In 1966 Richard Levins argued that applications of mathematics to population biology faced various constraints which forced mathematical modelers to trade-off at least one of realism, precision, or generality in their approach. Much traditional mathematical modeling in biology has prioritized generality and precision in the place of realism through strategies of idealization and simplification. This has at times created tensions with experimental biologists. The past 20 years however has seen an explosion in mathematical modeling of biological systems with the rise of modern computational systems biology and many new collaborations between modelers and experimenters. In this paper I argue that many of these collaborations revolve around detail-driven modeling practices which in Levins’ terms trade-off generality for realism and precision. These practices apply mathematics by working from detailed accounts of biological systems, rather than from initially idealized or simplified representations. This is possible by virtue of modern computation. The form these practices take today suggest however Levins’ constraints on mathematical application no longer apply, transforming our understanding of what is possible with mathematics in biology. Further the engagement with realism and the ability to push realistic models in new directions aligns well with the epistemological and methodological views of experimenters, which helps explain their increased enthusiasm for biological modeling.

1966 年，Richard Levins 认为，数学在种群生物学中的应用面临各种限制，迫使数学建模者在他们的方法中至少权衡现实性、精确性或普遍性中的一个。生物学中的许多传统数学建模通过理想化和简化策略，优先考虑普遍性和精确性，而不是现实主义。这有时会与实验生物学家产生紧张关系。然而，在过去的 20 年里，随着现代计算系统生物学的兴起以及建模者和实验者之间的许多新合作，生物系统的数学建模出现了爆炸式增长。在本文中，我认为这些合作中的许多都围绕着细节驱动用莱文的话来说，建模实践在现实主义和精确性之间权衡了普遍性。这些实践通过对生物系统的详细描述来应用数学，而不是从最初的理想化或简化表示。借助现代计算，这是可能的。然而，这些实践今天采取的形式表明，莱文斯对数学应用的限制不再适用，改变了我们对生物学中数学可能的理解。此外，对现实主义的参与以及将现实模型推向新方向的能力与实验者的认识论和方法论观点非常吻合，这有助于解释他们对生物建模的热情增加。