a mere issue of complexity. ;-)
> Take, for instance, the task of trying to determine whether a very
> large number is prime — that is, it cannot be split evenly into the
> product of any smaller components, except 1. (Six is the product of 2
> by 3, so it is not prime; 7 has no smaller factors, so it is.)
> Determining primeness has huge practical consequences — prime numbers
> are widely used in computer security codes, for instance — yet when
> the number is large it can take an astronomical amount of computer
> time to determine its primeness unequivocally. Mathematicians have
> invented statistical methods that will give a probabilistic answer
> that will tell you, for instance, a given number is 99.99% certain to
> be prime.
early last year, an indian institute of technology professor and two of his undergraduate students proved that the "primality test" (above) is in P (i.e., it can be solved in deterministic polynomial time). their algorithm will still run slower than the more probabilistic or heuristic methods, but there has been additional work on it, and it is expected to significantly reduce the computation.
> We may never fully solve the Navier-Stokes equations, but according to
> Davis it will not matter. Like so many other fields, mathematics is
> becoming less about some Platonic ideal of ultimate answers, and more
> a functional project of computational simulation and communal
> negotiation. Dare we say it: Math is becoming postmodern.
as it should be. of course (as documented by kline), every century there is a foundational crisis as the applied stuff gets too far ahead ... but why not? ;-)
--ravi