Hazewinkel wrote this article in 2005. Perhaps it's time for an update.

For example, updating item

34: Ordinary differential equations much work has been done on the underlying Hopf algebra (HA) of Lie-Butcher numerical methods for solving autonomous and non-autonomous ODE's (evolution equations) by , e.g., Ebrahimi-Fard, Hans Munthe-Kaas and their colleagues. See, e.g.,

i) "Butcher series: A story of rooted trees and numerical methods for evolution equations" by McLachlan, Modin, Munthe-Kaas, and Verdier

ii) "Lie-Butcher series, Geometry, Algebra and Computation" by Munthe-Kaas ander K. Føllesdal

This is closely allied to item

81: Quantum theory

through the HA (combinatorial Faa di Bruno bialgebra, trees, Feynman diagrams) of renormalization to which Alain Connes, Christian Brouder, David Broadhurst, Dirk Kreimer, Kurush Ebrahimi-Fard, Hector Figueroa, Jose Gracia-Bondia, Hans Munthe-Kass, Loic Foissy, Karen Yeats, Paul-Hermann Balduf, et al. have contributed.