President Obama's 2014 budget request includes programs for research, development, and education in STEM (science, technology, engineering, and mathematics) fields. He has called for 100,000 new STEM teachers and one million new STEM graduates over the next 10 years, increased participation by groups historically underrepresented in these fields, and additional resources to support networks focused on STEM education. Mathematics is a major component of improving and expanding the STEM-literate work force.
But mathematicians, and the profession as a whole, are under scrutiny and attack. In 2012, the President's Council of Advisors on Science and Technology labeled mathematics the "bottleneck that is currently keeping many students from pursuing STEM majors" and called for teaching of college-level mathematics courses "by faculty from mathematics-intensive disciplines other than mathematics." E.O. Wilson recently claimed that "many of the most successful scientists in the world today are mathematically no more than semiliterate." Paul Krugman agreed that researchers do not need much math and writes that "higher math isn't usually essential; arithmetic is."
Not only are these statements misguided, they also reinforce popular negative stereotypes. When someone learns that I am a mathematician, the inevitable comment is, "I was never good at math," often accompanied by a dismissive chortle. Society accepts such comments but would never accept the analogous "I was never good at reading." We accept the use of a calculator to add small numbers but not the use of software to read basic English. We accept T-shirts advertising how hard math is, popular caricatures of math geeks, and scientists who claim they are mathematically ignorant, but we do not condone illiteracy, and we work hard to eradicate it.
Unfortunately, these discussions are a distraction from the main issue: We need to train more people to be scientifically literate, and mathematics is a core component of such training. The precise nature of mathematics provides a framework for scientific advances. Without proficiency in the language of logical reasoning and quantifiers, it is impossible to work in a STEM field. The study of mathematics is thousands of years old, yet it is still a hot field.
Mathematics provides a tool box for the sciences. Mathematical models are used to explain and predict events around us, and rigorous mathematical thinking organizes ideas. Mathematics is used to model the spread of infectious diseases and then as a tool to halt the spread. It is used to develop rigorous standards for testing in drug trials that lead to major improvements in treatment, and it is used to design buildings that can withstand earthquakes and other natural disasters.
But mathematics is much more than a tool box. Its logical reasoning underpins all scientific discoveries, and it has transformed the way we understand our world. Long before experimental evidence was available, Galileo used mathematics to predict that the earth revolves around the sun. Centuries later, Albert Einstein used mathematics to show that the universe is curved, not flat; his theories were only experimentally verified years later.
Mathematics plays a role in the design of satellites, whose applications include communications, weather prediction, Internet access, and military uses. Before public encryption codes, a theorem of Pierre de Fermat established a rigorous foundation for a commonly used cryptographic system. Without Alan Turing's fundamental work, the modern computer would not be possible. Numerical analysis, modeling, and statistics—all branches of mathematics—played a significant role in mapping the human genome. This is mathematical theory turned into applications, but applications that developed long after the theory.
Sometimes mathematical theory turns into practice much more quickly, as happened with the use of complex analysis to develop sophisticated coding techniques that protect the transmission of personal data.
Simpler mathematical concepts are implicitly used in numerous other professions: A plumber computes volumes and understands angles; a nurse calculates doses and drip rates; and a mechanic understands torque, ratios, and volumes.
This is not to say that every scientist needs a degree in mathematics. But every scientist needs the rigorous language and logic afforded by mathematics. Equating this knowledge with the ability to do calculus is as nonsensical as equating a biologist's ability to hunt with the ability to map a genome. Mathematics should not be used as a gatekeeper for the sciences, but one cannot excel in science without basic mathematical reasoning.
Increasingly, students arrive at colleges without sufficient background to take basic mathematics courses. Nonetheless, we are expected to teach them the higher-level concepts they need for classes in biology, statistics, physics, and chemistry. But mathematics builds on a previous foundation and cannot be taught starting at the end. It is like asking a student unable to read a newspaper to analyze Shakespeare.
From an early age, children are directed to books appropriate to their individual reading levels. Working within guidelines for a third grader, a good teacher or librarian directs a student to appropriate material, and schools are equipped with reading material at a wide range of levels. But elementary education in mathematics does not have specialists like librarians to present students with appropriate-level material. The result is that we bore the good students and lose the weaker ones, helping only some in the middle. Improving the STEM work force starts early—focusing on individual needs and teaching the language of mathematics.
With all our debating, we have lost sight of the main issues: We need to support mathematics research at all levels and train more people to be mathematically literate. Does every scientific discovery depend on mathematics? Of course not. Can any scientist function without mathematics? Absolutely not.