The Mathematical Sciences in 2025

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The Mathematical Sciences in 2025

The Mathematical Sciences in 2025 PDF Free Download

Committee on the Mathematical Sciences in 2025

Board on Mathematical Sciences and Their Applications

Division on Engineering and Physical Sciences

Main Contents of Mathematical Sciences PDF Book

1. Introduction

  • Study Overview
  • The Nature of the Mathematical Sciences
  • Everyone Should Care About the Mathematical Sciences
  • Structure of this Report

2. The Vitality of the Mathematical Sciences

  • The Topology of Three-Dimensional Spaces
  • Uncertainty Quantification
  • The Mathematical Sciences and Social Networks
  • The Protein-Folding Problem
  • The Fundamental Lemma
  • Primes in Arithmetic Progression
  • Hierarchical Modeling
  • Algorithms and Complexity
  • Inverse Problems: Visibility and Invisibility
  • The Interplay of Geometry and Theoretical Physics
  • New Frontiers in Statistical Inference
  • Economics and Business: Mechanism Design
  • Mathematical Sciences and Medicine
  • Compressed Sensing

3. Connections Between the Mathematical Sciences and Other Fields

  • Broadening the Definition of the Mathematical Sciences
  • Implications of the Broadening of the Mathematical Sciences
  • Two Major Drivers of Expansion: Computation and Big Data
  • Mathematical Sciences Contributions to Science and Engineering
  • Mathematical Sciences Contributions to Industry
  • Mathematical Sciences Contributions to National Security

4. Important Trends in the Mathematical Sciences

  • Increasing Importance of Connections for Mathematical Sciences Research
  • Innovation in Modes for Scholarly Interactions and Professional Growth
  • The Mathematical Sciences Should More Thoroughly Embrace Computing
  • Funding Implications of Increasing Connectivity of the Mathematical Sciences

5. People in the Mathematical Sciences Enterprise

  • A Picture of the Changing Demand for the Mathematical Sciences
  • The Typical Educational Path in the Mathematical Sciences Needs Adjustments
  • Attracting More Women and Underrepresented Minorities to the Mathematical Sciences
  • The Critical Role of K-12 Mathematics and Statistics Education
  • Enrichment for Precollege Students with Clear Talent in Mathematics and Statistics

Preface to Mathematical Sciences PDF Book

When I was asked to chair a committee of mathematical scientists charged with examining the field now with an eye toward how it needs to evolve to produce the best value for the country by 2025,

I demurred because I am not a mathematical scientist.

The counter was that therefore I would not be biased, could be objective to prevent possible internal politics from “capturing” the report,

and would be continuing a tradition of having such committees chaired by nonexperts. The assignment was educational in many ways.

The committee was extraordinary in its makeup, with experts from the core of mathematics as well as from departments of statistics and computer science, from both academia and industry.

My eyes were opened to the power of the mathematical sciences today, not only as an intellectual undertaking in their own right,

but also as the increasingly modern foundation for much of science, engineering, medicine, economics, and business.

The increasingly important challenges of deriving knowledge from huge amounts of data, whether numerical or experimental, of simulating complex phenomena accurately,

and of dealing with uncertainty intelligently are some of the areas where mathematical scientists have important contributions to make going forward—and the members of this committee know it.

They have demonstrated a great capacity to envision an emerging era in which the mathematical sciences underpin much of twenty-first century science, engineering, medicine, industry, and national security.

I hope that this report persuades many others to embrace that vision. While all members of the committee contributed to this report, vice-chair Mark Green,

from the University of California at Los Angeles, and NRC staff, headed by Scott Weidman,

worked tirelessly to provide much of the writing and data that gives the report its coherence, organization, and credibility.

I especially thank them, for myself and for the rest of the committee, for their essential contributions.

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