Defending Robert Rosen’s claim that in every confrontation between physics and biology it is physics that
has always had to give ground, it is shown that many of the most important advances in mathematics
and physics over the last two centuries have followed from Schelling’s demand for a new physics that
could make the emergence of life intelligible. Consequently, while reductionism prevails in biology, many
biophysicists are resolutely anti-reductionist. This history is used to identify and defend a fragmented but
progressive tradition of anti-reductionist biomathematics. It is shown that the mathematicoephysico
echemical morphology research program, the biosemiotics movement, and the relational biology of
Rosen, although they have developed independently of each other, are built on and advance this antireductionist tradition of thought. It is suggested that understanding this history and its relationship to the broader history of post-Newtonian science could provide guidance for and justify both the integration of these strands and radically new work in post-reductionist biomathematics.