important roles in the life sciences. Hence, it strongly cautions against prejudging which subfields of mathematical research are most likely to contribute to biology.

Recommendation: Funding agencies supporting mathematical research related to the life sciences should give priority to research that addresses intrinsic characteristics of biological systems that reappear at many levels of biological organization: high dimensionality, heterogeneity, robustness, and the existence of multiple spatial and temporal scales.

Biological systems at all scales are characterized by high dimensionality, heterogeneity, robustness to perturbations, and the existence of strongly interacting, highly disparate spatial and temporal scales. While these characteristics also appear in some physical systems that have been successfully modeled mathematically—the modeling of heterogeneous and multiscale phenomena is in particular a vibrant topic of mathematical and engineering research—the modeling of biological systems will require greatly expanded capabilities in these areas. As is widely documented in the report, the characteristics enumerated above recur at all levels of biological organization, from molecules to ecosystems.

Recommendation: Funding agencies supporting mathematical research related to the life sciences should support the refinement of general-purpose tools whose broad biological utility has already been established. Such research might require specialized review criteria, particularly when the focus is on tool enhancement rather than breakthrough research.

Although the committee feels strongly that mathematical research based on premature abstraction of biological problems risks irrelevance, there are more and more instances where mathematical tools have already proven their utility in a broad range of biological applications. Many examples are described in this report. In some instances, as biological applications of these tools have expanded, limitations on their effectiveness have become apparent. Nonetheless, there are opportunities here for effective and important mathematical research that is less tightly tied to particular biological applications than is typically the case. Such research will have varying degrees of innate mathematical interest but can have an important impact on biology.

Recommendation: Funding agencies supporting mathematical research related to the life sciences should place increased emphasis on funding mechanisms and novel approaches to the



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