Become a mathematician and help invent the world
On this page, you will learn
- the difference between applied and pure (theoretical) mathematics
- what makes the job of a mathematician challenging and rewarding
- which degrees and classes you need to get a job
- where mathematicians work and what job titles they may have
Introduction to the Field: Applied and Pure Mathematics
Once you become a mathematician, you will work either in applied mathematics, or theoretical mathematics. Sometimes, theoretical mathematics is referred to as pure mathematics.
Gauss, Euler, and Cauchy were great mathematicians. Gauss is probably the greatest ever.
They have something in common. They all conducted research extensively.
Those who work in applied mathematics try to learn more about what math has to tell us or how math can be applied in almost any area of life, such as economics, social science, engineering, biology and many others.
This means that they must find mathematical models that can be used to solve real-world problems.
Those in pure mathematics just want to know more. They are the ones who are going to come up with new axioms, definitions, and theorems.
Then, they will devote their lives to proving those theorems. Throughout history they have given us many great achievements that have had profound effects in engineering, science and many other disciplines.
A researcher builds equations that predict how a flu spreads through a city. Is that applied or pure mathematics?
Show answer
Applied mathematics. The researcher makes a mathematical model to solve a real-world problem.
The Challenge of Being a Mathematician
Needless to say, one needs to be very good at math to become a mathematician.
Above all, a passion and a love for math are a must. I know some folks who are good at mathematics, yet they certainly do not want to do it every day.
Mathematicians do math every day and they are expected to come up with solid proofs for theorems and good mathematical models of real-world problems, and it can be rewarding when one has discovered something.
However, it can be very frustrating when one is looking, but has not found a solution.
Twin primes are two prime numbers that differ by 2, such as 3 and 5, 11 and 13, or 41 and 43.
For instance, no one has proved the twin prime conjecture yet (that there are an infinite number of twin primes). It has been proven, though, that there are an infinite number of prime numbers.
Which pair is a pair of twin primes: 17 and 19, 21 and 23, or 23 and 27?
Show answer
17 and 19. Both are prime and they differ by 2. 21 is not prime (21 = 3 × 7), and 23 and 27 differ by 4.
Getting the Job: Degrees, Classes and Employers
Many jobs require advanced degrees, such as a master's or a PhD. Some jobs ask only for a bachelor's degree.
For instance, to work for the government, you must have a four-year degree with a math major, or at least 24 semester hours of math courses, to get an entry-level position.
Recommended classes are calculus, linear and abstract algebra, and differential equations.
If you also know numerical analysis, topology, and probability and statistics, then it is a plus.
- Sam has a four-year degree, but not a math major. Sam took Calculus I, II and III (4 semester hours each), and linear algebra, abstract algebra and differential equations (3 semester hours each).
- Add the calculus hours: 4 + 4 + 4 = 12.
- Add the other three classes: 3 + 3 + 3 = 9.
- Total: 12 + 9 = 21 semester hours.
- Compare: 21 is less than 24, so Sam is 24 − 21 = 3 hours short.
- One more 3-hour math class, such as probability and statistics, brings the total to 24.
Answer: Not yet. Sam has 21 hours and needs one more 3-hour math class.
There are also entry-level positions available in the private sector. You may not have the title of mathematician, though; you may be called a programmer, systems analyst, systems engineer, or researcher.
Looking only for jobs called "mathematician". Many people who do mathematics at work have other job titles, such as programmer, systems analyst, systems engineer or researcher.
Most jobs are found in industries such as government, education, manufacturing, and the private sector.
Most jobs are found within the government realm.
Check the following website for more information: Government jobs
Which four classes does the page recommend most for a future mathematician?
Show answer
Calculus, linear algebra, abstract algebra and differential equations. Numerical analysis, topology, and probability and statistics are a plus.
Summary
- Mathematicians work in applied mathematics, which uses models to solve real-world problems, or in pure (theoretical) mathematics, which creates and proves new theorems.
- You need to be very good at math, and above all love it, because mathematicians do math every day.
- Finding a proof can take a long time: the twin prime conjecture is still unproved.
- Government jobs need a four-year degree with a math major or at least 24 semester hours of math; many other jobs need a master's or a PhD.
- Many mathematicians work for the government, and many have other job titles, such as programmer or researcher.