Mathematical computational biology (MCB) has proven fruitful for all three fields:
mathematics, computation, and biology. One approach to the intersection begins
with symbolic representations of models, so that high-level abstractions and
advantageous problem transformations can be applied computationally before
good numerical methods are called in to do the heavy work of simulation and optimization.
This is the potential advantage of “declarative” modeling. It opens up further connections
between applied mathematics, artificial intelligence (including current trends in hybrid
logical/statistical inference), and foundational mathematics including logic and type theory.
I will illustrate the possibilities with recent work in complex, multiscale computational
biology  including signal transduction in synapses and gene regulation/signaling networks
in  developmental biology, by means of stochastic model reduction, enriched graphical
models expressed using computer algebra, and declarative modeling languages for
multiscale heterogeneous dynamics.