The reason for the Math object is simple: because Java does it. Not the best of reasons, but here we are. I guess things made more sense back then, before Douglas Crockford started his campaign to suppress half the language*. Originally you were allowed, or meant, to do things like this:

with (Math) {

  var n = min( round(a) * round(b), sqrt(c) );

  var result = exp( n + d );

}

The drawback to extending Number.prototype is that someone else might do the same thing. Or worse, for example, define Number.prototype.round as a symmetrical rounding function.

If you are looking for ways to make your life easier, why stop there? Why not simply include Math functions as global functions?

var m = 'abs acos asin atan atan2 ceil cos exp floor log max min ' +

        'pow random round sin sqrt tan PI').split(' ');

for (var i=0,l=m.length; i<l; i++) {

  window[ m[i] ] = Math[ m[i] ];

}

This will drop all the math functions into the global scope, effectively allowing you to stop typing Math. Ask yourself: Is there any real difference between extending Number and extending window with these functions?

* Before you flame me: The Crockford comment is not meant to be taken too seriously. I do agree with him that with is very dangerous in an implicit global environment.