According the Bureau of Labor Statistics, mathematics is one of the oldest and most fundamental sciences. There are two broad areas within mathematics which often overlap:
- Advance mathematical knowledge by developing new principles and recognizing previously unknown relationships between existing principles.
- Seek to increase basic knowledge without necessarily considering its practical use
- Many pure/theoretical mathematicians are employed as university faculty, dividing their time between teaching and conducting research.
- Use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, engineering, and the physical, life, and social sciences.
- Start with a practical problem, envision its separate elements, and then reduce the elements to mathematical variables.
- Use computers to analyze relationships among the variables and solve complex problems by developing models with alternative solutions.