Math Is in Everything and There Is Life After Math
The largest employers of math graduates in the United States are the National Security Agency, high tech and information technology companies, financial and insurance companies, motion picture special effect companies, and educational institutions.
Many mathematicians work at educational institutions as college or university professors or as high school math teachers. A math major is the best preparation to teach college level math, but an advanced degree in math will almost always be required. Undergraduates preparing to teach college and university math usually do not have to take any education courses although those preparing to teach high school math do have to take a large number of education courses in order to meet Kansas State Board of Education teacher certification requirements. A math-ed major is the best preparation to teach high school math, but students sometimes double major in math-ed and math to have more career options.
The National Security Agency is the world's largest employer of mathematicians. NSA and other government agencies employ mathematicians in cryptology and related areas of communications, engineering, signals processing, speech research, and the design of specialized computers. For example, Robert Redford portrayed a bookish Central Intelligence Agency researcher in the 1975 movie Three Days of the Condor. In the 1999 video Decoding Nazi Secrets, NOVA presented a full account of history's greatest code-breaking coup. The German message-coding Enigma machine appeared invincible because of the 150 million million million ways it could encrypt a message. A group of American and British mathematicians working in a top secret research facility at the Bletchley Park estate outside London cracked the Enigma code and changed the outcome of World War II. Cryptanalysts, including mathematician Alan Turing, developed the mathematics necessary to analyze and crack the German and Japanese Enigma codes, and they created Colossus, the world's first computer, to examine the thousands of possibilities determined by the cryptanalysis of Enigma codes. With practice, the Bletchley Park team was able to decode intercepted Axis messages in just a few hours and give the Allies a tremendous strategic advantage.
The Internet could not function without a wide variety of mathematical tools ranging from data and image compression, data encryption, error correction techniques, and methods for routing messages. Mathematicians use affine transformations to compress pictures and videos into fractals that can be stored on compact disks, transmitted over the Internet, and quickly reassembled back into images virtually indistinguishable from the original pictures such as those in the Encarta encyclopedia. Cryptologists use mathematical encryption systems to secure cellular, internet, and satellite communications involving financial, military, and personal information. Information technologists use clever algorithms and error correcting codes to deconvolute and enhance corrupted or distorted data making it possible for CD players to read scratched compact discs and for the deep space probes Voyager I and II to send back stunning pictures of the outer planets. Systems analysts use graph theory to route data in telecommunication systems and fractal-based modeling to describe Internet data traffic.
Modern movie animation techniques and special effects are based on mathematics. Animators create characters, scenery and lighting and motion using software driven by mathematical equations and computers to do the tremendous number of calculations involved. Four fascinating examples are the liquid metal assassin in the 1991 movie Terminator 2: Judgement Day, the dinosaurs in the 1993 movie Jurassic Park, the launch sequence in the 1995 movie Apollo 13, and the stars shining over the ship in a night scene in the 1997 movie Titanic.
Scientists create antennas which approximate mathematical fractals to improve the performance of antenna arrays and cell phones. Engineers design fluid transporting fractals to control and improve fluid dynamics. Medical researchers use chaotic dynamics and fractal architecture to study disease and aging. Mathematical physicists used dynamical systems to discover low energy pathways along which space vehicles can travel using far less fuel. Analysts use techniques from nonlinear differential equations to enhance video images. In one famous case during the 1992 Los Angeles riots, a video of the beating of a truck driver revealed a fuzzy spot on the arm of a man who threw a brick at the truck driver. Mathematicians enhanced the fuzzy spot into a rose tattoo and helped identify and convict the assailant.
Financial and insurance companies also employ a large number of mathematicians. Those in the actuarial field work for insurance companies, consulting firms, commercial banks, investment banks, and retirement funds. They are employed by corporations as well as state and federal governments. Actuaries solve real-world problems involving money, probabilities, and future events. They help design and price insurance and retirement plans; evaluate and manage risks; and plan cash flow, claim payment, and investment strategies.
Mathematicians discover new, beautiful, and exciting mathematics all the time. Two recent examples are the classification of finite simple groups and The Proof of Fermat's last theorem which was dramatized in a 1997 NOVA video.
The Mathematical Moments web site http://e-math.ams.org/mathmoments provides more information about some of the applications of math mentioned above. The following links are from that web site.
- Boldly Going http://www.ams.org/ams/mm49-space.pdf
- Compressing Data http://www.ams.org/ams/mm41-compression.pdf
- Enhancing Your Image http://www.ams.org/ams/mm24-image.pdf
- Listening to Music http://www.ams.org/ams/mm6-music.pdf
- Making Movies Come Alive http://www.ams.org/ams/mm2-movies.pdf
- Routing Traffic Through the Internet http://www.ams.org/ams/mm14-routing.pd
- Securing Internet Communications http://www.ams.org/ams/mm4-internet-comm.pdf
- Seeing More Clearly http://www.ams.org/ams/mm35-adaptiveoptics.pdf
- Seeing the World Through Fractals http://www.ams.org//ams/mm11-fractals.pdf
- Tracing Your Routes http://www.ams.org/ams/mm33-tracing-your-routes.pdf
- Solving Crimes http://e-math.ams.org/ams/mm51-crime.pdf
"Texas Instruments (TI) is leading this math education initiative based on the hit series NUMB3RS. In partnership with CBS, and working in association with the National Council of Teachers of Mathematics (NCTM), TI has created an educational outreach program promoting the many uses of mathematics and supporting math teaching. The program includes TI and NCTM-developed math education activities for teachers and students based on the "NUMB3RS" TV show. The activities will be based on the mathematics presented in each episode. The math used in each episode of NUMB3RS is based on real FBI cases. Mathematics consultants work with NUMB3RS throughout production to ensure that the math used to help analyze and solve crimes is real and accurate as depicted by FBI agent Don Eppes (Rob Morrow) who recruits his mathematical genius brother Charlie (David Krumholtz) to help the Bureau solve a wide range of challenging crimes."
"The program was specifically designed to help students (and their parents) realize how relevant math is to everyday activity and understand the importance the subject plays in their future success. By tying the math used within each episode of NUMB3RS to classroom activities for teachers, teachers can increase student interest with these real-world examples. Each activity has been derived from the math used in the TV show and created by practicing classroom teachers and mathematicians especially for grades 9 - 12."