  This paper is an exposition of the relationship between Witten's Chern-Simons
functional integral and the theory of Vassiliev Invariants of knots and links
in three dimensional space. We conceptualize the functional integral in terms
of equivalence classes of functionals of gauge fields and we do not use measure
theory. This approach makes it possible to discuss the mathematics intrinsic to
the functional integral rigorously and without functional integration.
Applications to loop quantum gravity are discussed. We thank the organizers of
the Conference on 60 Years of Yang-Mills Gauge Field Theories (25 to 28 May
2015) for the invitation and opportunity to speak about these ideas in
Singapore.
