Jeremy Gunawardena: Are there theorems in biology?

Recently, the mathematical sciences have become increasingly engaged with biology. What can we expect from this disciplinary interaction? Is it to make biology a predictive science, as many suggest? Or are there fundamental problems for which new kinds of mathematics may be required? I will make some suggestions about this from the perspective of a pure mathematician working behind the lines in biology. I will then describe recent progress on the question of how cells integrate information, from which new problems, conjectures and theorems emerge.