Mathematicians are some of the most in-demand professionals in the world… and for good reason. Many problems in the most advanced industries can only be solved by professionals with an advanced understanding of mathematics.

You may have had to hire a mathematician yourself in the past, or you will soon. If you’ve never hired one, it might seem intimidating at first. You might ask, “How do I know if they have the necessary knowledge?” especially if you’re not a math person yourself. Or, “How can I hire someone when I don’t even understand fully what they do?” Don’t worry! This article will help you navigate the world of hiring mathematicians, without having to be one.

While there are many professions a person with a mathematics degree can venture into, we’re going to focus on professional mathematicians: the ones who develop new mathematical theories, concepts or rules in different disciplines, and/or use those theories, concepts or rules in the real world.

There are generally two main fields of mathematics to which your candidate will belong: theoretical or applied. That being said, there is usually overlap as no mathematician does only one or the other.

Theoretical mathematicians mainly work in academia as their work is to advance humanity’s understanding of whichever discipline they choose. If you are a university, this kind of mathematician is who you will be looking for. These are the people who advance our knowledge in mathematics and make the world better because of it.

Applied mathematicians use their advance knowledge of mathematics to solve concrete problems.

Theoretical Mathematicians

Theoretical mathematicians are researchers. Their main task is to think abstractly to solve unanswered questions in mathematics. Being researchers, they begin with a hypothesis or a topic they want to uncover more about, and then research it.

As part of their research, they read papers that others have written to see if they’ve already solved that problem or have solved similar problems. Much of their time is spent trying to prove things, as they use results that they or others have proven, and then logically structure that data to confirm or reject a certain claim.

Their education is quite challenging! Since the majority of theoretical mathematicians are in academia, it is essential that they acquire a Ph.D. in order to be eligible for employment at a university. Other theoretical mathematicians will tend to work in related fields and professions, for example, information technology. For private industries like I.T., a Master’s degree or a Ph.D. will be expected. There are also government jobs available which require at least a Bachelor’s degree.

Theoretical mathematicians, especially Ph.D.s, make it their mission to learn as many (and as much about) different mathematical disciplines as possible, as the more mathematical knowledge they have the more diverse the problems they can solve.

Applied Mathematicians

Applied mathematicians tend to have two majors: mathematics and a program of study geared towards whichever industry they want to enter.

For applied mathematicians who want to deal purely with mathematics, a day in their life would mainly include analysis of data, usually to identify trends or relationships among variables. This may be variables related to the business, finance or scientific arena. They will apply mathematical principles, or statistical approaches, to solve the problems their organization may have.

Just like with theoretical mathematicians, applied mathematicians, especially Ph.D.s, will want to have as much knowledge in as many disciplines as possible. It is even more important for applied mathematicians to update their knowledge continuously about emerging industry or technology trends.

Hiring Mathematicians

A potential employee who has a bachelor’s degree will have working knowledge of many of the major disciplines in mathematics. This will include the obvious basic mathematics subjects like logic, set theory, analysis, abstract algebra, topology, probability, and statistics.

With a master’s degree, topics for the programs they choose will often include advanced statistics, advanced probability, advanced algebra, category theory, advanced number theory, advanced topology, statistical computing, stochastic processes, regression, time series, and analysis of variance.

A candidate with a Ph.D. will have many of the above and possibly more, and will have several years of research experience from working on a dissertation and post-doctoral projects.

How to ask questions during the interview

You will need to include questions about the topics studied by the mathematician in the interview. Again, no reason to worry! You don’t actually have to have knowledge in any of those topics in order to hire a good mathematician!

What you do need is to find good questions for specific disciplines or topics. All you need here is a little research. Searching for “problems with solutions for (whichever discipline)” will usually yield example problems you can incorporate into the interview.

If that fails, you can always ask questions geared towards the theories themselves. For example, for Statistics you can ask, “What is the Central Limit Theorem and why is it important?” Know what the answer should be and why. This way, you don’t need to take a course in the subject to be able to determine if the potential hire is sufficiently knowledgeable.

Of course, there are other questions you should be asking aside from the technical ones. You don’t just want someone who’s good with math; you need a candidate with the proper additional skills. Here are some questions you can steal from us:

• What are you currently doing to become a better mathematician?You need to ensure the candidate is staying current with new technology and innovations.
• How would your former employer describe you?
  Even though mathematicians tend to be very busy with research, they still need to understand the importance of teamwork, hard work and communication.
• Tell me about your education experience.
  Listen carefully to this answer because this will tell you whether they took their education seriously and gained the proper amount of knowledge, along with how they get along with others.
• How do you help colleagues think more creatively?
  Mathematicians don’t just work with numbers; they work with concepts. The best mathematicians enhance their teams by communicating the logic of their methods and inspiring the same thought processes in others.
• What separates the good mathematicians from the “just okay” mathematicians?
  This is obviously subjective, but it will tell you a great deal about what the candidate values.
• What has been the most difficult situation in your career and how have you solved it?
  This will of course differ among candidates, but it’s a great question for finding out where their weaknesses might be and/or what strengths they possess.

What mathematicians bring to the table

Speaking of having the proper skills, the great thing about hiring mathematicians as a profession is that they require little formal training even right out of school; most training will involve company or school policy and industry updates (for recent graduates). This is because mathematicians in most industries will already have a great deal of knowledge of their field due to having a master’s or doctorate degree.

Since mathematicians are more logical, they usually will require a little more training when it comes to working with other professions. This is because they must communicate their findings in a way that their teammates understand them and can use their work to maximum benefit. Investing in this kind of training will reap huge dividends for employers as they “fill the gaps” often found in the “logician” personalities who are drawn to mathematics.

How much do they cost?

Now, let’s talk money: compensation for mathematicians is substantial. The average theoretical mathematician makes approximately $84,000 a year, with applied mathematicians making approximately $104,000 a year, according to payscale.com, with indeed.com showing an average between $80-110,000 across multiple industries. The majority of mathematicians make a yearly salary, which depends on location, industry, education level and experience, like most positions.

That said, there are plenty of freelance mathematicians in the new gig economy.

The prices for freelancers vary wildly. Generally, hiring a freelance mathematician from a western country will run you between $25 – 100+ per hour, with non-western mathematicians commanding between $10- 100+ per hour, according to peopleperhour.com and upwork.com. The main factors, besides the location of the freelancer, will be the same as salaried: industry, education and experience.

Salaried or freelance mathematicians who specialize in a high-demand area can command a pretty penny as they are already in an underpopulated field. The good news for budget-strapped enterprises is that mathematicians usually contribute so much to their organizations, their employers end up happy to pay the high wages or fees involved. While you might get away with hiring mathematicians in the developing world for positions that don’t require great communication, most positions will require it so it is something to consider.

Thanks for reading, and good luck in hiring your next mathematician!