Recommendation: Funding agencies supporting mathematical research related to the life sciences should be receptive to research proposals that pertain to any level of biological organization: molecules, cells, organisms, populations, and ecosystems. While much current research can be productively confined to a particular level, there are also substantial challenges and rewards associated with analyzing interactions between levels.

The biological sciences are already becoming more quantitative and data-intensive; indeed, the explosion of data production and the potential for quantitative analysis replete with estimates of precision are the most visible qualities of the biological sciences of the 21st century. Progress in the biosciences will increasingly depend on deep and broad integration of mathematical analysis into studies at all levels of biological organization. No one level of organization stands out as offering singularly attractive opportunities for mathematical applications. The challenges faced at different levels have distinctive characteristics, but there are also unifying themes. Some chapters of the report are organized around the different levels of biological organization, but others—including “The Nature of the Field,” “Historical Successes,” and “Crosscutting Themes”—look more broadly at the commonalities of past and current applications of mathematics to biology.

Recommendation: Funding agencies supporting mathematical research related to the life sciences should give preference to proposals that indicate a clear understanding of the specific biological objectives of the research and include a realistic plan for how mathematicians and biologists will collaborate to achieve them.

The committee regards the interface between mathematics and biology as biology-driven. Research that proceeds by abstracting biological problems away from specific biological contexts and explores the properties of the resultant abstraction is less likely to be effective than research that stays more tightly focused on actual biological questions. However, to maximize productivity, the most powerful and appropriate mathematical tools should be selected to address important biological problems, and this quest benefits from involving the dedicated expertise of mathematical scientists. There are also many cases where results developed within pure mathematics, or in applications of mathematics to physical systems and engineering, later find powerful applications to biology, but this process, too, is most productive when it is biology-driven. Furthermore, the committee was impressed with the sheer scope of mathematical applications to biology and the diverse types of mathematics that are playing



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