Knots and Feynman Diagrams

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Renormalization of multiple zeta values (2006, background): “Since then MZVs and their generalizations have been studied extensively by numerous authors from different point of views with connections to arithmetic geometry, mathematical physics, quantum groups and knot theory [5, 8, 11, 23, 24, 32, 34, 42].”
Matroids motives, and a conjecture of Kontsevich (2000, unknown): “(See [10] for a discussion of MZVs and their relationship to certain Feynman amplitudes).”
Combinatorics of rooted trees and Hopf algebras (2002, background): “C Now the symmetric algebra on the vector space of rooted trees (after a degree shift) can be endowed with a coproduct to make a Hopf algebra; this was defined by Kreimer in connection with renormalization.”
The evaluation of Tornheim double sums. Part 2 (2005, background): “n=1 1 mpnq(m+ n)r(m+2n)s under the parity restriction p+ q+ r+ sis odd. This is the Witten sum corresponding to SO(5). These sums also have appeared in connection with knots and Feynman diagrams, see [18] for details. The Bernoulli function (1.22) Ak(q) = kζ′(1−k,q), k∈ N introduced in [13], playsan”
Towards a Philosophy of Real Mathematics (2003, methodology): “We may have been led to use specific Hopf algebras to allow us to perform calculations with Feynman diagrams (Kreimer 2000), but it cannot be right to say that they are structures instantiated in the world.”