The new Institute for Mathematical and Statistical Innovation at the University of Chicago comprises a collaborative group of mathematicians and statisticians from UChicago, Northwestern University, the University of Illinois at Chicago and the University of Illinois at Urbana-Champaign who seek to bring powerful mathematical ideas to bear on key contemporary scientific and technological challenges. IMSI is funded with a five-year, $15.5 million grant from the National Science Foundation.

Researchers at IMSI will build a platform that accelerates the translation of applied mathematical and statistical techniques into solutions for urgent scientific and societal problems. Many of these problems arise naturally in a range of fields already being studied across the four partner institutions, including climate change, health care, quantum information theory, artificial intelligence, data science, economics and materials science.

The current complex environment of science and engineering research involves a deep interaction of multiple disciplines to address scientific problems. These interactions, which are often at very large scales, need sophisticated mathematical and statistical approaches that underpin solutions to the scientific problems. While enabling these applied mathematical approaches, IMSI will benefit from the institutional strengths of each of its university partners, both in the mathematical sciences as well as in the particular application areas of science, technology, economics and policy, drawing from the deep programmatic expertise of a network of centers and research groups.

“The Institute for Mathematical and Statistical Innovation will be a critical national resource for applied mathematics, purposefully connecting mathematical and statistical methods and discoveries to applied science and technology in a way that reaches across disciplines and brings together a wide range of collaborators to address some of the most challenging problems of our time,” said Robert J. Zimmer, president of the University of Chicago. “We are excited to launch the Institute at the University of Chicago and look forward to seeing the impact of its work in the years ahead.”

**Addressing the challenges of modern, massively connected systems**

Mathematics has always played a foundational role in establishing and exploring the theoretical and quantitative underpinnings of modern scientific discovery, often independently and years before the empirical science is established. However, recent advances in applied science and technology are challenging available models and paradigms developed by mathematicians and statisticians, providing a fertile ground for the discovery of new applied mathematical techniques and discoveries that have immediate applications to key modern applied scientific questions.

The rapidly developing field comprising data science, machine learning and artificial intelligence provides a topical example. Over the past decade, scientific institutions, government agencies and industry have accumulated vast amounts of data associated with complex biological, technological, physical and social systems. Simultaneously, new methods of machine learning and artificial intelligence have been developed to extract meaning and predictive outcomes from these data, becoming as essential a part of scientific discovery as theory, experiment and simulation. Yet as this work develops, the applied scientists have uncovered deeper layers and structures of these algorithms that are not yet fully understood from a mathematical theory perspective. Thus, science has served up a fertile area for fundamental mathematical work that will, once done and understood, instantly be useful to better understand and validate the very AI applications that pointed towards the mathematical problems. Such a potential for fundamental applied mathematics discovery, coupled with solutions to pressing applied problems, makes the establishment of IMSI an ideal and important platform at our institutions.

In the case of data and AI, these mathematical and statistical solutions will help explain a range of modern scientific and technological challenges characterized by massively connected systems and complex datasets, including the frequency and intensity of extreme weather events caused by climate change, the dynamics of global economic systems, interactions between genes and their environment, the organization and delivery of health care, the promise and limitations of quantum computing, and protecting individual privacy when dealing with large data sets containing sensitive information.

“There are many ways in which the mathematical sciences can help us come to grips with the massive growth in the amount of available data describing complex systems, as well as with the complex uses of computing now used to extract meaning from these data that may be leaving their mathematical and theoretical foundations behind,” said Kevin Corlette, Professor of Mathematics at UChicago and inaugural director of IMSI. “These include methods for evaluating the quality of data sets, simplification of models to improve their predictive power and their ability to provide insight into underlying principles, and new approaches to estimating the uncertainty of results predicted by models.”

“IMSI will be a vehicle for sustained engagement between mathematical scientists and researchers in a wide range of disciplines on these kinds of questions,” he said.

**A national platform for research, training and outreach**

The complexity and scale of such new scientific challenges demand a diversity of perspectives and deep expertise that makes it difficult for any single institution to accomplish alone. Instead, optimal solutions are better achieved by systematically building institutional partnerships that bring together public and private universities, national laboratories and corporate partners in order to draw strength from and amplify the effectiveness of each, while allowing the partnership as a whole to transcend scale limitations.