first time, there was no picture I could draw that would have any semblance of accuracy or utility, and yet at the end, the result popped right out just the same.
Unfortunately, I didn't make it to the independence of the Continuum Hypothesis that year, and had to move on to other courses. :/
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[0]: AC, ZL, and WO are also equivalent to the Hausdorf maximal principle: in any poset (P, ≤), every totally ordered subset S is contained in some maximal totally ordered subset T. In some ways, HM is kind of the "dual" of ZL by swapping totally ordered subsets for elements, ⊆ for ≤, and push the whole thing up into the power set realm, I think you just get ZL trivially. Of course, I always found HMP much more intuitive than ZL... basically, AC > HM > ZL > WO in my mind, in descending order of intuitiveness.
I never met Paul Cohen, but he started out in my field, analysis, not logic. When he realized he would not make it to the top he started looking around for easier pickings. He came up with "forcing" that applies ideas from game theory.
When I visited IU in the '90's there was a new stoplight on E 3rd. Max got hit by a car when trundling into his office every day in Swain Hall East and his colleagues somehow convinced the city of Bloomington to put one up.
While misspending my youth playing 5-minute chess at Bear's Place up the street, Raymond Smullyan showed up and asked if he could kibitz. I can write a very short book titled "What is the Answer to that Question?" It would be much shorter than https://www.amazon.com/Million-Zeros-Douglas-Crockford/dp/19.... Bjarne told me the guy had gone crazy. He is right.
I actually picked up a copy of Cohen's book [0] on CH a few weeks ago. It's in my "actually going to read this" pile right now. Looks pretty accessible, even for an ersatz graph theorist/combinatorialist such as myself.
