So-called "algebraic" knots are the ones obtainable by intersecting a small 3-sphere S^3(eps) about 0 in complex 2-space C^2 with the locus of a complex polynomial equation P(z,w) = 0 having an isolated singularity (where the locus is not a smooth surface) at 0. The (p,q) torus knot (assuming gcd(p,q) = 1) is obtained from the polynomial P(z,w) = z^p + w^q. that way. (I even made a computer graphic picture of that (2,3) trefoil, using the same polynomial Adam cited, stereographically projected into 3-space, a few months ago.) It's known that algebraic knots form a proper subset of all "iterated torus knots", which are defined via: Start with a torus knot and imagine another torus knot, possibly different, drawn on the boundary of a thin solid-torus neighborhood of that; repeat finitely many times. There are some knots that aren't algebraic. For example, a (p,q) torus knot with p < 0 and q > 1. —Dan