It has now become so easy to construct knot invariants that mathematicians have started looking more closely at the geometrical structure of knots. There has been remarkable observational progress in recent years. We observe distant galaxies whose light set out when our universe was a tenth its present age, and which are being viewed in a newly-forming state. This observational progress is being complemented by increasingly elaborate numerical simulations of the emergence of cosmic structure. This progress brings into sharper focus a new set of fundamental questions.
Answers depend on what happened in the initial microsecond of cosmic expansion.
Cosmologists are now probing the exotic high-energy conditions that prevailed in the initial instants, in the hope of learning how the physical laws permitted our universe to develop the complexity we see around us, and of which we are part.