Realizing our vision requires combining biological experimentation and new theories grounded in mathematics. Research supported by the NSF-Simons National Institute for Theory and Mathematics in Biology is structured so that theorists and experimentalists collaborate on experimental design and data analysis, as well as modeling. NITMB research also supports the development of new mathematics inspired by biology. Internal research projects support NITMB researchers and bring together faculty from participating institutions. A National Pilot Projects Program funds high-risk projects, each with a one-year funding period.  The program's aim is to recruit new mathematical scientists and biologists into collaborating on seed projects. NITMB has an innovative research program organized around five interrelated themes, selected because they reflect key capabilities of biological systems and interconnect with open mathematical problems. These themes establish bridges across subdisciplines of biological and mathematical sciences, ensuring that research in one domain will support advances in the others. The themes also reflect our cross-disciplinary organizational structure, insuring that our training and community-building activities foster deep interactions across disciplines.