<i>0 and the negative numbers turned up very late in our history</i><p>I believe it's also true that the ancients distrusted polynomials (e.g., <i>x^3+7x^2+2x+9=0</i>) because who would be silly enough to add a volume to an area to a length, etc.<p>If they had just done the mathematics without relating the numbers to real world, we might have far more advanced maths today. All the more reason to pursue topics for their own sake.