>He won't accept sqrt(2) as a number because it can't be represented in Hindu-Arabic notation.
You sure of that? Based on another of his other blog posts [1], his objection seems to be about uncomputable real numbers. Very roughly, a real number R is computable iff there exists a Turing machine that, given a natural number n on its initial tape, terminates with the nth digit of R. See [2] for a formal definition. Sqrt(2) and all familiar real numbers are computable. Of course, since there is only a countable infinity of Turing machines, but an uncountable infinity of reals, some reals must be uncomputable. Some versions of constructivist mathematics do differ from standard mathematics by rejecting the uncomputable reals and instead defining "real numbers" in such a way that they are essentially the computable reals.
Yeah, pretty confident. He doesn't like the computable or uncomputable reals; although I suspect he would like the uncomputables less.
Eg, "These phoney real numbers that most of my colleagues pretend to deal with on a daily basis ... such as sqrt(2), and pi, and Euler’s number e." [0]
Even in the article you cite, the irony of a pure mathematician of all people complaining that a concept has no tangible link to reality is a bit of a give away that he is speaking from the heart rather than the head. That isn't a valid complaint about pure mathematics; the point is patterns for patterns sake. So what if there are no known examples of your pattern? Study it anyway!
Great case of the flaw maketh the masterpiece; apart from that one little quirk with infinite things he is a lovely character and a force to be reckoned with. And I expect his personality motivates a lot of interesting research from him regardless.
You sure of that? Based on another of his other blog posts [1], his objection seems to be about uncomputable real numbers. Very roughly, a real number R is computable iff there exists a Turing machine that, given a natural number n on its initial tape, terminates with the nth digit of R. See [2] for a formal definition. Sqrt(2) and all familiar real numbers are computable. Of course, since there is only a countable infinity of Turing machines, but an uncountable infinity of reals, some reals must be uncomputable. Some versions of constructivist mathematics do differ from standard mathematics by rejecting the uncomputable reals and instead defining "real numbers" in such a way that they are essentially the computable reals.
[1] https://njwildberger.com/2016/01/01/uncomputable-decimals-an...
[2] https://en.wikipedia.org/wiki/Computable_number#Formal_defin...