Today’s mathematical research, both **pure and applied**, is paving the way for major scientific, engineering, and technological breakthroughs. Cutting-edge work in the mathematical sciences is responsible for advances in artificial intelligence, manufacturing, precision medicine, cybersecurity, and more. Find out how the mathematical sciences are helping to improve our everyday lives by checking out the stories and infographics below.

New breakthroughs in mathematics can reverberate for decades and across different applications. This crosscutting applicability is possible because mathematicians frame problems in a generalizable way. This mathematical abstraction is propelling advances across research communities.

From roots in abstract mathematics, some new and some very old, cryptosystems and authentication schemes have grown to meet evolving threats inherent in Internet usage.

Abstract geometry is important to technology developments in cryptocurrency, automation, quantum computing, and space exploration.

Mathematics and statistics have shaped almost every aspect of our transportation system, including transportation planning, trip planning and logistics, and the future of autonomous vehicles.

We often depend on images to make sense of our surroundings, but what we think of as images often start as raw (and sometimes messy) data that need to be converted to something that can be interpreted by the human eye. Mathematical and statistical techniques make this possible.

Personalized therapeutic approaches are made possible by mathematical and statistical methods that integrate data from diverse sources with other knowledge of how the human body works. These connections can improve diagnoses, guide surgeries in real-time, and offer more precise treatments.

Mathematics helps manufacturers make things faster, cheaper, and better through increased efficiencies and quality in manufacturing, assembly, operations, and distribution.

Mathematical and statistical advances have improved weather forecasting significantly over the past decades, ensuring that the best weather estimates are available when we need them most.

Mathematics leverages ever-increasing sets of data for improved outcomes in the use of machine learning technology.

Mathematics and statistics shape the world around us in sometimes surprising ways. Innovations spurred by mathematical and statistical advances are improving all aspects of our daily lives, often without us even knowing it.

This series of illustrations shows how advances in the mathematical sciences anticipate and enable later technologies that profoundly impact our daily lives, including life-saving advances in medical imaging and treatment, predictive traffic-avoiding routing, communications advances enabling GPS and high-speed cellular communications, safer online commerce with cryptographic security protocols, development of novel materials based on advanced simulations, improved forecasting of extreme weather events, and much more.

The leaps forward in technology have often built upon theoretical work whose impact would not have been predicted at the time of their creation. The same is true today: researchers and practitioners in the mathematical sciences continue to innovate, and we can only begin to imagine the future inventions their work will enable. Mathematical and statistical advances are playing a key role in emerging areas such as cyber warfare, quantum computing, artificial intelligence and machine learning for automation, genetic sequencing and related advances in vaccine creation to fight novel and existing viruses, and supply chain management.

The increasing pace of technological and social development will require many more advances in the mathematical sciences because they are a foundation for advances across science, medicine, business, finance, and even entertainment. New discoveries in mathematics happening today will reverberate for decades and centuries to come.

Tamara Kolda (Chair)

Russel E. Caflisch

Irene Fonseca

Montserrat “Montse” Fuentes

Ryan (Skip) Garibaldi

Tom Grandine

Trachette Jackson

Xiao-Li Meng

Jill Pipher

Terence Tao

**Kaushik Bhattacharya**, Caltech**Wei Chen**, Northwestern**Rita Colwell**, Univ. Maryland**James Crowley**, SIAM (retired)**Ingrid Daubechies**, Duke**David Donoho,**Stanford**Margot Gerritsen**, Stanford**Kenneth M. Golden**, Univ. Utah**Cara Gormally**, Gallaudet**Mark L. Green,**UCLA**David M. Higdon**, Virginia Tech**Rebecca Hubbard**, Univ. Pennsylvania**Lydia E. Kavraki**,**Therese Langer,**American Council for an Energy-Efficient Economy**Kristin Lauter**, Meta**Tiffany Lohwater**, UC Berkeley**Daniele Micciancio**, UCSD**Regina Nuzzo**, ASA**Karen Saxe**, AMS**Bjorn Stevens**, Max Planck Institute for Meteorology**Francis Su**, Harvey Mudd**Dawn Woodard**, Uber

__Review Oversight __

**Bryna Kra**, Northwestern**Jordan Ellenberg**, Univ. of Wisconsin

This activity was supported by the **National Science Foundation** (Award 1933194) and overseen by the National Academies' **Board on Mathematical Sciences and Analytics**. Please contact Michelle Schwalbe (mschwalbe@nas.edu) with any questions or requests.