Interdisciplinary Research—Mathematical Interactions Viewed from Four Portrayals Goong Chen Introduction: Interdisciplinarity with Mathematics You’ve been approached by a colleague from the college of agriculture at your university, asking you to help solve a mathematical problem. You’ve pon- dered curious problems from engineering, physics, chemistry, biology, or social sciences and wanted to delve deeper into them. You’ve read calls from funding agencies inviting mathematicians’ par- ticipation, and suddenly someone from another department of your university is organizing a drive to submit a group proposal and is giving you a cold call to solicit your input and cooperation. He is also promising a share of summer grant support for you if the proposal is funded. Do any of the above situations sound familiar to you? If not, then you will surely encounter these scenarios more and more in the future. We are living in an ever more complex world. Inter- actions among mathematicians themselves and, more importantly, engagements between mathe- maticians and those in other disciplines are on the rise. Interdisciplinary research involving mathe- matics almost inevitably is becoming the trend, as the universality of mathematics can be felt in so many different forms. A quick survey of sev- eral major contemporary research themes shows Goong Chen is professor of mathematics at Texas A&M University (TAMU) and Texas A&M University-Qatar. He is also a member of the Institute for Quantum Science and Engineering at TAMU. He gratefully acknowledges par- tial support by grant NHARP-010366-0149-2009 from the Texas Higher Education Coordinating Board and by the Qatar National Research Fund’s grant National Priority Re- search Project (NPRP) 4-1162-1-181. His email address is gchen@math.tamu.edu/. DOI: http://dx.doi.org/10.1090/noti892 what relevant disciplines are involved and where mathematical components are either present or in demand: (A) Bioinformatics : biology, computer science, probability and statistics, medicine, systems the- ory, combinatorics, optimization, ... ; (B) Nanotechnology : physics, chemistry, elec- trical and chemical engineering, mathematical analysis, ... ; (C) Genomics : genetics, molecular and cell biology, biochemistry, scientific computing, ... ; (D) Proteomics : pharmaceuticals, biology, chem- istry, physics, scientific computing, ... ; (E) Conflict and resolution: sociology, psychol- ogy, political science, game and control theory, stability and chaos, ... ; (F) Homeland security and the war on terror- ism: engineering, cybernetics, finance and banking, cryptography, social sciences, linguistics, search algorithms, tomography, mathematics in general, ... ; (G) Renewable energy technology : engineering, physics, chemistry, fluid dynamics, computational mechanics and mathematics, ... ; (H) Climate change and global warming: atmo- spheric science, chemistry, physics, oceanography, glaciology, forestry, soil science, mathematical modeling, ... . According to a 330-page government- and industry-commissioned report published by the National Academy Press [2], a definition is given as follows: Interdisciplinary research (IDR) is a mode of research by teams or individuals that inte- grates information, data, techniques, tools, perspectives, concepts, and/or theories from two or more disciplines or bodies of 1246 Notices of the AMS Volume 59, Number 9