Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century

National Research Council

doi:10.17226/13373

Consensus Study Report

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Fueling Innovation and Discovery

The Mathematical Sciences in the 21st Century

(2012)

The mathematical sciences are part of everyday life. Modern communication, transportation, science, engineering, technology, medicine, manufacturing, security, and finance all depend on the mathematical sciences. Fueling Innovation and Discovery describes recent advances in the mathematical sciences and advances enabled by mathematical sciences research. It is geared toward general readers who would like to know more about ongoing advances in the mathematical sciences and how these advances are changing our understanding of the world, creating new technologies, and transforming industries.

Although the mathematical sciences are pervasive, they are often invoked without an explicit awareness of their presence. Prepared as part of the study on the Mathematical Sciences in 2025, a broad assessment of the current state of the mathematical sciences in the United States, Fueling Innovation and Discovery presents mathematical sciences advances in an engaging way. The report describes the contributions that mathematical sciences research has made to advance our understanding of the universe and the human genome. It also explores how the mathematical sciences are contributing to healthcare and national security, and the importance of mathematical knowledge and training to a range of industries, such as information technology and entertainment.

Fueling Innovation and Discovery will be of use to policy makers, researchers, business leaders, students, and others interested in learning more about the deep connections between the mathematical sciences and every other aspect of the modern world. To function well in a technologically advanced society, every educated person should be familiar with multiple aspects of the mathematical sciences.

Contributor(s): National Research Council; Division on Engineering and Physical Sciences; Board on Mathematical Sciences and Their Applications; Committee on the Mathematical Sciences in 2025

RESOURCES AT A GLANCE

Video(s):

Math Story: Bridges and DNA

Math Story: Pixels and Animations

Topics

Suggested Citation

National Research Council. 2012. Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. Washington, DC: The National Academies Press. https://doi.org/10.17226/13373.

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Publication Info

64 pages | 8.25 x 10 |

ISBNs:

Paperback: 978-0-309-25473-1
Ebook: 978-0-309-25476-2

DOI: https://doi.org/10.17226/13373

Chapters		skim
Front Matter	i-vi
Introduction	1-2
Compressed Sensing / Through the Kaleidoscope	3-6
Eigenvectors / From the Mathematical Sciences to . . . an IPO	7-10
Mathematical Simulations / When the Lab Isn't Big Enough	11-19
Bayesian Inference / Not an Enigma Anymore	20-23
Diffusion Tensor Imaging / A New View of the Brain	24-28
Fast Multipole Method / A Long-Term Payoff	29-35
Cellular Automata / Sublimely Complex	36-39
Graph Spectra / Sparsest Cuts in Minimum Time	40-43
Bioinformatics / Interpreting the Human Genome	44-48
Geometry and Physics / Endlessly Intertwined	49-52
Probability and Statistical Physics / Connecting Microscopic and Macroscopic	53-58

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The Chapter Skim search tool presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter. You may select key terms to highlight them within pages of each chapter.

Videos

Math Story: Bridges and DNA

What is the math that allows us to read our DNA? And what does it have in common with bridges in a 18th century Prussian city? This video explores the story behind Eulerian and Hamiltonian paths and the role they play in DNA sequencing.

Math Story: Pixels and Animations

What is the math behind a computer-animated film or a compressed internet image? This video explores the story behind the discovery of compressed sensing and its application in new technologies.

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