Gerry Myerson wrote: > In article <firstname.lastname@example.org>, > "Gene Ward Smith" <email@example.com> wrote: > > >>Gerry Myerson wrote: >> >> >>>I personally don't put set theory in the same category as astrology >>>or creation science. Maybe Norm does. I don't know. >> >>Norm apparently puts number theory in that category. > > > For what it's worth, Norm has written papers in number theory, > e.g., > > MR1314396 (96a:11029) Wildberger, N. J. Row-reduction and invariants of > Diophantine equations. Proc. Indian Acad. Sci. Math. Sci. 104 (1994), > no. 3, 549--555. > > Whether this was before he came to his current views on set theory, > I do not know.
This affirms what I felt about the OP, that while his views are unpopular, he is not a crank. (I also just checked him out on MathSciNet, and it is obvious that he is an active research mathematician.) In my opinion, his remarks about the natural numbers are spot on. The only way I disagree with him is that I don't think that now is the time to work on these problems.
This whole thread has left a bad taste in my mouth because of the speed at which people were willing to spew abuse on him. Just because he has a superficial resemblence to crankpot anti-Cantorians doesn't make him one. His views are controversial, but that doesn't mean we respond rudely, rather it gives us an opportunity to engage in civilized conversation. Even if we end up still disagreeing, we might have learned something, or at least honed our arguments better.
Now, one of the respondents said that Norm had rejected the axiom of infinity, and so how is he supposed to do number theory. But nowhere in his article has he rejected the axiom of infinity. He has rejected the whole notion that axioms are the way to go. I would paraphrase what he said slightly differently - axioms (might) describe the natural numbers, but they don't define them. There is clearly a problem that there are numbers between 1 and googolplex that we can never write down or meaningfully describe. What makes us think that they are really there? The evidence is at best empirical.
The responses have led me to think that some people here believe in the modern axiomatic system like a religion.