In a paper on the role of mathematics in fisheries science, Jon T. Schnute (Electronic Journal of Differential Equations, Conf. 12, 2005, pp. 143 – 158) quotes the ‘fisherman’ (in reality, one of their advocates) James O’Malley’s views on they use of mathematics in fisheries science:
Mathematics has been elevated to a status which suppresses knowledge and acutally detracts from our efforts to aquire knowledge. [The problem is] not mathematics per se, but the place of idolatry we have given it. […] Like any priesthood, it has developed its own language, rituals and mystical signs to maintain its status, and to keep a befuddled congregation subservient, convinced that criticism is blasphemy. Late at night, of course, many members of the scientific community will confess their doubts. But in the morning, they reappear to preach the catechism once again [p. 153].
O’Malley do however believe that appropriate use of mathematics can help advance knowledge:
What is happening out there on the ocean, and why is it happening? What willl we do about it? […] We owe it to ourselves, to the ocean, and especially to science itself, to assemble that great body of knowledge, those millions of observations, and to use every tool, including mathematics, to further our understanding of that knowledge. Knowledge and understanding are not the same. They may, in fact, be separated by a wide chasm. Mathematics is neither knowledge nor understanding. It may be a useful tool to help us bridge that gap. That is where it belongs, that is how we should use it, and we need to start now – before the bean-counters destroy us all [pp. 156-157].
The whole O’Malley thing is available online. Being a mathematician by training, I naturally feel a bit threatened by critique like this, particularly since I think there is something to it. O’Malley’s somewhat optimistic views of mathematics appropriate role in science is comforting, though. When not quoting O’Malley, Schnute puts out an idea for how fisheries management could work without all the modeling and the uncertainty that follows with it. He briefly touches upon nonlinear methods and chaotic behaviour and quotes May (presumably Robert May, longtime collaborator with George Sugihara [might even have been his supervisor], who both have made fundamental contributions to the use of nonlinear methods) commenting on the rise of chaos theory and nonlinear dynamic modeling:
It’s the best possible time to be alive, when almost everything you knew is wrong [p. 155].