Nice article, definitely piqued my interest in the lambda calculus, but there were a few points that were confusing for me as my first glimpse at the lambda calculus.
The first confusing point was the lack of definition of the order of operations. I first stumbled at the line (λy.(λx. x) y) a b . Is this supposed to be (λy.(λx. x) y) (a b) or ((λy.(λx. x) y) a) b . In this case both give the same answer, but it's not obvious that associativity holds in general.
It gets worse with the Y combinator: λf. (λx. f (x x))(λx. f (x x)) . Is this (λf. (λx. f (x x)))(λx. f (x x)) or λf. ((λx. f (x x))(λx. f (x x))) . Peeking ahead, it seems to be the latter, which makes more sense (otherwise the letter f would be pressed into service in two different contexts), but it's totally ambiguous from the rules that have been presented in the article.
The other point of confusion was regarding rule #3 (If t and s are both valid λ-terms, then t s is a valid λ-term.) The article tells is a certain manipulation we can do if t is a "function" (i.e. something that begins with a λ, I don't know the technical name for this), but doesn't say what to do if t is not a "function". As far as I can tell the answer is: do nothing, there is no simplification in this case. It would be nice if this was said explicitly.
This interview with Robert Wilson is totally bonkers: https://youtu.be/sKFVorIvpAo?si=LbfQFK8-7OziqyUI&t=1322