Παρασκευή, 4 Ιουνίου 2010

What is mathematics?

Recently, I read in a certain forum the idea that mathematics should be identified with ZFS. Another idea discussed in the same forum is the idea that mathematics is a closed "thing". IMHO, both ideas are problematic. First of all, ZFS is one formalization of set theory, yet it is not sure whether sets are the most fundamental entity. Indeed, Mac Lane put forth the idea that categories are more fundamental than sets. Thus, it is not sure whether there is an "atom", in the sense of Democritus's atomic theory, in mathematics. The closeness of mathematics is one more absurd idea that seems to stem from finitism, which, in turn, has its root to intuitionism. Although, intuitionism was instrumental in development of certain ideas, especially in computer science, still I believe its ideas are not generally applicable. As a matter of fact, I am convinced that hypercomputation and intuitionism refute each other. Back to the closeness of mathematics. I had always the idea that, for example, complex numbers are a "proof" that mathematics is expandable. Are there any limits? No, of course not because if there are linits, then, in the end, mathematics is closed!

A "Solution" to Riemann Hypothesis

Riemann hypothesi s is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex n...